In this video, I want to talk about how you can simplify difference quotients for which the function in play is itself a rational function. So there's some fractions involved in some kind. So if you want to evaluate this one, delta y over delta x, the difference quotient, you're going to be taking this to be f of, let's let me back up for a second here. So one thing to remember when you have these functions, think of it not as a variable, think of it as just a placeholder, right? So we're thinking of what is f of blank, right? This should look like one over blank squared. That's what we're going to do here. So in your numerator, you're going to have a one over blank squared minus one over blank squared. The denominator is always an h. And then what goes in the blank for the first one, you get x plus h, that's in the blank. And then for the second one, you just get an x. So you get something like this. Rewriting it a little bit simpler, you're going to get one over x plus h, x plus h squared minus one over x squared all over h. So in this situation, what we have is we have a bunch of nested fractions. Sometimes we call it compounded fractions or complex fractions. We have fractions inside of fractions. We have to deal with that. So you're going to notice that with these fractions, there's one big fraction bar. So that's like the mother bar.  These are little babies. We want the babies to move out. So what we're going to do is we're going to identify the least common denominator of the babies. In which case we then see the least common denominator is going to be x plus h squared times x squared. We're going to times the top and bottom by the LCD. We're going to time the top and bottom of the mother fraction by the LCD of the babies, okay? Now on the top, since you have a difference, you're going to distribute. And so this makes it look like something like the following.  You're going to subtract from that x squared over x plus h squared over x squared. And then this sits above h times x squared times x plus h squared. Now in the denominator, do not factor that thing out because we don't want denominators multiplied out. We want to leave a factor. Don't multiply out the denominator. Leave it factored. Denominators should always be factored. But you're going to see if you look at the baby fractions in the numerator, there's some cancellation that happens. X plus h squared cancels, x squared cancels. So now all the baby fractions have moved out of mommy's fractions basement. Then we have x squared minus x plus h squared sitting above h times x squared and x plus h squared. While we don't multiply out denominators, we do want to multiply out the numerator. So you're going to need to foil up that x plus h quantity squared there. And upon doing so, you're going to get x squared plus two x h plus h squared sitting above that our denominator, h x squared x plus h squared. For which you can see that the x squares cancel. You get these x squares that cancel out. Then everything in the numerator is now negative. I'm just going to put it in front of the fraction. So you have a negative like this. What's left behind? You have a two x h plus h squared over h times x squared times x plus h. You'll notice that the numerator, now everything's divisible at h, right? You have an h right here and you have an h right here. Let's factor it out. Our goal is to factor out an h from the numerator so we can cancel with the h in the denominator. That's our goal. H here stands for hate. We hate the h in the denominator so we have to get rid of it. I know that's a violent image there. I apologize, but you'll remember it.  So factor out the h so you get two x plus h left in the numerator and then you have this h times x squared times x plus h squared. For which then the h on the top cancels with the h in the bottom. And we see now that the average rate of change of our function has the formula delta y over delta x is equal to negative two x plus h over x squared times x plus h. So this gives us a formula for the average rate of change for which we could then insert any interval a comma a plus h. We can find the slope of that secant line, the average rate of change. But we're also interested in the instantaneous rate of change, the so-called derivative dy over dx for which we get the derivative here by setting h equal to zero. We see what happens as h goes to zero. For which case you're gonna get negative two x plus zero over x squared times x plus zero squared. Simplifying that we get two x over x to the fourth in the denominator for which that negative two x over x to the fourth. So we get negative two over x cubed as our instantaneous rate of change for which we can then plug in any value in for x and get the instantaneous rate of change at that moment. These fractional ones can be a little bit tricky. So I wanna do yet another example. Let's find the average rate of change and the instantaneous rate of change of the function x over x plus one. So when we start off, we always have to start off with the average rate of change, right? Cause we can't plug in h equals zero yet. We have to do that at the very end. So we have to take f of x plus h. So that's gonna give us x plus h over x plus h plus one. And then we subtract from that x over just x plus one. Like so, so each of the x's in the original formula I replaced with an x plus h. And then we have to subtract f of x and this all sits above h. The approach is gonna be the same. We have to identify the LCD of the baby fractions, which is nearly always good in these situations. It's nearly always just gonna be the product of the two. So we get x plus h plus one times x plus one, right? So we need to times the top and bottom by that LCD, all right?  Hesitate to multiply out the numerator, right? We always wanna wait to multiply until it's actually beneficial to us. Then for the second fraction, we get x times x plus h plus one times x plus one all above x plus one. And this then sits above my denominator for which the denominator always leave it factored. h times x plus h plus one times x plus one. That's gonna be, that's where we are right now. So cancel will be canned. x plus h plus one cancels here, x plus one cancels right there. And so then with the simplified fractions, what do we have? We have an x plus h, we have an x plus one.  And this sits above our denominator, leave it factored. h times x plus one times x plus h plus one. Now in the numerator, we do have to expand things in combined like terms. So FOIL and multiply is what's gonna be necessary. You have an x plus h times an x plus one.  And then you just subtract from that, just distribute the x there.  And this sits above our denominator, which is along for the right right now. All right. In which case now we need to combine terms that we can, the x squares cancel, the x cancels, and the x plus h cancels. Wow, that really decimated that group. The only thing who survived was the h there. So we have h over h times x plus one times x plus h plus one. Like so, for which then we can see the h on top cancels with the divisor of h on the bottom. So we now see that the simplified average rate of change is equal to one over x plus one times x plus one plus h or something like that. That's the simplified average rate of change. If we want the instantaneous rate of change, right, we set h equal to zero. We end up with one over x plus one times x plus one plus zero. That is this becomes in the simplified form one over x plus one quantity squared. Like so.


