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Experimental Design for Missing Physics

arXiv cs.LG / 4/3/2026

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Key Points

  • The paper addresses the challenge of “missing physics” in process systems when the underlying model structure is incomplete and must be inferred from experimental data.
  • It combines universal differential equations (using neural networks for unknown components) with symbolic regression to recover interpretable representations of the missing physics.
  • Because accurate recovery depends on data quality, the authors develop a sequential experimental design method that selects experiments to optimally discriminate among candidate model structures proposed by symbolic regression.
  • The proposed approach is demonstrated on discovering missing physics in a bioreactor, showing how guided experiment planning can improve structure identification.
  • Overall, the work links machine-learning-based model discovery with active experiment selection to reduce ambiguity and improve identifiability of true governing equations.

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.

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