# Structural Constraints for Physics-augmented Learning

arXiv: https://arxiv.org/abs/2410.05507 · HTML: https://mlsanity.com/paper/2410.05507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 11 of 11)

- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Learning Discrepancy Models From Experimental Data](https://mlsanity.com/paper/1909.08574/) (2019)
- [Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects](https://mlsanity.com/paper/2203.05164/) (2022)
- [Learning About Structural Errors in Models of Complex Dynamical Systems](https://mlsanity.com/paper/2401.00035/) (2023)
- [Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response](https://mlsanity.com/paper/2402.17233/) (2024)
- [Learning Absorption Rates in Glucose-Insulin Dynamics from Meal Covariates](https://mlsanity.com/paper/2304.14300/) (2023)

## Built on by (most cited first, 1 of 1)

- [Data Enrichment for Symbolic Regression Using Diffusion Models](https://mlsanity.com/paper/2606.00988/) (2026)

## Abstract (arXiv)

When the physics is wrong, physics-informed machine learning becomes physics-misinformed machine learning. A powerful black-box model should not be able to conceal misconceived physics. We propose two criteria that can be used to assert integrity that a hybrid (physics plus black-box) model: 0) the black-box model should be unable to replicate the physical model, and 1) any best-fit hybrid model has the same physical parameter as a best-fit standalone physics model. We demonstrate them for a sample nonlinear mechanical system approximated by its small-signal linearization.