Double Coupling Architecture and Training Method for Optimization Problems of Differential Algebraic Equations with Parameters
This addresses optimization problems in simulation modeling for product development, offering a method to handle diverse requirements efficiently, though it appears incremental as it builds on existing physics-informed neural network approaches.
The paper tackles the challenge of multi-task optimization for parametric differential algebraic equations in simulation modeling by proposing a dual physics-informed neural network architecture that decouples constraints and objective functions, achieving generalization for multi-task objectives with a single training while maintaining real-time responsiveness.
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.