Physics-informed Neural Networks for Encoding Dynamics in Real Physical
  Systems
Hamza Alsharif
This dissertation investigates physics-informed neural networks (PINNs) as
candidate models for encoding governing equations, and assesses their
performance on experimental data from two different systems. The first system
is a simple nonlinear pendulum, and the second is 2D heat diffusion across the
surface of a metal block. We show that for the pendulum system the PINNs
outperformed equivalent uninformed neural networks (NNs) in the ideal data
case, with accuracy improvements of 18x and 6x for 10 linearly-spaced and 10
uniformly-distributed random training points respectively. In similar test
cases with real data collected from an experiment, PINNs outperformed NNs with
9.3x and 9.1x accuracy improvements for 67 linearly-spaced and
uniformly-distributed random points respectively. For the 2D heat diffusion, we
show that both PINNs and NNs do not fare very well in reconstructing the
heating regime due to difficulties in optimizing the network parameters over a
large domain in both time and space. We highlight that data denoising and
smoothing, reducing the size of the optimization problem, and using LBFGS as
the optimizer are all ways to improve the accuracy of the predicted solution
for both PINNs and NNs. Additionally, we address the viability of deploying
physics-informed models within physical systems, and we choose FPGAs as the
compute substrate for deployment. In light of this, we perform our experiments
using a PYNQ-Z1 FPGA and identify issues related to time-coherent sensing and
spatial data alignment. We discuss the insights gained from this work and list
future work items based on the proposed architecture for the system that our
methods work to develop.