Physics-informed Neural Networks for Encoding Dynamics in Real Physical Systems

Abstract

Predictive data-driven models are gaining widespread attention and are being deployed in embedded systems within physical environments across a wide variety of modern technologies such as robotics, autonomous vehicles, smart manufacturing, and industrial controllers. However, these models have no notion or awareness of the underlying physical principles that govern the dynamics of the physical systems that they exist within. This dissertation studies the encoding of governing differential equations that explain system dynamics, within predictive models that are to be deployed within real physical systems. Based on this, we investigate physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assess 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 18× and 6× 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 9.3× and 9.1× 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.