7 papers
Algorithms and Differential Game Representations for Exploring Nonconvex Pareto Fronts in High Dimensions
Shanqing Liu, Paula Chen, Youngkyu Lee +1
We develop a new Hamiton-Jacobi (HJ) and differential game approach for exploring the Pareto front of (constrained) multi-objective optimization (MOO) problems. Given a preference…
Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks
Elham Kiyani, Khemraj Shukla, Jorge F. Urbán +2
Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network's trainin…
On the role of fractional Brownian motion in models of chemotaxis and stochastic gradient ascent
Gustavo Cornejo-Olea, Lucas Buvinic, Jerome Darbon +3
Cell migration often exhibits long-range temporal correlations and anomalous diffusion, even in the absence of external guidance cues such as chemical gradients or topographical co…
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…
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…
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…