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 (P INNs) for fluid mechanics: a review
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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.
Hybrid neural-process model derives biokinetic parameters from genomic traits for soil organic matter turnover, with ecological constraints, and outperforms baselines on synthetic and real data.
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.
An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.
PINNs and DeepONets solve Newtonian plane Couette flow with dynamic wall slip; DeepONet achieves 0.36% mean relative error on unseen cases and 540X speedup over numerical methods.
The review summarizes progress toward faster, automated imaging-derived FFR using ML/DL and physics-informed approaches like PINNs and PINOs, while noting challenges in generalizability and the need for clinical validation.
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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Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systems
Hybrid neural-process model derives biokinetic parameters from genomic traits for soil organic matter turnover, with ecological constraints, and outperforms baselines on synthetic and real data.
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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.
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Auto-Adaptive PINNs with Applications to Phase Transitions
An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.
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Solution of the Newtonian plane Couette flow with dynamic wall slip using machine-learning methods
PINNs and DeepONets solve Newtonian plane Couette flow with dynamic wall slip; DeepONet achieves 0.36% mean relative error on unseen cases and 540X speedup over numerical methods.
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Imaging-Derived Coronary Fractional Flow Reserve: Advances in Physics-Based, Machine Learning, and Physics-Informed Methods
The review summarizes progress toward faster, automated imaging-derived FFR using ML/DL and physics-informed approaches like PINNs and PINOs, while noting challenges in generalizability and the need for clinical validation.