Hello I am Kayla Simonson. Today we will be exploring creating a digital learning community with Google Sites. It is a web app that can be used to develop a web page. Before we get started don't forget to subscribe and hit that bell to enable notifications for our channel by clicking our logo during the video. Also leave us a comment or check out our related videos by clicking the pop-up cards in the upper right corner. Here's how to get started with creating your own digital learning community. Our three goals of creating a digital learning community are to develop autonomy in the classroom, increase participation, and increase parent knowledge of and access to what is happening in our classroom. We will use these five tools to accomplish those goals. Google Sites, Screencastify, Canva, Flippity, and YouTube. Today we will talk about why to utilize these tools and see them in action. Our first tool is Google Sites. This website builder allows us to create a single location that houses all of our information and organizes it in an iconic fashion instead of simply text-based. Google Sites is free and easy to use. Let's look at two examples of digital classrooms and you pick your favorite. Here is example number one, the old version, Google Classroom. This platform quickly becomes a wall of text which can be hard to navigate and overwhelming to students especially if they are absent or fall behind. Or example number two, the new version, a website that is built on Google Sites. Google Sites can easily be organized by chapters, units, or your preferred method and information can be stored on different pages rather than being presented all at once. This format is more eye-catching, engaging, and easier for students to navigate because of the reliance on icons and pictures instead of just words. You can even add pictures of student work. Our second tool is Screencastify. This program allows you to record your screen and voice simultaneously as well as edit for clarity. Recorded videos give students autonomy and allow for individualization and differentiation. Teacher-led review while completing homework or other out-of-class assignments and these videos give parents a reference when helping their children with homework. Screencastify can be used to record new material, review, or provide more in-depth learning. Let's view an example. In this video, Screencastify was used to record while a Google slide deck was presented on the computer. This video was utilized both by students who needed extra help and by students who came into the class in the middle of the semester. Today we're going to review level one rhythms. You're going to be my echo. My turn first. This is the quarter note. It is equal to one beat and when we see it, we will say ta. Let's practice. One, two, ready and say. Ta, ta, ta, ta. Good job. Our third tool is Canva. This website is used to create engaging materials that will capture the attention of your students. These days, students are interested in things that are pleasing to look at so it's time to approach education like marketing a company. Canva makes this easy by providing templates for almost everything you need. Presentations, worksheets, infographics, and more. Plus, you can get an educator account for free. Here you can see the studio view in Canva where this presentation was created. On the left side, you see samples of editable templates. The elements tab includes shapes, lines, and clip art. You can upload your own images and video, add text, and change the background. The options are endless. Our fourth tool is Flippity. This is a website that provides multiple Google Sheets templates to create games, activities, and other clever items. The Flippity badge tracker allows students to see their progress in real time and teachers to give feedback without grading more assignments. Badges help motivate students to develop a strong work ethic while encouraging mastery and allowing students to work at their own pace. Here is an example of the finished badge tracker project. Students can clearly see what badges they have earned and on the right you see the editable spreadsheet where you enter tracking information. Flippity does include instructions and demonstrations for how to use the Google Sheets templates. Our fifth and final tool is YouTube. There are two ways to utilize YouTube. You can either upload your own videos or utilize others already hosted on the platform. You can discover and share primary sources, news stories, performances, read-alouds, and just about anything else you seek. You can also easily embed YouTube videos into Google sites so that students do not have to leave the website to view the video. Here you see Michelle Hull's example of utilizing YouTube videos on her Google site. She has provided text directions on the left and YouTube videos demonstrating the activities on the right. Thanks so much for watching. Be sure to like, comment, and reply to one of our other videos or share the playlist below. Subscribe to our channel and enable notifications so you don't miss out on the next episode. Don't forget to check out our other resources like this podcast and see what else is going on in our county schools. Be sure to follow at Dear Dis is on social media or contact us via email or our blog.


My name is Will Chu. I'm a professor in the Department of Material Science and Engineering. I'm also a fellow in the Precourt Institute. And now for the next hour, Yi Tui and myself will give an overview on the energy storage activities at Stanford. And it's my great pleasure to introduce my colleague Yi. And he's a very prolific scientist in three ways. The first is his scientific contributions. I don't have to go into his metrics, but the most cited material scientists were wide. And one of the most cited scientists were wide. In terms of mentorships, he has produced countless graduates. About 100 of them are now in academia, were wide as professors and scientists elsewhere. And then also in terms of innovation, he has started, I think, four companies, right? Or five? Or more to come? Three, three, OK. So one more ends in the making. And Yi is a true pillar of the energy research community at Stanford, focusing on many aspects. And today he will tell us about what's going on in the energy storage space. Yi, please. Well, thank you, Will. Now you see my younger colleague, how he set up the expectation for the senior colleague to move forward. I would like to start by welcoming you to Stanford. This is the best place in the world. Simply saying that, Will and I are going to spend the next hour also to introduce to you the activity, research activity at Stanford related to energy storage. I believe some of you come to Stanford interesting in energy. Energy storage, you know, it's very, very important. This is the central piece of that, right? The way to store energy becomes the very important link in the whole energy landscape. Whether it could enable the electrical cars or store solar and wind electricity to help stabilizing the grid. And from the port of electronics you already have personal experience on, this is very, very important topic. I want to start by introducing Storage X Initiative to you. This is a new initiative at Stanford right here. Professor Chu and I are the co-directors of this initiative. It's the help of Jimmy Chen in the back. We are really putting a lot of time for a reason because it's very important. So in these technology areas and just a number of grand challenges, the whole Stanford research community try to address developing, for example, the battery technology, the low cost, very safe, long lifetime, and so on. And also how do we understand and address the challenges of scale in manufacturing? Sometimes you think about this is the problem industry should be doing. But when you look into deeper, the science of scaling in manufacturing is not clear. We need to work on those. And how do we do the energy storage we use, recycle, and regeneration? And this represents a very exciting opportunity with the batteries. For example, you take back from the electric car, how do you better utilize the batteries after it's the first life? Can you inject a second life or even the third life of the batteries? And with AI, artificial intelligence, all these new tools right there, how do you predict? How do you do diagnostics of the life, the health condition of your energy storage? And this really provides a big opportunity right there. Now let's look at Stanford. We actually have a large number of faculties by now working related to storage. And this is the plot we like to use. This is the land scale. This is the time scale. If you look at this, like going from, let's say, femtosecond, picosecond, all the way to years, we need to care about what's happening. Years is the better life. Fundamental process electrons are moving. You're talking about picosecond or faster time scale. And from the atomic structure, angstrom scale, all the way to meter scale in the system level, there's many scientific engineering questions we could work on. So this timely is this year. We want to initiate these very important research areas. So we will have a kickoff meeting on October 17 to officially launch this initiative under the support of Preco Institute. So well, let's look at some of the very important perspective right here. Usually at academia, we are doing research on this fundamental understanding. But industry is doing a prototype scale-up manufacturing. So these are years of research in these areas. We find out there's a missing gap right there. So we hope, using Storage X, we can adjust this missing gap to do pre-competitive translational type of research in addition to the existing strength already on the fundamental research here at Stanford. So that's the key idea of this initiative. So next, about 25 