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

arXiv: https://arxiv.org/abs/2401.03534 · HTML: https://mlsanity.com/paper/2401.03534/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 114 references that are in the map.
- First posted on arXiv 7 Jan 2024.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [FINN-R: An End-to-End Deep-Learning Framework for Fast Exploration of Quantized Neural Networks](https://mlsanity.com/paper/1809.04570/) (2018)
- [Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks](https://mlsanity.com/paper/2105.00862/) (2021)
- [TensorFlow: A system for large-scale machine learning](https://mlsanity.com/paper/1605.08695/) (2016)
- [Newton: A Language for Describing Physics](https://mlsanity.com/paper/1811.04626/) (2018)

## Abstract (arXiv)

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.