Enhancing Neurodynamic Approach with Physics-Informed Neural Networks for Solving Non-Smooth Convex Optimization Problems
Résumé
This paper proposes a deep learning approach for solving non-smooth convex optimization problems (NCOPs), which have broad applications in computer science, engineering, and physics. Our approach combines neurodynamic optimization with physics-informed neural networks (PINNs) to provide an efficient and accurate solution. We first use neurodynamic optimization to formulate an initial value problem (IVP) that involves a system of ordinary differential equations for the NCOP. We then introduce a modified PINN as an approximate state solution to the IVP. Finally, we develop a dedicated algorithm to train the model to solve the IVP and minimize the NCOP objective simultaneously. Unlike existing numerical integration methods, a key advantage of our approach is that it does not require the computation of a series of intermediate states to produce a prediction of the NCOP. Our experimental results show that this computational feature results in fewer iterations being required to produce more accurate prediction solutions. Furthermore, our approach is effective in finding feasible solutions that satisfy the NCOP constraint.
Mots clés
Non-smooth convex optimization problem Neurodynamic optimization Physics-informed neural network Numerical integration method Ordinary differential equation
Non-smooth convex optimization problem
Neurodynamic optimization
Physics-informed neural network
Numerical integration method
Ordinary differential equation
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)