minutes or so, I want to introduce you to my own group research and giving you a little bit of detail to look after that Professor Che will be talking about his own research, also giving you very different type of ideas, but very, very exciting what I wish I were a graduate student another time. I could join his research group. But it's probably too late for me to do so. So let me give you an overview of what's happening in my lab. I've been at Stanford for about 14 years now. I still remember hiring my first graduate student working on energy storage at the time I didn't know much about energy storage. But 14 years passed, let me list some of the grand challenges in the energy storage and the battery-related research. What we want to do, we want to increase energy density, the amount of energy you store per unit weight or volume by a lot. We want to double. We want to triple. How do we do that? We want to answer this question. How do we extend the battery life by three times or more? Life means charging, discharging, cycle life. It also means the calendar life. Instead of seven, eight years, can you go to 30 years of calendar life? That means very different impact to the whole society. And how fast can we charge up the batteries? Every one of you would like to have your phone charged up within five minutes, right? I would say, well, let's see. If we can do our car within 10 minutes, that would be amazing. That would just like feeling the gas tank type of timescale. And can we make the batteries completely safe? Never worry about catching fire or the explosion. Can we reduce the cost by three times? If it's three times, that's done for the electric car. The cost would be really, really low for the electric car. Very, very competitive. So battery use and recycle. How do we do grisky and seasonal storage? Each one of these questions is very, very big. If you have great ideas, giving answers to one question, I think you will be doing really well at Stanford. So everybody will know you for sure. I will know you for sure. So this is the overall research program I set up in my lab. So some of them is for addressing the question of, how do you get to high energy? How do you do the safety? How do you do the grisky? How do you understand what's happening inside the battery? Now let me pick a few examples to share with you. The first one, this is the one I really like. I've been working on this really right at the beginning when I joined the faculty. High energy density of batteries. How high can it go? We come back to the very simple understanding or equation, basically, general chemistry. So let's use lithium as an example. In order to increase the energy density, you want to store a lot more charges. That's lithium ions. So this is current technology using all this material. This is the plot we made. It's the atomic ratio of lithium to the host material structure. We only utilize one lithium per six atoms, roughly the host material. So you actually have a heavy weight, big volume. But lithium coming in and out, the relative volume change of this material is very small. We are talking about right here, nearly zero, but it's not zero. It's about 10% or less.  To store more energy, you have to increase the ratio of lithium versus the host material until this is virtually infinite because this is metallic lithium. You don't have any host atoms right there. But the volume expansion, volume change in the relative sense is infinite. So it becomes harder and harder and harder using new materials. But if you can make this happen, this is current technology using graphite to get lithium in and out with this lithium metal oxide right there. This is somewhere you get to 250, 260 while per kilogram. That's what in the Tesla car, the amount of energy you store per unit weight. If you can use a new chemistry such as silicon anode to work, lithium metal anode, lithium sulfur, and so on, you could keep advancing this amount of energy. If you can get here 500 while per kilo, this is the equivalent to one charge per charge of your electric car with the reasonable size of the graphite pack. Your car will run 500 miles. Remember this number? 500 while per kilo, 500 miles. That's where we want to go to. So the past number of years, we look at silicon, for example. That could store a lot of charges by volume expansion and breaking. It would cause the problem. We started design using nanotechnology to solve this problem. This is the paper we published back in 2008 using silicon nanowires to take in a lot of lithium, 10 times more than graphite. We have the breaking problem. It has many issues showing up by using this nanotechnology design. We were able to overcome the breaking problem. So fast forward, we have been through 12th generation of design to solve instability of the interface issue and so on. Along this process, actually, students are very important. And each one of these generations, I will develop one student and become the academia superstar. And some of them are professors here in the US and also around the world right now. That's a process of development of research and developing people in parallel. And Stanford right here in Silicon Valley, it's very hard not to start our company. So as Bill mentioned, so here I did. This is Ampereus. I first company I started to work on silicon nanowires. I can tell you it's very, very hard to commercialize a technology. So $150 million so far has been put in. And the outcome is now having this batteries, energy density is quite high. Instead of $250,000, now you have $430,000. And supplying to the Airbus Cypress S, this is commercial drone flying the sky. 70,000 feet elevation. Continuing flying 25 days, no stopping. So you don't need to really ever need to go to the ground to charge. This uses solar cells right here on the wind but requires very high energy density batteries to power. Otherwise this drone cannot take off. So this is an example of a high energy. So what's going further is we need to go to 500 miles per kilo. We have to work on materials such as metallic lithium. This is a half a century old problem. In 1980s, there are people trying to get metallic lithium to work. But metallic lithium has so many problems. A notorious problem is during battery charging. And it grows out of the stand dry. This stand dry causes shorting and battery catching fire and explode. In 1980s, one company started to commercialize the lithium metal and no technology. And a few months later, the battery catch fire, the company was gone. And nobody wanted to touch metallic lithium since. But we are running out of the capacity. We have to work on this. So at Stanford right here, we have quite a bit of activity. Try to solve this problem. So I won't go into the detail. Just to show you, we have a team consisting of previous secretary of energy, Professor Steve Chu and Professor Bao and chemical engineering right there, designing the new materials to work on this problem. So let me just give you one or two very simple ideas. But actually, it might be very important for the whole research field. Because lithium metal can grow these dendritic structure. Then how do you really control its plating behavior during the battery charging? In 2016, we come up with an idea. We say, well, let's design a host material to host lithium plating. We made this hollow carbon structure. And the size diameter is about a few hundred nanometer with this gold nanoparticle seed in there. It doesn't need to be gold. It can be low cost, other metals seeding the growth of metallic lithium. If you play lithium, lithium goes in. And then you can isolate lithium metal from the electrolyte and contain metallic lithium in there. We actually made this structure. Let me show you an in situ electron microscopy video. Here at Stanford, we have these beautiful tools, right? They're so important. You can charge and discharge the battery inside electron microscope to see what's happening. This is the video. We have hollow carbon right here. This is gold nanoparticle. Now we put lithium in. You can see gold function as the seed. And it actually gets dissolved away in metallic lithium and promote the lithium deposition going inside of this hollow carbon sphere, instead of outside. So using an idea like this, we can really understand how the lithium plating is taking place. Once lithium get extract out, this gold particle comes back. A structure like this with a new host, we could now stabilize metallic lithium deposition a lot more. This other host design, for example, using graphene oxide, let me jump through this. I don't have to show you all the video for the time consideration. Let me show you another example going