Discovering governing equations via moving horizon learning: The case of reacting systems

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AbstractGoverning equations in the form of differential equations are fundamental modeling elements for understanding, controlling, and optimizing chemical processes. While significant advances in machine learning allow for high‐performance surrogate modeling, the resulting models typically fail to extrapolate to regimes beyond the training data and provide little physical insight regarding the underlying phenomena. In this work, we propose a moving horizon dynamic nonlinear optimization strategy that recovers parsimonious governing equations from large‐scale, noisy data sets. 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 systems involving chemical reactions occurring under nonisothermal conditions. The main advantages and contributions of our proposed approach are demonstrated through two numerical case studies consisting of a continuously stirred tank reactor operated under isothermal and nonisothermal conditions.