Abstract: This talk presents a control-oriented perspective on Scientific Machine Learning (SciML) for modeling, optimization, and control of dynamical systems. SciML provides a unifying computational paradigm that integrates physics-based models, optimization algorithms, and control policies within a differentiable programming framework. This synthesis enables computation of gradients for constrained optimization, system identification, and control problems while preserving interpretability, stability, and physical consistency.
Three recent advances will be highlighted. First, differentiable predictive control (DPC), a SciML approach that merges model predictive control with gradient-based learning to enable scalable, self-supervised training of control policies for ODEs and PDEs [1,2]. Second, an operator-splitting formulation for neural differential-algebraic equations that integrates mechanistic dynamics with neural components [3]. Third, a learning-to-optimize (L2O) methodology where differentiable relaxations of integer rounding and feasibility-preserving projection layers enable scalable gradient-based training of policies for large-scale parametric mixed-integer nonlinear programming (MINLP) [4]. Together, these advances demonstrate how SciML can unlock new capabilities for the modeling, optimization, and control of complex systems.