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Kinetics-informed neural networks improve fit quality for multi-pulse and noisy temporal analysis of products datasets. 

Modeling the non-linear dynamics of a system from measurement data accurately is an open challenge. Over the past few years, various tools such as SINDy and DySMHO have emerged as approaches to distill dynamics from data. However, challenges persist in accurately capturing dynamics of a system especially when the physical knowledge about the system is unknown. A promising solution is to use a hybrid paradigm, that combines mechanistic and black-box models to leverage their respective strengths. In this study, we combine a hybrid modeling paradigm with sparse regression, to develop and identify models simultaneously. Two methods are explored, considering varying complexities, data quality, and availability and by comparing different case studies. In the first approach, we integrate SINDy-discovered models with neural ODE structures, to model unknown physics. In the second approach, we employ Multifidelity Surrogate Models (MFSMs) to construct composite models comprised of SINDy-discovered models and error-correction models. 

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.