PIDSolver:A Sequential Physics-Informed Diffusion Solver for Optimization with Algebraic Constraints

Physics-informed diffusion models have emerged as a promising tool for solving large optimization problems with hard constraints. These models iteratively generate solutions, thereby improving the accuracy of end-to-end artificial neural networks (ANN) based solvers. However, for a class of optimization problems involving complex algebraic constraints, a traditional solver is required to repeatedly solve for latent variables and perform gradient estimation for ANN-based solver training, incurring prohibitively high time costs. In this work, we present a sequential Physics-informed Diffusion Solver (PIDSolver) to address this challenge. Specifically, PIDSolver couples two sequential networks: the former performs a physics-informed denoising process, while the latter handles the algebraic constraints solving process and concurrently performs gradient-based corrections to guide the former in satisfying inequality constraints. The effectiveness of the proposed method is validated in practical alternating current optimal power flow scenarios, where PIDSolver generates solutions within a second-level time scale while outperforming state-of-the-art ANN-based solvers. Our code will be released at https://anonymous.4open.science/r/PIDSolver-D822/.