on in the group and also quite broadly right now. Will and I and a few other faculties, we team up, try to adjust the challenges of the battery fast charging. We want to see whether we can go below 15 minutes. If we can go to 10, that would be even better. But it's really hard problem. It's really, really challenging problem. For the first year graduate student coming in, you guys will have five years probably to work on this problem. That should be very exciting. I have 20, 30 years right here keep working on this problem. I hope some of you can join me to be part of it. Let's look at one of the challenges right here. So this is where Tesla supercharges at. You are talking about 130 kilowatt, 150 kilowatt of power. This is where we want to get to. Will and I extremely fast charging. Well, this we are talking about 300, 350 kilowatt of power coming in. Well, Tesla will say, well, 40 minutes or so, I will get to somewhere probably 80%. Here we want to do 15 minutes to get there. But along the way, there's so many challenges. Number one is, you just keep pushing electrons and lithium in and out so fast, you're going to build up inside the batteries of this concentration gradient of lithium. How do you handle that? Promote the lithium ion transport. And also, for each of this material, lithium coming in and out through liquid electrolyte into your solid state. And liquid electrolyte, lithium carry this solid molecule called solvation shell. Lithium needs to take off the clothes in order to go in. Taking off the clothes takes energy. It is a resistance right there. You want lithium to be naked very fast. How do you do that? This is a challenge we try to solve. And also, inside a battery, when you do fast charging, and then you are going to generate a lot of heat in the middle of the batteries, the outside will dissipate the heat fast, but the inside will be very hot. You're going to have a temperature gradient right there.  What sounds familiar? That's heat, right? That's transport. If you're a material science looking at this, you say, well, a chemist, you say, well, this sounds familiar. If you're a chemical engineering student, you say, well, now mass transfer or mechanical engineering, this sounds familiar. So it requires many different type of background to come together to solve this type of issue. So we have a few ideas how to do that. So I probably won't have time to go into the detail ideas. And I will skip that. But last, let me just show you one example before I hand the podium to Will. We need new tools to understand what's inside the batteries. We really need new tools. All these batteries material, many of them, they are not stable. If you want to look at them, for example, using electron microscopy, you are going to destroy them really fast. They are really not stable under the beam. They are not stable chemically. They react with oxygen, with air, with water. And it's painful. It's painful. But we do need to understand, down to atomic scale, what's happening if you have the battery charging and discharging. So several years ago, three years ago, we developed this technique. And we still graduate student right there. And in 2016, we actually bought a technique we learned from biologists. That's the cryogen electron microscopy. That was the Nobel Prize-winning technique in 2017. And structural biologists use liquid nitrogen, or liquid methane, really cold, to stabilize their protein molecules, to solve the structure of the protein, down to, like, say, two angstrom resolution. So there's several major advancement right there. Cold, being cold, stabilize your sample. And also, the direct electron detector, that can detect nearly every single electron coming from your sample during imaging. So you don't have to expose your sample for too long. The dosage is very small. Then you can get the structure information. And there's also computational power to solve 3D structure of protein. So we bought some of this technique. It's a very collaborative place at Stanford right here. I remember when I started this project. I went to talk to Professor Roger Combergs. I asked Roger's group to help us to really study the technique. We knew nothing about cryoEM. So now we develop a technique. We could see this is metallic lithium. The lithium is a really light element. A lithium-low melting point in the past is no way to obtain atomic-scale resolution of lithium metal. Now it's possible. Now you see these beautiful images right there. We obtain atomic column of lithium right there. And it turned out to be this paper come out in science in 2017. It took nine months to reveal. That's my record of the longest reveal time of my paper. Guess what? Because when we show this image to reviewers, reviewers couldn't believe you can see lithium metal, atomic-scale resolution. That's because lithium metal is not stable. Now it is the cryoEM technique. If you talk to biologists, they believe right away because they can see protein. Looking at lithium metal is trivial. But when I actually talk to material scientists, it's actually much harder. So now a number of groups can really see this now. So everybody starts to believe in it. So not only that, using a tool like this, we solve about a 30, 40-year-old puzzle. What's the interfacial structure on your lithium battery materials? That can show how fast lithium coming in and going up to a certain degree, determining the fast charging to a certain degree. And these two models of structure propose so-called a solid electrolyte interface, this SEI. But turn out to be it's not like what people propose. After we could see this on the cryogenic electron microscopy, this is lithium metal. This 20 nanometer thick is the interfacial layer of SEI. And this consists of inorganic grain embedded into amorphous mages, different from what people think. This is using the electrolyte. This is a carbonate electrolyte. If you know a little bit about the battery, each battery company have the secret ingredient of the electrolyte. They add in the additive, this one and that one, just like cooking. Certain shelf can cook you really good food, but you don't know what's the secret ingredient in there. That's the status of the battery industry. So after you add in this one of the secret ingredients right there, what turn out to be not as secret anymore. It's fluorinate, containing fluoride in this molecule. This whole SEI structure, interfacial structure, completely change, become multilayer. This is beautiful inorganic coating on the surface. And then we use the cryoEM10. It combines with electrochemistry. We can correlate one structure, give you a better battery performance. The other one is bad. So this correlation of structure with performance will be very important down the road for us to design the best batteries. You know, I really hope to have forever batteries never die and let's see whether that's possible through this type of understanding. So I think I will jump to the end. I'll give you a number of examples already. So we are very focused and a very research. We know this is important to the industry. We also know this is full of very exciting scientific problems. And we'll be continue doing that for a long time. I better just stop right here. We'll maybe I'll take a couple of questions before I let you take over the podium. Any questions from you guys? Thank you. Thanks for the talk. It's very interesting. So you've shown us you can make all sorts of different shapes for your anodes. I was just wondering what other kinds of shapes can you actually make and what sorts of advantages might they have? Yeah, you're probably referred to the silicon. Silicon has we made 12 generation. They all look beautiful. By the way, they're functional as well. Not only beautiful, right? So battery has many problems. The materials expansion and breaking. Once expand the interface is not stable. So for addressing this problem, we have to design the right material to solve this problem. So that's a 10 years, more than 10 years of effort. So we'll learn about all these problems step by step. So each generation, we decide different shape to solve those problems. Eventually we also find out we need it to be low cost. And we also need to design, use the right structure for the low cost. So that's the motivation why we have so many different shape. If you're asking me, what's the best shape right there? I cannot tell you yet, because the whole industry need to look at that. They need to get the cost to work out manufacturing ability to work out, then they really understand. They are the people understand what eventually the shape will win. For me, I have my favorite shape. It's my number 12 