Enhancing neurodynamic approach with physics-informed neural networks for solving non-smooth convex optimization...

Area of Science:

• Optimization
• Machine Learning
• Applied Mathematics

Background:

• Non-smooth convex optimization problems (NCOPs) are prevalent across various scientific and engineering domains.
• Existing numerical methods for NCOPs can be computationally intensive, often requiring intermediate state calculations.

Purpose of the Study:

• To develop an efficient and accurate deep learning framework for solving NCOPs.
• To overcome the limitations of traditional numerical integration methods in NCOP solutions.

Main Methods:

• A novel approach combining neurodynamic optimization with physics-informed neural networks (PINNs).
• Formulation of NCOPs as an initial value problem (IVP) using ordinary differential equations.
• Development of a specialized algorithm for simultaneous IVP solution and NCOP objective minimization.

Main Results:

• The proposed method eliminates the need for computing intermediate states, reducing computational steps.
• Achieved more accurate predictions with fewer iterations compared to existing methods.
• Demonstrated effectiveness in finding feasible solutions that adhere to NCOP constraints.

Conclusions:

• The deep learning approach offers a computationally efficient and accurate solution for NCOPs.
• This method provides a significant advancement over traditional numerical integration techniques.
• The framework successfully addresses complex optimization challenges in science and engineering.