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.

本文通过研究物理信息驱动的神经网络（PINNs）来编码控制方程，并评估其在两个不同系统的实验数据上的表现。我们发现，在简单的非线性摆系统中，PINNs 在理想数据情况下胜过了等效的无信息神经网络（NNs），在 10 个线性间隔和 10 个均匀分布的随机训练点上的准确度分别提高了 18 倍和 6 倍。在使用来自实验的真实数据进行类似测试的情况下，PINNs 相对于 NNs 的准确度提高了 9.3 倍和 9.1 倍，分别对应于 67 个线性间隔和均匀分布的随机点。此外，我们还研究了物理信息驱动模型在物理系统中的可行性，并选择 FPGA 作为部署计算的基板。鉴于此，我们使用了一台 PYNQ-Z1 FPGA 进行实验，并找出了与时间相干感知和空间数据对齐相关的问题。根据提出的系统架构和方法，我们讨论了从这项工作中获得的见解，并列出了未来工作计划。