Researchers have developed a new method to solve complex mathematical problems known as Hamilton--Jacobi--Isaacs (HJI) equations. These equations are used in fields like robotics and finance to model decision-making under uncertainty. The new approach combines classical dynamic programming with physics-informed neural networks (PINNs), allowing for more efficient and accurate solutions. The authors claim that their method can solve high-dimensional, nonconvex HJI equations, which is a challenging problem in the field. Numerical experiments demonstrate the accuracy and scalability of the method. --- Why it matters: This matters to researchers in AI because it provides a new tool for solving complex optimization problems, particularly those with uncertain or dynamic environments. The ability to efficiently solve high-dimensional, nonconvex HJI equations has potential applications in robotics, finance, and multi-agent reinforcement learning. Source: https://arxiv.org/abs/2507.15455