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:2507. 15455v3 Announce Type: replace-cross Abstract: We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic differential games and robust control.
By Hee Jun Yang, Minjung Gim, Yeoneung Kim
arXiv:2509. 23960v2 Announce Type: replace-cross Abstract: Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge.
By Manan Tayal, Aditya Singh, Shishir Kolathaya, Somil Bansal
arXiv:2508. 01718v2 Announce Type: replace Abstract: We develop a physics-informed policy-iteration method for stationary second-order Hamilton--Jacobi--Bellman equations arising in continuous-time stochastic control.
By Yeongjong Kim, Minseok Kim, Yeoneung Kim, Namkyeong Cho
arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).
By Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar
arXiv:2601. 04120v2 Announce Type: replace-cross Abstract: Optimal control of obstacle problems arises in a wide range of applications and is computationally challenging due to its nonsmoothness, nonlinearity, and bilevel structure.
By Yongcun Song, Shangzhi Zeng, Jin Zhang, Lvgang Zhang