# Experimental Design for Missing Physics

arXiv: https://arxiv.org/abs/2604.01231 · HTML: https://mlsanity.com/paper/2604.01231/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 9 of 9)

- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [Machine Learning for Prediction with Missing Dynamics](https://mlsanity.com/paper/1910.05861/) (2019)
- [ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling](https://mlsanity.com/paper/2103.05244/) (2021)
- [Learning orbital dynamics of binary black hole systems from gravitational wave measurements](https://mlsanity.com/paper/2102.12695/) (2021)
- [Non-Negative Universal Differential Equations With Applications in Systems Biology](https://mlsanity.com/paper/2406.14246/) (2024)
- [Efficient hybrid modeling and sorption model discovery for non-linear advection-diffusion-sorption systems: A systematic scientific machine learning approach](https://mlsanity.com/paper/2303.13555/) (2023)
- [Learning COVID-19 Regional Transmission Using Universal Differential Equations in a SIR model](https://mlsanity.com/paper/2310.16804/) (2023)

## Abstract (arXiv)

For most process systems, knowledge of the model structure is incomplete. This missing physics must then be learned from experimental data. Recently, a combination of universal differential equations and symbolic regression has become a popular tool to discover these missing physics. Universal differential equations employ neural networks to represent missing parts of the model structure, and symbolic regression aims to make these neural networks interpretable. These machine learning techniques require high-quality data to successfully recover the true model structure. To gather such informative data, a sequential experimental design technique is developed which is based on optimally discriminating between the plausible model structures suggested by symbolic regression. This technique is then applied to discovering the missing physics of a bioreactor.