Learning System Physics Using Symbolic Neural Integration (SyNISM) with Applications to Chemical Processes

Learning the underlying physics of complex systems is a fundamental step in advancing data-driven modeling and engineering design. Symbolic regression (SR) is crucial for deriving data-driven, interpretable mathematical models that provide insights into complex systems, particularly in chemical engineering. While neural networks (NNs) excel at modeling nonlinear relationships, they often lack interpretability, making it difficult to extract explicit mathematical expressions. SR addresses this challenge, but combining it with NNs presents difficulties in handling complex mathematical operations, such as multiplication, division, and transcendental functions. To address these challenges, we propose a hybrid framework, SyNISM, that learns system physics by combining SR and NNs. Using a parameter hypernetwork to dynamically generate sparse parameters, SyNISM ensures interpretability while learning physically consistent representations of the system dynamics. This approach resolves challenges related to the differentiability and parameter selection using custom activation functions and probabilistic sampling. The framework is validated through case studies on batch reactors, continuous stirred tank reactors (CSTRs), series reactions, unsteady-state heat transfer, and thermophysical property modeling, where it accurately learns underlying physics and produces symbolic equations aligned with analytical solutions. SyNISM also performed better than traditional SR approaches in more than 75% of the applied cases in predicting beyond the training data.