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。

面向实际物理系统编码动力学的基于物理信息的神经网络