GAIA introduces a geometry-adaptive integral autoencoder that unifies forward, boundary-value, and inverse PDE operator learning on arbitrary domains via geometry tokens and cross-attention.
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Factorized fourier neural oper- ators
19 Pith papers cite this work, alongside 9 external citations. Polarity classification is still indexing.
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representative citing papers
PNOT combines graph attention on boundary heat flux with a physics-aware neural operator and gradient-constrained loss to reconstruct divertor temperature fields for real-time fusion control.
HAMNO introduces adaptive gating between local and global operators in a hierarchical setup, with PI-HAMNO adding PDE residual constraints, demonstrating better performance on Allen-Cahn, Cahn-Hilliard, and Swift-Hohenberg equations.
Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.
A latent Structured Spectral Propagator enables stable autoregressive PDE forecasting by decoupling spatial details from recurrent modal dynamics.
CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.
Isotropic Fourier Neural Operators enforce spatial symmetries in Fourier layers, improving PDE-solving performance while reducing parameters by up to 16x in 2D and 96x in 3D.
Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
WHNO using Walsh-Hadamard transforms outperforms Fourier Neural Operators on PDEs with discontinuous coefficients, and optimal WHNO-FNO ensembles cut mean-squared error by 35-40 percent.
DGPFM stacks GP-based linear and nonlinear transformations in function space via kernel integrals and inducing-point variational learning for function-on-function regression.
WLNO augments LNO with a parallel Haar wavelet branch and learnable gate to capture multi-scale spatial features, outperforming LNO on five PDE benchmarks especially those with sharp structures.
U-HNO uses adaptive per-point routing in a U-shaped hybrid architecture to achieve state-of-the-art accuracy on PDE benchmarks with sharp localized features.
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.
Low-Rank Spatial Attention unifies global mixing in neural operators with standard Transformer components and reduces error by over 17%.
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or SSM approaches.
EP-FNO, a residual Fourier neural operator with an invariant mass/energy projection, reduces long-time rollout error versus standard FNO on three 2D Hamiltonian soliton benchmarks.
citing papers explorer
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GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems
GAIA introduces a geometry-adaptive integral autoencoder that unifies forward, boundary-value, and inverse PDE operator learning on arbitrary domains via geometry tokens and cross-attention.
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Temperature Field Reconstruction of Tungsten Monoblock Divertor on EAST using Physics-aware Neural Operator Transformer
PNOT combines graph attention on boundary heat flux with a physics-aware neural operator and gradient-constrained loss to reconstruct divertor temperature fields for real-time fusion control.
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HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems
HAMNO introduces adaptive gating between local and global operators in a hierarchical setup, with PI-HAMNO adding PDE residual constraints, demonstrating better performance on Allen-Cahn, Cahn-Hilliard, and Swift-Hohenberg equations.
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Discovering Physical Directions in Weight Space: Composing Neural PDE Experts
Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.
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Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators
A latent Structured Spectral Propagator enables stable autoregressive PDE forecasting by decoupling spatial details from recurrent modal dynamics.
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CATO: Charted Attention for Neural PDE Operators
CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.
-
Isotropic Fourier Neural Operators
Isotropic Fourier Neural Operators enforce spatial symmetries in Fourier layers, improving PDE-solving performance while reducing parameters by up to 16x in 2D and 96x in 3D.
-
Hybrid Fourier Neural Operator-Lattice Boltzmann Method
Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
-
Walsh-Hadamard Neural Operators for Solving PDEs with Discontinuous Coefficients
WHNO using Walsh-Hadamard transforms outperforms Fourier Neural Operators on PDEs with discontinuous coefficients, and optimal WHNO-FNO ensembles cut mean-squared error by 35-40 percent.
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Deep Gaussian Processes for Functional Maps
DGPFM stacks GP-based linear and nonlinear transformations in function space via kernel integrals and inducing-point variational learning for function-on-function regression.
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WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations
WLNO augments LNO with a parallel Haar wavelet branch and learnable gate to capture multi-scale spatial features, outperforming LNO on five PDE benchmarks especially those with sharp structures.
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U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics
U-HNO uses adaptive per-point routing in a U-shaped hybrid architecture to achieve state-of-the-art accuracy on PDE benchmarks with sharp localized features.
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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.
-
Simple yet Effective: Low-Rank Spatial Attention for Neural Operators
Low-Rank Spatial Attention unifies global mixing in neural operators with standard Transformer components and reduces error by over 17%.
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Deep Learning for Subspace Regression
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
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Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or SSM approaches.
-
Structure-Informed Neural Operators for Long-Time Prediction of Parametric Hamiltonian PDEs
EP-FNO, a residual Fourier neural operator with an invariant mass/energy projection, reduces long-time rollout error versus standard FNO on three 2D Hamiltonian soliton benchmarks.
- RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics
- A neural operator framework for data-driven discovery of stability and receptivity in physical systems