🤖 AI Summary
This work addresses the persistent challenge in process systems modeling of simultaneously achieving accuracy, simplicity, and physical interpretability—particularly in control applications where nonlinear expressiveness must be balanced against a preference for linear structures. The authors propose a convex hybrid modeling paradigm grounded in operator theory, which constrains models to interpretable subspaces or nonlinearly parameterized interpretable manifolds. By introducing a reparameterization technique based on “canonical features” in an augmented parameter space, the approach effectively integrates kernel methods with convex optimization. This framework enables the construction of kernel-based hybrid surrogate models over families of interpretable static and dynamic systems, significantly enhancing both predictive accuracy and computational efficiency while preserving physical interpretability across diverse process systems modeling scenarios.
📝 Abstract
While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear ones, promoting the use of operator theory, which ``universally'' represents a nonlinear system by a nonparametric operator. On the other hand, interpretability requires by a ``non-universal'', parametric nonlinear model family satisfying first principles; these constraints tend to complicate the learning procedure. This paper considers hybrid modeling by formulating convex learning problems that account for interpretability systematically and give surrogate models efficiently. Three settings are discussed -- (i) regularization around a particular ``reference model'', (ii) restriction on an ``interpretable subspace'', and more generally, (iii) restriction on a ``interpretable manifold'' that is nonlinearly parameterized. In the more general setting, by introducing an operator-theoretic technique to re-parameterize models in the ``lifted'' parameters (``canonical features'', potentially infinite-dimensional), the system is regarded as a kernel-based mixture of interpretable models. Application to both static and dynamic models are exemplified in numerical studies.