Experimental Design for Missing Physics
This work addresses the challenge of gathering high-quality data for model discovery in systems with incomplete physics, which is incremental as it builds on existing universal differential equations and symbolic regression methods.
The paper tackles the problem of learning missing physics in process systems by developing a sequential experimental design technique that optimally discriminates between plausible model structures suggested by symbolic regression, applied to a bioreactor to recover the true model structure.
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.