mlsanityData to 7 Oct 2026

Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity

arXiv 2203.08802 ↗First posted 15 Mar 2022physics.flu-dyn cs.LGcited by 21

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Abstract (arXiv)

Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of physical phenomena described by partial differential equations (PDE). However, it has been observed that PINNs are difficult to train in certain "stiff" problems, which include various nonlinear hyperbolic PDEs that display shocks in their solutions. Recent studies added a diffusion term to the PDE, and an artificial viscosity (AV) value was manually tuned to allow PINNs to solve these problems. In this paper, we propose three approaches to address this problem, none of which rely on an a priori definition of the artificial viscosity value. The first method learns a global AV value, whereas the other two learn localized AV values around the shocks, by means of a parametrized AV map or a residual-based AV map. We applied the proposed methods to the inviscid Burgers equation and the Buckley-Leverett equation, the latter being a classical problem in Petroleum Engineering. The results show that the proposed methods are able to learn both a small AV value and the accurate shock location and improve the approximation error over a nonadaptive global AV alternative method.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 6 of its 29 references that are in the map. First posted on arXiv 15 Mar 2022.

Builds on

6 of 29 references.

References · 6

  1. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  2. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  3. 2020A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecturecited by 50
  4. 2022PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimizationcited by 11
  5. 2020Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problemcited by 10
  6. 2021Physics-informed attention-based neural network for solving non-linear partial differential equationscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 5; 2024: 4; 2025: 4; 2026: 5.

21 papers.

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  1. 2025Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Studycited by 11
  2. 2022Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spreadcited by 10
  3. 2024Binary structured physics-informed neural networks for solving equations with rapidly changing solutionscited by 8
  4. 2022Characteristics-Informed Neural Networks for Forward and Inverse Hyperbolic Problemscited by 5
  5. 2023A Critical Review of Physics-Informed Machine Learning Applications in Subsurface Energy Systemscited by 4
  6. 2023Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controlscited by 4
  7. 2024PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEscited by 4
  8. 2023GRINN: A Physics-Informed Neural Network for solving hydrodynamic systems in the presence of self-gravitycited by 3
  9. 2025LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blockscited by 3
  10. 2022Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scalingcited by 2
  11. 2024Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fieldscited by 2
  12. 2023A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part Icited by 0
9 more
  1. 2023Spectral-Bias and Kernel-Task Alignment in Physically Informed Neural Networkscited by 0
  2. 2024Label Propagation for Physics-Informed Neural Networks and Physics-Informed Gaussian Processescited by 0
  3. 2025Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructionscited by 0
  4. 2025Extended Physics Informed Neural Network for Hyperbolic Two-Phase Flow in Porous Mediacited by 0
  5. 2026A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Lawscited by 0
  6. 2026SPLIT-PINN: Separable Probability Learning Technique via Physics-Informed Neural Networks for High-Dimensional Probabilistic Modelingcited by 0
  7. 2026Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variablescited by 0
  8. 2026Physics Informed Random Feature Neural Networks for Solving PDEscited by 0
  9. 2026Adaptive Physics-Informed Neural Networks for the Blasius Boundary-Layer Problemcited by 0