arXiv:2608. 11480v1 Announce Type: cross Abstract: Hamilton-Jacobi (HJ) reachability provides a mathematically rigorous framework for safe control of dynamical systems, but its practical application is bottlenecked by the computational complexity of solving Hamilton-Jacobi-Isaacs variational inequality PDEs in high dimensions.
By Sungje Park, Stephen Tu
arXiv:2607. 25608v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks.
By Pinki Khatun, M. Sajid, Abhinav Jha, M. Tanveer
The paper introduces a mesh‑free policy iteration framework that blends classical dynamic programming with physics‑informed neural networks (PINNs) to solve high‑dimensional, nonconvex Hamilton–Jacobi–Isaacs (HJI) equations. The method alternates between solving linear second‑order PDEs under fixed feedback policies and updating controls via pointwise minimax optimization using automatic differentiation. The authors prove local uniform convergence of the value function iterates to the unique viscosity solution under standard Lipschitz and uniform ellipticity assumptions, and demonstrate the approach’s accuracy and scalability in two‑, five‑, and ten‑dimensional stochastic games, outperforming direct PINN solvers.
By Hee Jun Yang, Minjung Gim, Yeoneung Kim
Hamilton-Jacobi (HJ) reachability provides a mathematically rigorous framework for safe control of dynamical systems, but its practical application is bottlenecked by the computational complexity of solving Hamilton-Jacobi-Isaacs variational inequality PDEs in high dimensions. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to classical mesh-based solvers, yet their performance is highly sensitive to the choice of collocation sampling.
arXiv:2606. 29436v1 Announce Type: cross Abstract: We study operator learning for random obstacle-to-solution maps arising from elliptic variational inequalities with finite-band self-affine random obstacle fields.
By Chenhui Zhu, Fei Wang
arXiv:2606. 13825v1 Announce Type: cross Abstract: Deep unfolding (DU) accelerates iterative optimizers by introducing learnable components and training them through unrolled iterations, but extending DU to the large-scale semidefinite programs (SDPs) common in robotics has remained limited.
By Alex Oshin, Rahul Vodeb Ghosh, Evangelos A. Theodorou