Constructing Physics-Informed Neural Networks with Architecture Based on Analytical Modification of Numerical Methods...

Area of Science:

• Computational Science and Engineering
• Artificial Intelligence
• Applied Mathematics

Background:

• Traditional neural networks often struggle with complex physical systems due to challenges in architecture selection and weight initialization.
• Physics-Informed Neural Networks (PINNs) integrate physical laws but face limitations in efficient training and parameterization.
• Existing numerical methods require significant analytical modifications for effective neural network integration.

Purpose of the Study:

• To introduce a novel neural network architecture grounded in physics (PBA-PINN).
• To address key challenges in PINN development, including architecture selection and weight initialization for rapid convergence.
• To enable effective surrogate modeling and simulation of real-world systems using multi-fidelity data.

Main Methods:

• Developed a three-stage network construction process.
• Stage 1: Created a neural network solution based on numerical schemes for initial low-fidelity results.
• Stage 2: Employed physics-based architecture (PBA) training to solve differential equations by minimizing loss functions.
• Stage 3: Utilized high-fidelity sensor data for training PBA-PINNs, parameter identification, and solving specific tasks.

Main Results:

• The proposed physics-based architecture (PBA) with trainable parameters of governing equations facilitates efficient neural network training.
• PBA-PINNs effectively address the challenges of architecture selection and weight initialization, ensuring faster convergence.
• Demonstrated high accuracy in modeling chemical reactor processes, showing significant improvements with retraining on high-accuracy data.

Conclusions:

• PBA-PINNs offer a robust framework for solving complex problems previously intractable for standard PINNs.
• The approach is particularly suitable for surrogate modeling and simulating real-world objects with multi-fidelity data.
• Experimental validation confirms the effectiveness of PBA-PINNs in achieving high accuracy through targeted retraining.