generation, if you look at that. The last one, that's my ideal shape. I think it accumulate all the features right there to solve the problem yet at the same time low cost. Hello, just a quick question. I was just looking through the topics of your research. I was wondering, do you also work with lithium air battery, for example? I did for about six months, but I didn't publish any papers on that. It's really exciting topic. I decided not to do lithium air because I don't have good enough idea in that area, so I decided not to. But some other people might do. I think this is a really interesting research area. Hi, thank you, this is a really cool talk. Just wondering, you mentioned about the heat problem. Could you share a bit about the research or some directions that you're currently working on to solve the heat issue? So, let me tell you once you have the heat problem, what will come? What's the problem you have to do? If you have temperature or gradients inside your battery, the hotter side, any psychchemical reaction will happen faster. And the colder side will happen slower. That's one outcome. That's more of the kinetics. This also recently we discovered there's a lot more implication beyond that. That can damage the health of the batteries. The understanding really, really near not published yet. So, we see that that can induce thermodynamic potential shift of the electrochemical reaction. That has even bigger implication to the battery's health condition. Then how do I solve that? So, I don't have a direct idea yet. We are still brainstorming together. I brainstorm with my students every subgroup meeting. We try to come up. That's part of the fun. I know I don't have an idea right now, but it sounds like, you know, if I continue to brainstorm for the next two weeks, two months, maybe two years, I might have something coming up. So, I don't know yet. I don't know at this moment how to solve all this problem, but we are trying. That's the beauty about research. That's also the beauty about coming to graduate school. You don't know what's ahead. I know it's exciting. Yes, thank you for the talk. What I wanted to ask was, apart from looking for alternatives for cobalt, what would you suggest are other ways by which we can drive down the cost of batteries? Yeah, so what's a lithium ion? Now, a lithium ion case, you want to use less of cobalt or no cobalt. Maybe in the future, still less nickel. Well, I think Professor Chiu will probably can tell you a little bit, can mention at least a little bit, he's working along that direction. So my group is trying to do solver, because solver will be also high energy, but no expensive stuff. Solver is very low cost. However, solver is very difficult. I've been doing that for 10 years right now. Still has no full confidence that this will work. Okay, Professor, one question. I remember the silicon in the solar cells is very fragile, and oh, okay, and it is in the sand is very rigid. Yeah, I remember lithium and iodine, lithium dendrites is something, is something that would penetrate the material. So is it good to find a soft material to store the lithium and prevent the possible leakage problem? Yeah, so you say, yeah, silicon is brittle.  For the barest case, no single crystal is individual small particle. So in terms of brittleness, that problem is, I think it's gone. But the problem is lithium coming and silicon particle, each one, expand four times roughly in that range. That break the materials, that's the challenge. And then you ask the question, whether we want to find a soft materials. I think soft material to store lithium has its benefit, the processability, mechanical flexibility is good. There's value on that. One example is using polymer, using organic materials. I mean, indeed, that's a direction Professor Bowen Chemical Engineering and my group, we work closely together to develop a new type of organic to store charge for the electrode. That's a really exciting direction. I have zero minutes left, maybe I'll take one last question and this, because she already has the microphone. Thank you, sorry. I'll try to make this quick, but this is slightly a different angle. So you mentioned it's very, very hard to take it to market or your research and you're clearly wearing multiple hats between a researcher and also an entrepreneur yourself. So just curious, how do you toggle between these different roles and what do you see as the biggest challenges? Yeah, the biggest challenge is time, absolutely. When you're debating, you want to get more sleep or wake up to work, I mean, every day, right? Until now, 40, 43 years, I've been debating that. Maybe the first year of my life, I didn't know how to think, I didn't debate, but 42. So yeah, my function in the company, I found in the company, I'm sitting in the board of director, chairman of board, and I never take any office title in the company. So I spent one day per week, I told the company, I mean, that's the maximum I could spend. That's also the maximum amount Stanford allowed me to spend, so I did that. I told investors about that, okay, so when you smile about your time management, I think this is doable, this is doable. I have a really great team, great CEO to run the company. That's the only way this can happen. Well, thank you very much. Well, while Will is setting up, let me introduce him. By the way, we didn't talk beforehand how to introduce each other, so we will just, we're joining faculty for six years now, roughly? Seven, oh yeah, I still remember when you were baby assistant professor, now already, my God. So Will got ten years this year, by the way.  Yeah. It's very clear the first day, he step onto Stanford campus, we married him, we say, this is the person we want to bring onto Stanford campus to be a faculty. Very clear superstar from day one. I think when you come to Stanford to interview, you have not graduated from Caltech yet, you were still graduate student. So that could be achieved. This is an example right there. So past seven years, he has been doing amazing work, completely open everybody's eyes. You know, I worked on ballet for a long time when Will started to work on ballet. My God, the idea, he come out. I never thought about it, I said, well, this is just amazing, solving major problem. He's probably going to tell you one or two today, you will be impressed. As I said, if I will graduate student once, I will join his group as a graduate student. He didn't buy me lunch or anything, you know. I mean, that's truly coming from here. With that, Will. So that was an implanted question. So today I want to talk a little bit about accelerating the pace of R&D for batteries. So if we, E and I, convince all of you to contribute your time and effort toward realizing energy storage that is inexpensive and abundant, that would be a 100 person year worth of research for the next five years or so. But if you look at the scale of the problem, lithium-ion battery, just lithium-ion battery alone will go from a $50 billion industry to $1 trillion in the next 15 years. So the pace of R&D is very much weight limiting. I'm going to tell you what the limiting factors are and what we are doing at Stanford in particular, trying to accelerate the pace of R&D by intersecting artificial intelligence and batteries. I'm a material scientist, this is all very new to me, but I am motivated by the fact that we can do maybe not 100 person year worth of research in the next five years, but 1000 person year by accelerating the pace. So battery is kind of a funny technology. It has several characteristics. One, a good battery lasts a long time. So even the mere simple task of assessing how long a battery is going to last, so if you design a new battery you want to know it's going to last 20 years or two years, it's going to take 20 or two years to assess that. And batteries are complex. It's like a chemical plant in a small device. So the design space is very large, often you're dealing with optimizing 50 parameters simultaneously. So E talked about fast rechargeability, energy density, safety and so forth. Some of the events we're trying to design for are very rare. So we hear about all the bad examples of battery catching on fire, but they are one out of tens of millions of batteries. And then the act of designing, manufacturing, assessing batteries are also very resource intensive. So if you look at all these requirements, it tells us that the goals should be, can we learn and optimize across the design space as quickly as possible? To address the issues of long assessment time, can we make accurate predictions of future outcome? For rare events, can we predict the probability that will