Information-distilled physics informed deep learning for high order differential inverse problems with extreme...

Area of Science:

• Computational Science
• Artificial Intelligence
• Applied Mathematics

Background:

• Standard physics-informed deep learning struggles with inverse problems involving extreme discontinuities and high-order parameterized differential equations.
• Globally smooth activation functions in deep learning models lead to ill-conditioned gradients when parameters are spatially distributed or exhibit abrupt changes.

Purpose of the Study:

• To develop a novel physics-informed deep learning framework capable of accurately solving inverse problems with severe discontinuities.
• To address the limitations of existing methods in handling singularities and ill-conditioned gradient flows.

Main Methods:

• The proposed framework integrates reduced-order modeling, multi-level domain decomposition, and an ill-conditioning-suppression mechanism.
• It employs an information propagation and distillation strategy to manage ill-conditioned gradient information.
• The approach is designed to capture rapid variable changes in localized regions caused by discontinuities.

Main Results:

• The framework successfully captures rapid variations in variables within highly localized regions induced by discontinuities.
• Ill-conditioned information in the system's gradient flow is effectively suppressed through information propagation and distillation.
• The framework maintains accuracy in most subnetworks even when some individual subnetworks encounter failures.

Conclusions:

• The developed information-distilled physics-informed deep learning framework offers a robust solution for inverse problems with extreme discontinuities.
• This novel approach enhances the stability and accuracy of deep learning models in complex scientific and engineering applications.
• The method demonstrates resilience and maintains predictive power despite localized failures within the network.