A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
Physics-informed neural networks (pinns) for fluid mechanics: a review
5 Pith papers cite this work. Polarity classification is still indexing.
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A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
A PINN transfer learning framework for coal methane sorption reaches R²=0.932 on held-out data with 227% improvement over classical isotherms and identifies Monte Carlo Dropout as the best uncertainty method while ensembles degrade under shared physics constraints.
A unified training framework for mesh-based ML surrogates in CFD improves accuracy and long-horizon stability by enforcing spatial derivative consistency via multi-node prediction, using temporal cross-attention correction, and adding 3D rotary positional embeddings.
citing papers explorer
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Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
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Robust Deep FOSLS for Transmission Problems
A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
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NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
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Physics-Informed Neural Networks for Methane Sorption: Cross-Gas Transfer Learning, Ensemble Collapse Under Physics Constraints, and Monte Carlo Dropout Uncertainty Quantification
A PINN transfer learning framework for coal methane sorption reaches R²=0.932 on held-out data with 227% improvement over classical isotherms and identifies Monte Carlo Dropout as the best uncertainty method while ensembles degrade under shared physics constraints.
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Mesh Based Simulations with Spatial and Temporal awareness
A unified training framework for mesh-based ML surrogates in CFD improves accuracy and long-horizon stability by enforcing spatial derivative consistency via multi-node prediction, using temporal cross-attention correction, and adding 3D rotary positional embeddings.