We propose a novel method that makes use of deep neural networks and gradient decent to perform automated design on complex real world engineering tasks. Our approach works by training a neural network to mimic the fitness function of a design optimization task and then, using the differential nature of the neural network, perform gradient decent to maximize the fitness. We demonstrate this methods effectiveness by designing an optimized heat sink and both 2D and 3D airfoils that maximize the lift drag ratio under steady state flow conditions. We highlight that our method has two distinct benefits over other automated design approaches. First, evaluating the neural networks prediction of fitness can be orders of magnitude faster then simulating the system of interest. Second, using gradient decent allows the design space to be searched much more efficiently then other gradient free methods. These two strengths work together to overcome some of the current shortcomings of automated design. Automated Design is the process by which an object is designed by a computer to meet or maximize some measurable objective. This is typically performed by modeling the system and then exploring the space of designs to maximize some desired property whether that be an automotive car styling with low drag or power and cost efficient magnetic bearings BID1 BID4 . A notable historic example of this is the 2006 NASA ST5 spacecraft antenna designed by an evolutionary algorithm to create the best radiation pattern (Hornby et al.) . More recently, an extremely compact broadband on-chip wavelength demultiplexer was design to split electromagnetic waves with different frequencies BID17 . While there have been some significant successes in this field the dream of true automated is still far from realized. The main challenges present are heavy computational requirements for accurately modeling the physical system under investigation and often exponentially large search spaces. These two problems negatively complement each other making the computation requirements intractable for even simple problems.Our approach works to solve the current problems of automated design in two ways. First, we learn a computationally efficient representation of the physical system on a neural network. This trained network can be used to evaluate the quality or fitness of the design several orders of magnitude faster. Second, we use the differentiable nature of the trained network to get a gradient on the parameter space when performing optimization. This allows significantly more efficient optimization requiring far fewer iterations then other gradient free methods such as genetic algorithms or simulated annealing. These two strengths of our method overcome the present difficulties with automated design and greatly accelerate optimization.The first problem tackled in this work is designing a simple heat sink to maximize the cooling of a heat source. The setup of our simulation is meant to mimic the conditions seen with an aluminum heat sink on a computer processor. We keep this optimization problem relatively simple and use this only as a first test and introduction to the method. Our second test is on the significantly more difficult task of designing both 2D and 3D airfoils with high lift drag ratios under steady state flow conditions. This problem is of tremendous importance in many engineering areas such as aeronautical, aerospace and automotive engineering. Because this is a particularly challenging problem and often times unintuitive for designers, there has been considerable work using automated design to produce optimized designs. We center much of the discussion in this paper around this problem because of its difficulty and view this as a true test our method. While we only look at these two problems in this work, we emphasize that the ideas behind our method are applicable to a wide variety of automated design problems and present the method with this in mind.As we will go into more detail in later sections, in order to perform our airfoil optimization we need a network that predicts the steady state flow from an objects geometry. This problem has previously been tackled in BID5 where they use a relatively simple network architecture. We found that better perform could be obtained using some of the modern network architecture developments and so, in addition to presenting our novel method of design optimization, we also present this superior network for predicting steady state fluid flow with a neural network. In this work we have presented a novel method for automated design and shown its effectiveness on a variety of tasks. Our method makes use of neural networks and gradient descent to provide powerful and fast optimization. There are many directions for future work such as applying this method to new domains like structural optimization and problems related to electromagnetism. One area of particular interest is design optimization on airfoils in turbulent time dependent flows. Another interesting area to explore is hybrid approaches where the neural network method is used to generate a rough design and then fine tuned with a high fidelity simulation. DISPLAYFORM0 The parameters present are n 1 , n 2 , A i s, and h. We also add the parameter θ that determines the angle of attack. In this work we fixed n 1 to 0.5 and n 2 to 1.0 as this will produce a rounded head on the airfoil. We also fix h to zero making the tail the same height as the head. Thus the trainable parameters are the 42 values corresponding to the A i s for the upper and lower surface. A illustration showing the parameterization can be found in FIG7 . The 3D airfoil has similar parameterization.S(φ, y) = φ n1 (1 − φ) This tells the height of the airfoil at a point (x, y). The trainable parameters here are n 1 , n 2 , A i s, B j s, h, s, and l. Again, n 1 , n 2 , and h are fixed to the values in the 2D case. We also have 2 parameters for the angle θ and ψ that determine the rotation in the x and y direction. We keep ψ at zero and only vary θ at the desired angles during the optimization. The parameters s and l correspond to the sweep present in the wing. This leaves the A i s and B j s for optimization. We split the remaining 39 parameters equally so that 13 values are used for B i s and the remaining 26 are split between the A i s for the upper and lower surface. For a much more in depth look at this parameterization, see BID13 .
A method for performing automated design on real world objects such as heat sinks and wing airfoils that makes use of neural networks and gradient descent. Neural network (parameterization and prediction) and gradient descent (back propogation) to automatically design for engineering tasks.  This paper introduces using a deep network to approximate the behavior of a complex physical system, and then design optimal devices by optimizing this network with respect to its inputs.