Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study
Solving partial differential equations (PDEs) with discontinuous solutions , such as shock waves in multiphase viscous flow in porous media , is critical for a wide range of scientific and engineering applications, as they represent sudden changes in physical quantities. Physics-Informed Neural Networks (PINNs), an approach proposed for solving PDEs, encounter significant challenges when applied to such systems. Accurately solving PDEs with discontinuities using PINNs requires specialized techniques to ensure effective solution accuracy and numerical stability. A benchmarking study was conducted on two multiphase flow problems in porous media: the classic Buckley-Leverett (BL) problem and a fully coupled system of equations involving shock waves but with varying levels of solution complexity. The findings show that PM and LM approaches can provide accurate solutions for the BL problem by effectively addressing the infinite gradients associated with shock occurrences. In contrast, AM methods failed to effectively resolve the shock waves. When applied to fully coupled PDEs (with more complex loss landscape), the generalization error in the solutions quickly increased, highlighting the need for ongoing innovation. This study provides a comprehensive review of existing techniques for managing PDE discontinuities using PINNs, offering information on their strengths and limitations. The results underscore the necessity for further research to improve PINNs ability to handle complex discontinuities, particularly in more challenging problems with complex loss landscapes. This includes problems involving higher dimensions or multiphysics systems, where current methods often struggle to maintain accuracy and efficiency.
Code (0)
등록된 구현이 없습니다.
Tasks
BenchmarkingMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
A physics-aware deep learning model for shear band formation around collapsing pores in shocked reactive materials
Modeling shock-to-detonation phenomena in energetic materials (EMs) requires capturing complex physical processes such as strong shocks, rapid changes in microstructural morphology, and nonlinear dynamics of chemical rea…
Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and sl…
Extended Physics Informed Neural Network for Hyperbolic Two-Phase Flow in Porous Media
The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally de…
Reduced Order Modeling of Energetic Materials Using Physics-Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)
Physics-aware deep learning (PADL) has gained popularity for use in complex spatiotemporal dynamics (field evolution) simulations, such as those that arise frequently in computational modeling of energetic materials (EM)…
POSEIDON: Physics-Optimized Seismic Energy Inference and Detection Operating Network
Earthquake prediction and seismic hazard assessment remain fundamental challenges in geophysics, with existing machine learning approaches often operating as black boxes that ignore established physical laws. We introduc…