Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains

arXiv:2608.08114 · physics.flu-dyn, cs.LG · Submitted 2026-08-08 · Read on arXiv

Jeeeun Lee, Denis Korolev, Miro Duhovic, Seong Su Kim

physics.flu-dyn, cs.LG

Submitted: 2026-08-08

Updated: 2026-08-11

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Spectral Bias — 21× in this paper · explained in 2 episodes
• Accuracy — 14× in this paper · explained in 1 episode
• PDE residual — 14× in this paper · explained in 2 episodes
• Gradient Flow — 7× in this paper · explained in 2 episodes
• Benchmark — 6× in this paper · explained in 2 episodes
• Overfitting — 6× in this paper · explained in 2 episodes
• Inverse Problem — 4× in this paper · explained in 2 episodes
• Adam — 3× in this paper · explained in 3 episodes
• Physics-Informed Neural Networks (PINNs) — 3× in this paper · explained in 8 episodes
• Robustness — 3× in this paper · explained in 6 episodes
• Embeddings — 2× in this paper · explained in 2 episodes
• Homogenization — 2× in this paper · explained in 2 episodes
• Hyperparameters — 2× in this paper · explained in 2 episodes
• Inductive Bias — 2× in this paper · explained in 3 episodes
• Surrogate Modeling — 2× in this paper · explained in 2 episodes
• Calibration — 1× in this paper · explained in 9 episodes
• Cosine Similarity — 1× in this paper · explained in 3 episodes
• Gating Network — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Hybrid Approach — 1× in this paper · explained in 4 episodes
• Inverse Design — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Machine Learning (ML) — 1× in this paper · explained in 2 episodes
• Neural Operators — 1× in this paper · explained in 2 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Preconditioner — 1× in this paper · explained in 2 episodes
• Preconditioning — 1× in this paper · explained in 2 episodes
• Self-Supervised Learning — 1× in this paper · explained in 8 episodes
• Transfer Learning — 1× in this paper · explained in 16 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes
• Unified Framework — 1× in this paper · explained in 6 episodes

Sources

• Simulating Three-dimensional Turbulence with Physics-informed Neural Networks
• An Expert's Guide to Training Physics-informed Neural Networks
• Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings
• Constrained Neural Parameterization for Optimization in Function Spaces
• ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks
• Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective
• Adam: A Method for Stochastic Optimization

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