happen without having to test 10 million individual devices to have the one failure? And then also we have to somehow balance between the throughput and the accuracy of doing these experiments. So for today I'm gonna talk a little bit about our work, along with computer scientists and engineers at Stanford, to look at addressing the issues of the large design space in batteries and also the long assessment time. To give you a few flavors of assessment time and the type of problems we can solve for a given battery chemistry, so take one of the ones that E had mentioned, you wanna be able to charge them quickly, you want to be able to manufacture them quickly because that contributes to cost, and then you wanna be able to predict whether the battery is good or not where you're using an electric vehicle. All of these problems have a common attribute, is the number of parameters it involves. For example, you're dealing with maybe just 10 parameters, sorry, five parameters, you have 10 values each, you repeat the measurement 10 times, and each repetition you run at 1,000 cycles, that's roughly a lifetime of a modest battery, and this comes out to one billion battery cycles, so it's pretty resource intensive, and there are other problems like R&D pipelines, so if you're engineering a new battery chemistry, you will have to iterate on a daily basis and you have to go through these billion battery cycles. Things like quality insurance during manufacturing, so if you make a new battery, you wanna make sure it works well time to time as you produce it, and each time you produce it, you have to wait another 20 years to find out how long it's gonna last. Safety prediction I already mentioned, so this common challenge is a large hyper-dimensional design space with very long assessment time and optimization time, and I think personally this is one of the big limiting factors, just how much time we have and how many people we have devoted to solving the problem. So I will continue to make the goal to convince all of you to work in this space, but not all of you will work, but those of you who will work with us will try to multiply your effort by a factor of 10 or 100 if possible. For a variable battery chemistry, so now you're in the business of, say, going from one chemistry to another, from one geometry to another, you also have to optimize the chemistry, you have to optimize the synthesis, you have to optimize the design, you have to optimize the manufacturing, exactly the same thing. So what I wanna talk about today is something that we have been working on for the past five years, and this is looking at a way to optimize and learn about battery design space in a closed-loop manner. A fancy way to view this is an autonomous optimization of batteries. So the way it works as follows, you start with some process, so it could be making the new battery chemistry, then you would assess the battery chemistry by charging and discharging the battery, mimicking the functionality of an electric vehicle, for example, then the second box there, you want to be able to predict the future outcome without having to actually perform all those experiments, so can we predict the 2000th cycle behavior of the battery using just the first five cycles? This will require some training data, and once you have the ability to predict the future behavior, then you can explore the design space. Here, this is just a simple four-by-four-by-four design cube, for three parameters, but in actuality, this could be a 50-dimensional space with maybe 10 or 20 blocks along each axis, so very quickly, the problem become intractable. So you have to be able to pick the right cube to test, so you have to hone in on the right part of the design space to focus on the ones that will work and to make repetition where the statistics count, and then you want to iterate the entire thing, so now with some idea how the design space is laid out, you do a second iteration, a 20th iteration, a 200th iteration of the cycle, and slowly but surely you modify your materials, your process in order to achieve the objective, and that could be, for example, the charge of battery faster or to decrease the manufacturing time. And my talk has two parts. The first part is the ability to predict the future behavior batteries accurately. And to do that, a number of students and postdocs in my group, and then we're one sitting in this room as well who has already committed to solving this problem of energy storage, we have the Stanford Battery Informatics Lab which has the ability to test about 600 batteries simultaneously. So if you think about this as a parallel, multi-node data generation, this is about as best as it gets because batteries are rather small and we can parallel process them in an efficient manner. So those of you interested can take a look at these facilities, so we're testing hundreds of batteries at a time. And we're able to generate a data cube that is actually rather large. This data cube here is about 400 million data points, so we took about 100 batteries, we charge and discharge them in a variety of ways, we record temperature, voltage, resistance, current, over time, okay? So along the three access, we have basically the cycle of the battery, the capacity of the battery, and the voltage of the battery. And we're able to record that. So the objective initially is, can we predict the future behavior of the battery with very limited data? So if you take a look at this cycling behavior, so the y-axis is basically the capacity and the x-axis is the cycle number, so you want the line to be as flat as possible to be as close to 100% as possible. So those are the battery that's well behaving, it lasts maybe 3,000 cycles. So that will translate to close to a million miles driven on an electric car, so that's very desirable. But not all batteries behave like that, some batteries behave very poorly, so they may only have 1,000 cycle in lifetime or even just 200. Now if I zoom in on just the first 100 cycle, okay, so that's just the first 10% of this plot, and say ignore the rest, can I predict the behavior of the battery? Which one's gonna last a long time? Which one will last just briefly? The color are coded in such a way that blue is short lifetime and red is long lifetime. And if you look at the first 100 cycle, so this is blown up 10x, you can see there's no order in the line. The only thing I can predict is this one here, that this is really poor, but between red and green and blue on the top, I can't really tell. So simply by looking at how the capacity of the battery degrades, it's not sufficient, and if I do a rigorous statistical analysis, I can see that the cycle life has very weak correlation with the performance at the 100th cycle, and also if you look at the slopes of the degradation rate, there's also very weak correlations, almost a straight line, which means there's no correlation in this case. So that means whatever the degradation mechanism it is, the thing we're trying to predict is very silent. So it doesn't show up until it shows up. So this is a very challenging problem, and what we thought to do is rather than just using this capacity curve, each data point here also contains about 10,000 data points on voltage and current and temperature versus time. So why don't we look at one level deeper? And when we do that, we're able now to follow basically not just the evolution of the battery capacity, so that's the runtime of the battery, but also the change in the subtle change in the voltage of the battery as a function of time for each charge and discharge cycle you do, and that's plotted there. The green is the difference between two cycles, in this case between cycle 10 and 100, and we ran a very simple machine learning exercise using a methodology called ElasticNet. This is 20 years old, nothing fancy, but we take the 10th and the 100th cycle, so just two cycles, and we train the model to predict the lifetime all the way out to 2,500, and we're able to achieve a level of prediction just using 100 batteries of around 10%. So that means we can predict with 90% confidence what is the battery's lifetime by just recording this amount of data. So this will then translate on average into a saving of 15x just by not having to cycle the battery to failure. So you might say, well, 100 cycle that's still quite a bit, that's still a couple of days to run, and in the factory you don't have the luxury of cycling 100 times just because you're eating 100 times into the battery cycle life. So can we do it just with five cycles? So then we change the objective a little bit rather than predicting the lifetime of the battery. I just wanna predict