Experimental Design for Missing Physics

TL;DR

This paper presents a sequential experimental design method that uses symbolic regression and neural networks to identify missing physics in process models, demonstrated on a bioreactor.

Contribution

It introduces an optimal data collection approach for discovering missing physics using universal differential equations and symbolic regression.

Findings

The method effectively discriminates between plausible model structures.

Application to a bioreactor successfully identified missing physics.

High-quality data is crucial for accurate model discovery.

Abstract

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.