Neuro-PINN: A hybrid framework for efficient nonlinear projection equation solutions

Abstract

Nonlinear projection equations (NPEs) provide a unified framework for solving various constrained nonlinear optimization and engineering problems. This paper presents a deep learning approach for solving NPEs by incorporating neurodynamic optimization and physics-informed neural networks (PINNs). First, we model the NPE as a system of ordinary differential equations (ODEs) using neurodynamic optimization, and the objective becomes solving this ODE system. Second, we use a modified PINN to serve as the solution for the ODE system. Third, the neural network is trained using a dedicated algorithm to optimize both the ODE system and the NPE. Unlike conventional numerical integration methods, the proposed approach predicts the end state without computing all the intermediate states, resulting in a more efficient solution. The effectiveness of the proposed framework is demonstrated on a collection of classical problems, such as variational inequalities and complementarity problems.