whether the battery will be good or bad. If it's good, I will proceed. If it's bad, I will stop. This is called a classification problem. So once we post a problem this way, our algorithm is able to predict with 95% accuracy, whether it's a good battery or bad battery, and I define that as a battery with below 550 cycles or above 550 cycles. And this kind of classification problem, I think you can see, it's gonna be a very helpful in the hands of graduate students because now when you make a new battery rather than waiting until the end of your PhD to know if it worked or not, you can know within a few days, but there would be a probability, right? It's not for sure, but you can say 95% confidence, this is not gonna work. So I will move on. So I think this will be a tool liked by many of you as well. Things in the red box are good. Things in the green box are good. So these are basically the correct predictions. So these are batteries that actually doesn't last a long time and we predict not to last a long time and the green is the vice versa. So anything outside is a bad prediction. So basically one out of 100 specimen we could not predict correctly. So I think this is rather good. And overall, the theme here is we generate the data we learn from the data, which is what I presented and then I will finish up at the end of the talk to how we can rationalize it because we learned something but this trend has a physical meaning. So far no physics has been imparted to the problem. But before I get into that I wanna talk about the design of experiment. So we show that it is possible to reduce the time of experiment by maybe 15x by just not having to run the battery to failure by predicting with statistical relevance the future behavior of the battery. But this still doesn't solve any problem because this is not an optimization problem. The optimization problem comes in the third block here where I'm trying to choose the best block out of that four by four by four space and say what is the best way to do a certain task involving a battery and I wanna iterate it and basically hone in on the right answer as quickly as possible. And I think Eve gave a great introduction on the necessity to increase our battery charging time. So the biggest, one of the biggest obstacle for battery deployment in an electric vehicle is the difference between charging versus refueling time. So refueling time is typically about six minutes currently and can be faster and battery charging time for the same range is about 70 minutes. So if you can design something that can charge in 10 minutes, this will increase the rate of adoption for electric vehicle. And the problem is very well suited for the optimization task at hand. Let me define the problem for you. So we have chosen the battery chemistry and we're asking what is the best way to deliver 80% of the energy in 10 minutes. So there are many ways, actually infinite number of ways to deliver it. For example, you can do it really quickly initially and then taper it down. That's how Tesla does it. You can also maybe start low, go high and go back down again or you can do the reverse. So this is basically the optimization of the charging profile. How do you vary voltage and current with time? And this picture here depicts it. This is current versus time. So it has five individual steps and you can arrange the step in many different ways to satisfy the constraint of being 10 minutes. So the various lines I show there are the various possible values that will add up to 10 minutes at the end. On the right is the visualization of the design space. We chose 200 possible combination of these lines over here. There are various time and current and voltage versus time. And our goal is to identify the statistically best 10 minute charging protocol as quickly as possible. Benchmark, if we do a grid search which means we carefully examine each one of them with a triplicate measurement, we'll take 500,000 battery cycles. If I'm able to test 50 batteries at the same time, this will take 600 days. So roughly about 50% of your PhD thesis. So my student, Peter Otea, who's working on this said, no way, we're not gonna do this for two years. So that was a personal motivation for him to do this faster. So what we're really doing here in the machine learning world is active learning. So how do we learn this design space hone in on the correct part of the space that delivers the best 10 minute, which is classified as giving the highest cycle life? I won't get into the details of the algorithm, but this is the outcome. We start with 50 experiments at a time. So we do it four different times. So it's 50 times four. Initially the 50 experiments are spread out randomly in the design space. So we get a sense of what the design space looks like. This is the act of exploration. But then as we explore, we also record and predict what is the lifetime of the battery, and this is incorporating the early prediction I showed in the first part of the talk. So basically within 100 cycles, I'm predicting cycle life all the way out to 1200. Then I iterate it again. But the second time you run it, you can see that the algorithm has honed in on the part of the design space that performs well. And this is called exploitation. So you're exploiting the part of the design space that's worth repeating. So we're now increasing the repetition. Round three, round four, just honing in. And you can see on the bottom row, the design space emerges. So this is lifetime as a function of the three design parameters. Initially it's very uniform, but as you go further and further out, it becomes more structured. So this is the objective. I want to learn the design space and focus my efforts on the part that counts. This is the performance metric. This is the number of repetition per design point. Actually out of the 200 protocols, more than half were never tested because they're not good. So there's no need to waste our resource in testing it. About 60 is tested once, and only less than 45 are tested more than two times. And only three were tested four times. So basically we're focusing on decreasing the error because batteries have very high variabilities by only doing those on the part of the design space that matters. And then to wrap a bit, these are the result. These are the top performance in terms of how the current should be ramped with time. So contrary to what Tesla uses, it's actually quite flat so we're still trying to understand what's going on here. And actually the worst performer are exactly the one that ramps down. So this was a bit confusing to us, but it's possible without such a design optimization process, it's easy to overlook the really good part of the space because the top is counterintuitive. In the next three minutes, I'm gonna tell you how this can be brought to the next level. And this is really at the frontier of the research we do today. So batteries are very multi-link scale devices. If you start with a cylindrical battery like your AA battery or the battery used in a Tesla car, it has maybe 10 watt hours in energy. You zoom in all the way from the device to the particles and then to the atoms. You're spanning more than 12 orders of magnitude in energy and 10 orders of magnitude in time and length. So this is a very difficult problem. And so far I've only showed you battery cycling at the very top length scale. And I showed this earlier, this is the apply I like to use is to show the type of length and time scale we're able to address from picoseconds to years, from nanometers to meters. And the goal here is basically to see if we can control batteries across scales. Not just one of them, but across them. What we need to do here is to embrace other forms of data stream. So so far I showed you one kind of data stream, which is battery cycling. So those of you from new with devices, these are device characteristics. Just like a solar cell, I run an IV curve. A battery, I can run a charge and discharge sequence. But there are other kind of data stream. For example, if I open up the battery, I can use an optical microscope. Look at the scale bar here. This is 10 centimeters, so you can see this with the naked eye. If you look at the microscale, so the previous speaker showed tomography results in geological context, we can do this also in the battery context. So this is now two micron scale bar and you can see the porosity and the structure of the battery and the color here represents how many lithium you have in the battery. You can simulate, for example, stress and strain distribution because this is why batteries fail. They have developments of internal stress. We can take one of these particle