3 papers
math.OC2025
Adversarial Physics-Informed Machine Learning for Robust Optimal Safe Predefined-Time Stabilization: A Game-Theoretic Approach
Nick-Marios T. Kokolakis, Shanqing Liu, Jerome Darbon +2
We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost…
math.NA2025
A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We propose a novel neural preconditioned Newton (NP-Newton) method for solving parametric nonlinear systems of equations. To overcome the stagnation or instability of Newton iterat…
cs.LG2025
A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Juan Diego Toscano, Daniel T. Chen, Vivek Oommen +2
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these…