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We present a differentiable programming methodology that combines Differentiable Predictive Control (DPC) with neural operators for learning policies for control of partial differential equations (PDEs). DPC reformulates parametric model predictive control as an offline gradient-based policy optimization problem, enabling policies to be optimized by backpropagating objectives and constraint penalties through differentiable PDE solvers and surrogates. To overcome the limitations of fixed-dimensional policy representations, we further cast PDE control as an operator learning problem that maps state fields to continuous control functions, enabling policies that naturally adapt to varying sensor, actuator, and multi-agent configurations. Remarkably, policies trained on small agent populations exhibit cardinality invariance, enabling zero-shot transfer to significantly larger populations and robustness to partial agent failure. We demonstrate the methodology on tracking, stabilization, and density transport across linear, nonlinear, chaotic, and turbulent PDE systems.

Biography: Jan Drgona is an Associate Professor of Civil and Systems Engineering, with a secondary appointment in Electrical and Computer Engineering, at Johns Hopkins University. He is affiliated with the Ralph S. O'Connor Sustainable Energy Institute (ROSEI) and the Data Science and AI Institute (DSAI). Previously, he was a Senior Data Scientist at Pacific Northwest National Laboratory and a postdoctoral researcher at KU Leuven. He earned his PhD in Control Engineering from the Slovak University of Technology. His research focuses on scientific machine learning for modeling, optimization, and control of complex systems.