Causal Physics-Informed Neural Networks Training System For Physical Simulation

A computer-based training system improves physics-informed neural networks (PINNs) training by weighted residual loss terms to account for physical causality.
Problem:
Conventional PINNs can struggle with dynamical systems that show multi-scale, chaotic, or turbulent behavior. Existing formulations may fail to respect the spatio-temporal causal structure of evolving physical systems. This can steer models toward erroneous solutions during training. Reliable simulation of PDE-governed systems can therefore remain difficult.
Solution:
The technology reformulates PINN loss functions to account for physical causality during training. It assigns weights in residual loss terms while differentiating at least one governing partial differential equation. In some embodiments, the weights are updated iteratively during gradient descent. The approach can also provide a stopping criterion based on weight convergence.
Technology Overview:
The system can include a training system, a production system, training samples, and a PINN trainer. The trainer uses labeled and unlabeled samples to train a physics-informed neural network. A trained model can then be deployed to predict movement of at least one component of a mechanical system. The technology can be implemented as methods, systems, software modules, or non-transitory computer readable media.
Advantages:

• Accounts for physical causality during PINN training through weighted residual loss terms
• Supports iterative weight updates during gradient descent training
• It can be implemented as software modules for incorporation into PINN models
• Uses labeled and unlabeled training samples within the training framework
• Provides a convergence-based stopping criterion in some embodiments

Applications:

• Mechanical system prediction: The technology can predict movement of at least one component of a mechanical system
• Design optimization: The technology can be incorporated into PINN models for design optimization
• Optimal control: The technology can be incorporated into PINN models for optimal control
• Digital twins: The technology can be incorporated into PINN models for building Digital Twins
• Physical simulation: The technology can be used where PDEs model physical phenomena requiring simulation or prediction

Stage of Development:

• Minimum Viable Product

Intellectual Property:

• US Application Filed US20250077875A1 

Reference Media:

• Wang, S. et. al., Science Direct, 2024 March 1; Vol. 421: Article 116813
• Perdikaris, P., 2024 Apr. 18; PirateNets: Physics Informed Deep Learning with Residual Adaptive Networks: YouTube 

Desired Partnerships:

• License

Docket #22-9985