# Applying physics-based loss functions to neural networks for improved generalizability in mechanics problems

arXiv: https://arxiv.org/abs/2105.00075 · HTML: https://mlsanity.com/paper/2105.00075/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 12 of 12)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [A Survey on Object Detection in Optical Remote Sensing Images](https://mlsanity.com/paper/1603.06201/) (2016)
- [Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport](https://mlsanity.com/paper/1912.02968/) (2019)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Deep learning of free boundary and Stefan problems](https://mlsanity.com/paper/2006.05311/) (2020)
- [GINNs: Graph-Informed Neural Networks for Multiscale Physics](https://mlsanity.com/paper/2006.14807/) (2020)
- [A New Open-Access Platform for Measuring and Sharing mTBI Data](https://mlsanity.com/paper/2010.08485/) (2020)

## Built on by (most cited first, 5 of 5)

- [Zero-Shot Transfer Learning for Structural Health Monitoring using Generative Adversarial Networks and Spectral Mapping](https://mlsanity.com/paper/2212.04002/) (2022)
- [Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems](https://mlsanity.com/paper/2204.12972/) (2022)
- [A Review of Physics-Informed Machine Learning Methods with Applications to Condition Monitoring and Anomaly Detection](https://mlsanity.com/paper/2401.11860/) (2024)
- [Physics-Enhanced TinyML for Real-Time Detection of Ground Magnetic Anomalies](https://mlsanity.com/paper/2311.11452/) (2023)
- [Aeroengine performance prediction using a physical-embedded data-driven method](https://mlsanity.com/paper/2407.00501/) (2024)

## Abstract (arXiv)

Physics-Informed Machine Learning (PIML) has gained momentum in the last 5 years with scientists and researchers aiming to utilize the benefits afforded by advances in machine learning, particularly in deep learning. With large scientific data sets with rich spatio-temporal data and high-performance computing providing large amounts of data to be inferred and interpreted, the task of PIML is to ensure that these predictions, categorizations, and inferences are enforced by, and conform to the limits imposed by physical laws. In this work a new approach to utilizing PIML is discussed that deals with the use of physics-based loss functions. While typical usage of physical equations in the loss function requires complex layers of derivatives and other functions to ensure that the known governing equation is satisfied, here we show that a similar level of enforcement can be found by implementing more simpler loss functions on specific kinds of output data. The generalizability that this approach affords is shown using examples of simple mechanical models that can be thought of as sufficiently simplified surrogate models for a wide class of problems.