DS-HGNN achieves lower RMSE for stress and displacement prediction on stiffened panels than six benchmark GNN models and matches top accuracy with 19-38% fewer training samples.
hub
Physics-Informed Neural Operator for Learning Partial Differential Equations.ACM/IMS Journal of Data Science, 1(3):1–27
13 Pith papers cite this work. Polarity classification is still indexing.
13
Pith papers citing it
hub tools
citation-role summary
background 3
citation-polarity summary
roles
background 3polarities
background 3representative citing papers
Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.
FLASH-MAX embeds exact Maxwell solutions as neurons in a neural network to reconstruct homogeneous EM fields from sparse data with guaranteed zero PDE residual and proven universal approximation on arbitrary domains.
Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
NPSolver trains neural Poisson solvers label-free by supervising with a small number of preconditioned conjugate gradient steps and adds Boundary-Aware Transolver for mixed boundaries, outperforming baselines on 2D/3D irregular geometries.
CLDNet is a conditional latent dynamics network surrogate for the shallow water equations that delivers 115x faster 96-hour flood forecasts on irregular metropolitan basins while maintaining usable accuracy against gauge data.
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
MscaleFNO learns mappings from oscillatory media to wavefields for Helmholtz inverse problems and pairs it with diffusion regularization for partial-aperture 2D reconstructions.
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
-
A Diagnostic Software Suite for Auditing Learned PDE Simulators
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.