(139b) Discovering Governing Equations Via Moving Horizon Learning: The Case of Continuous and Batch Reacting Systems

Governing equations in the form of differential equations are fundamental modeling elements for understanding, controlling, and optimizing dynamical systems that drive chemical manufacturing processes. While significant progress in machine learning has allowed for high performance surrogate modeling, these approaches often fail to extrapolate to regimes beyond the training data and provide little (if any) physical insight regarding the underlying phenomena. In this work, we introduce a moving horizon dynamic nonlinear optimization strategy that recovers parsimonious governing equations from large-scale, noisy data sets. Advanced discretization schemes are embedded in the optimization problem allowing for reduced gradient approximation error and improved numerical stability for stiff systems. Differently from prior works, our approach does not rely on significant structural assumptions (mainly concerning linearity with respect to estimated model coefficients) which provides greater modeling flexibility and permits distilling governing equations of chemical systems. The main advantages and contributions of our proposed approach are demonstrated through numerical case studies consisting of a continuously stirred tank reactor operated under isothermal and non-isothermal conditions. Furthermore, we introduce extensions for dealing with batch processes, which present their own inherent challenges relative to their continuous counterparts.