Double Coupling Architecture and Training Method for Optimization Problems of Differential Algebraic Equations with Parameters

TL;DR

This paper introduces a dual physics-informed neural network architecture combined with a genetic algorithm-enhanced training method to efficiently solve multi-task optimization problems involving complex differential algebraic equations in product simulation.

Contribution

It proposes a novel dual neural network architecture and a genetic algorithm-based training framework that improve efficiency and generalization in multi-task DAE optimization.

Findings

Ensures solution equivalence with a relaxation variable and error bounds.

Reduces redundant solving of differential algebraic equations during training.

Achieves real-time responsiveness for multi-task product optimization.

Abstract

Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The growing diversity of product requirements demands multi-task optimization, a key challenge in simulation modeling research. A dual physics-informed neural network architecture has been proposed to decouple constraints and objective functions in parametric differential algebraic equation optimization problems. Theoretical analysis shows that introducing a relaxation variable with a global error bound ensures solution equivalence between the network and optimization problem. A genetic algorithm-enhanced training framework for physics-informed neural networks improves training precision and efficiency, avoiding redundant solving of differential algebraic equations. This approach enables generalization for multi-task objectives with a single, training maintaining real-time responsiveness to product requirements.