(394u) Improving Dynamical System Model Quality Using Symbolic Regression

At the edge of feasible operations often lie more efficient process design and control. Operating near these boundaries, however, can be risky as uncertainty in measurements or poor model representations can compromise safety margins. Despite the rich data collected in modern chemical plants and advances in methods enabling digital twins and process optimization, human-interpretable models remain crucial for designing processes with robust safety margins.

We propose a novel data-driven strategy that combines existing system models with symbolic regression to improve model quality. Our approach identifies solutions to existing models, then learns symbolic coordinate transformations to align these models with state measurements. By performing symbolic regression in a low-dimensional coordinate space rather than a high-dimensional state space, we decompose complex modeling problems into smaller, more tractable components. These learned transformations yield solutions that build upon prior knowledge using data while enabling the use of automatic differentiation and symbolic regression to develop improved dynamical system models that maintain interpretability for domain experts.

Our method was validated on two dynamical systems: Burgers’ equation and a reaction-diffusion process. Starting with the diffusion equation as a poor-quality model, we successfully recovered Burgers’ equation from 100 randomly sampled simulation points. For the reaction-diffusion process, our method corrected the kinetic representation to capture the simulated ground truth. This approach extends symbolic regression to more complex systems by strategically redefining the symbol space while leveraging domain knowledge, reducing computational demands and improving model quality.