and then go to one of the particle that makes up it. And then we can go to 500 nanometer scale bar and then observe the dynamics of how the lithium is going in now. So this is a movie showing lithium leaving and entering the material. And then you can also go smaller from say 500 nanometer to two nanometer by tracking how atoms move around in the lattice and e-show the electron microscopy image to look at interfaces. So what we have to do, and this is my final slide, is to accelerate the pace of R&D in a budget constrained world. And budget here is basically the cost per experiment and the number of experiment. And this could be in terms of money, in terms of graduate student time, so on and so forth. So our idea here is to take experiments like device characteristics, which is low fidelity, low cost, go to more high fidelity measurements like average property, mesoscale dynamics or atomic properties. But as you go down, the number of experiment you can do becomes fewer and fewer. At the same time, the theoretical simulations are the same thing. You can start with device models, which are very simple, you can run them in a fraction of a second or you can run these molecular dynamics simulation that will take days or weeks to perform. So you also shrink down the number of experiment. Currently, the way we do things is to approach each one of these box independently. Maybe there's pairwise interaction, but there's no effort currently trying to combine all of them at the same time. And what we propose to develop is a fully integrated experiment and simulation planning. So choosing what experiment and what simulation to run cross interpretation across scales. Okay, so how do we interpret all seven things at a time? Validate and optimize. So I think this can help us to give us that one order of magnitude boost, so taking the 100-person year worth of research in the next five years and maybe multiplying that to 1,000. So with that, I'd like to thank you for your attention. Thank you for the talk. I wanted to ask what is the industry's perspective of using machine learning and AI for their battery research as you have been applying it? Yeah, they're really looking to us for directions. So we are working with many of the leading industry partners to try to practice this for the type of data they have. But I think machine learning is still viewed as a very high-risk direction because it's not certain it's gonna work. So the university has to roll to demo it to say it works. An industry can take our 500 nodes experiment and then do so for 50,000 nodes. So there is a demonstration that is needed and that's precisely our role here and then to develop the fundamental science behind the methodology. So the codes, the algorithm are all very scalable. Thank you. The prediction stuff at the start, which was super interesting, was based on differences between the discharge of 100 cycles, which I think is based on like a given physical configuration, having some difference, creating some difference which the model picks up on. Is this universal or would that also change when you have a different, for example, shape as mentioned in the previous talk? Right, so in principle, you need training data for each new chemistry that you're identifying, but I think where you're picking up is basically the degradation mechanism. So that's why there's such a strong trend. I should emphasize there's not just one descriptor, we use 20 different features to predict it. So it's a combination of everything. So as you switch different chemistry, in principle, you will need new training data, but once you encode in some of the physics in chemistry, it may be possible to move chemistry without say generating all the training data again. So that's sort of moving to the direction of incomplete training data, and that's going to be important too, because you're not going to be able to wait 20 years for your full training data to come in. Hi, thanks a lot for the talk, it was a great talk.  And I wanted to comment on that because I think from their perspective, they're trying to sell EVs and range anxiety is a thing, and so they want to maximize the battery capacity during that time. And your goal also is to eventually help the adoption of EVs. So how do you marry your research with this, like the industry's perception where they want to sell more cars and help alleviate the range anxiety while you know that the charging profile currently being used isn't ideal for the batteries? I think another way to phrase the problem is what is the objective function? So the objective function for us was maximizing lifetime. But the other objective function could be deliver as many coulombs as possible in the first 30 minutes. So properly designing the objective matters a lot. So we don't have the resources to try every single objective out. And what we are trying to do here is to develop the tools, the methods, and then the demonstrations that this can work, and industry can take this and incorporate it into their own and choose the objective that matters to them. And each company would have a different objective. And that's the beauty of this is you can change the objective very easily, right? You can have a three-front objective if you like. Thank you for Professor's talk. I have two questions. The first one is you mentioned your experiment it for to predict the 2,000 or more circles and I want to know what happened if I want to predict 10,000 circles. Is this still accurate to predict for so many and so long times? And the second question is from AI or machine learning is result, how is this result to be connect, be linked with the chemical change, I mean how to link the results with the materials change and the chemical change? That's my two questions. So the first question is a very easy one to answer but a very difficult one to actually take actions on is can we predict out to 10,000 cycles? Well to do so you have to have validation experiments at 10,000 cycle and that will take a few years to generate. So I think the not so easy answer is can we just not validate it? Can we validate it using a combination of modeling so you can extrapolate using some sort of a mathematical model to 10,000 cycle without testing? If you look at easy example of the Airbus drones they're supposed to last 10 years in the sky. You're not going to have 10 years to develop the battery and then try it out for another 10 years in the sky. This is not possible and that's why I'm mentioning this difficult tax of accelerating R&D because battery just lasts too long. That's the problem. If they can only last a shorter amount of time then we don't have to iterate on the 10 year timescale. The second question is precisely why I showed the other facets of the research we do here is once the batteries fail you should take it apart and understand what happens at the interfacial level, at the microstructure level and combining those data stream for example these average property atomic characterization then it will give you a better idea why it's failing. So you're not just learning the design space, you're also learning why the design space is the way that it is. So I think that's the overall goal here it's not just data. I'm a material scientist so I want to understand why things are happening. Thank you. This is one last question I think I'm standing in the way of lunch. Sorry about that. So using machine learning you typically look for patterns. So I guess you assume that similar batteries work in similar ways in a continuous fashion. So I was wondering if you run into limits of discontinuities or like for example I guess these kinds of models are not good at predicting rare events or stuff like that. Yeah so I think again it has to concern with the type of training data you have but it's possible here this is a single degradation mechanism. Basically it tells you that our data only has one predictable mechanism but if you get two lines out then there could be a bimodal degradation mechanism. So I think if your data set is large enough you will be able to tease apart different kinds of mechanism but it does increase the cost of having more training data and this comes back to the theme at the very end is at some point you need physics and chemistry. Without it you don't know how the two mechanisms are related or not related. So the future goal is really to incorporate and this is what we're doing right now is to incorporate the right amount of physics, the right amount of chemistry and then merge that with the vast amount of data that we have access to and join them in a holistic manner. All right with that thank you very much and enjoy lunch. Thank you. Thank you.