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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23 Pith papers cite this work. Polarity classification is still indexing.
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HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.
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.
McMg is a learned phase-space multi-channel multigrid preconditioner that maps residuals to corrections for heterogeneous Helmholtz equations and shows fewer iterations than classical and neural baselines in tests.
HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
PPDNO decomposes DtN maps into an FFT-computed geometry-independent principal part and a DeepONet-learned residual, improving accuracy over direct neural baselines on Laplace and Helmholtz problems.
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.
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.
Spatio-Temporal MeanFlow adapts MeanFlow to PDEs by replacing the generative velocity field with the physical operator and extending the integral constraint to the spatio-temporal domain, yielding a unified solver for time-dependent and stationary equations with improved accuracy and generalization.
DynaDiff uses weight-graph diffusion with a functional consistency loss and dynamics-informed prompting to generate adapted predictors, reporting 10.78% average accuracy gains over baselines while amortizing adaptation cost offline.
SPAMoE reduces average MAE by 44.4% on ten OpenFWI sub-datasets via a spectral-preserving DINO encoder plus frequency-routed MoE of FNO, MNO and LNO experts.
IKNO replaces first-order kernel integrals in neural operators with infinite-order versions that have efficient closed-form approximations and reports SOTA accuracy on time-dependent and time-independent benchmarks.
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.
DW-Net improves the accuracy versus computational cost Pareto front over standard U-Nets for 2D and 3D multi-scale flow benchmarks by stacking multiple waves while keeping training settings identical.
PerFlow decouples observation conditioning from physics enforcement in rectified flows using constraint-preserving projections and invariance guarantees for fast, physics-consistent reconstruction of spatiotemporal dynamics.
Multi-scale wavelet transformers learn operator dynamics of chaotic systems in the wavelet domain, yielding lower errors and higher spectral fidelity on benchmarks and ERA5 climate data.
DIANO builds coarse-grid latent spaces for fluid dynamics data via neural operator encoding and decoding while integrating a differentiable PDE solver directly in the latent space for end-to-end physics-constrained training.
A linear estimator for the Schrödinger evolution operator is introduced that enforces weak unitarity, supplies uniform prediction error bounds and time-extrapolation bounds, and reports up to 100x lower relative error than FNO and DeepONet on hydrogen, ion-trap, and optical-lattice Hamiltonians.
AFNO learns continuous-time dynamics in latent space via flow matching for time-dependent PDEs to reduce error accumulation in long-horizon forecasts.
MENO restores multi-scale structure in neural-operator PDE surrogates via one-step improved MeanFlow, claiming up to 2× better power-spectrum accuracy and up to 14× faster inference than DDIM enhancement.
Empirical benchmarks indicate CViT-based PINOs with adapted PINN mitigations can match or exceed data-driven neural operators on parametric PDE tasks.
PhysicsFormer applies a lightweight Transformer PINN with pseudo-sequential representations to convection, Burgers, lid-driven cavity, and inverse Navier-Stokes problems, reporting near-zero error in parameter identification and flow reconstruction from sparse noisy data.
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.
-
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.
-
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.
-
McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation
McMg is a learned phase-space multi-channel multigrid preconditioner that maps residuals to corrections for heterogeneous Helmholtz equations and shows fewer iterations than classical and neural baselines in tests.
-
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
-
Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps
PPDNO decomposes DtN maps into an FFT-computed geometry-independent principal part and a DeepONet-learned residual, improving accuracy over direct neural baselines on Laplace and Helmholtz problems.
-
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.
-
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.
-
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.
-
Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow
Spatio-Temporal MeanFlow adapts MeanFlow to PDEs by replacing the generative velocity field with the physical operator and extending the integral constraint to the spatio-temporal domain, yielding a unified solver for time-dependent and stationary equations with improved accuracy and generalization.
-
Generative Adaptation of Dynamics to Environmental Shifts via Weight-space Diffusion
DynaDiff uses weight-graph diffusion with a functional consistency loss and dynamics-informed prompting to generate adapted predictors, reporting 10.78% average accuracy gains over baselines while amortizing adaptation cost offline.
-
SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion
SPAMoE reduces average MAE by 44.4% on ten OpenFWI sub-datasets via a spectral-preserving DINO encoder plus frequency-routed MoE of FNO, MNO and LNO experts.
-
IKNO: Infinite-order Kernel Neural Operators
IKNO replaces first-order kernel integrals in neural operators with infinite-order versions that have efficient closed-form approximations and reports SOTA accuracy on time-dependent and time-independent benchmarks.
-
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.
-
Deep Wave Network for Modeling Multi-Scale Physical Dynamics
DW-Net improves the accuracy versus computational cost Pareto front over standard U-Nets for 2D and 3D multi-scale flow benchmarks by stacking multiple waves while keeping training settings identical.
-
PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics
PerFlow decouples observation conditioning from physics enforcement in rectified flows using constraint-preserving projections and invariance guarantees for fast, physics-consistent reconstruction of spatiotemporal dynamics.
-
Multi-Scale Wavelet Transformers for Operator Learning of Dynamical Systems
Multi-scale wavelet transformers learn operator dynamics of chaotic systems in the wavelet domain, yielding lower errors and higher spectral fidelity on benchmarks and ERA5 climate data.
-
Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling
DIANO builds coarse-grid latent spaces for fluid dynamics data via neural operator encoding and decoding while integrating a differentiable PDE solver directly in the latent space for end-to-end physics-constrained training.
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Operator Learning for Schr\"{o}dinger Equation: Unitarity, Error Bounds, and Time Generalization
A linear estimator for the Schrödinger evolution operator is introduced that enforces weak unitarity, supplies uniform prediction error bounds and time-extrapolation bounds, and reports up to 100x lower relative error than FNO and DeepONet on hydrogen, ion-trap, and optical-lattice Hamiltonians.
-
Autoregression-Free Neural Operators for Time-Dependent PDEs
AFNO learns continuous-time dynamics in latent space via flow matching for time-dependent PDEs to reduce error accumulation in long-horizon forecasts.
-
MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems
MENO restores multi-scale structure in neural-operator PDE surrogates via one-step improved MeanFlow, claiming up to 2× better power-spectrum accuracy and up to 14× faster inference than DDIM enhancement.
-
On the training of physics-informed neural operators for solving parametric partial differential equations
Empirical benchmarks indicate CViT-based PINOs with adapted PINN mitigations can match or exceed data-driven neural operators on parametric PDE tasks.
-
A Simple but Efficient Transformer-Based Physics-Informed Neural Network for Incompressible Navier--Stokes Equations
PhysicsFormer applies a lightweight Transformer PINN with pseudo-sequential representations to convection, Burgers, lid-driven cavity, and inverse Navier-Stokes problems, reporting near-zero error in parameter identification and flow reconstruction from sparse noisy data.