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.
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Physics-Informed Neural Operator for Learning Partial Differential Equations.ACM/IMS Journal of Data Science, 1(3):1–27
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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
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Physics-Guided Dual-Stream Heterogeneous Graph Neural Network for Predicting Full-Field Structural Response of Stiffened Panels
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.
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Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
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.
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Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
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.
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Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale
Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
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Solving Convolution-type Integral Equations using Preconditioned Neural Operators
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.
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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.
-
NPSolver: Neural Poisson Solver with Iterative Physics Supervision
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.
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Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations
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.
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A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
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Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence
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.
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A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results
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.
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Multiscale Fourier Neural Operator for Inverse Wave Scattering in Highly Oscillatory Media
MscaleFNO learns mappings from oscillatory media to wavefields for Helmholtz inverse problems and pairs it with diffusion regularization for partial-aperture 2D reconstructions.
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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.