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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Geometry aware operator transformer as an efficient and accurate neural surrogate for pdes on arbitrary domains.arXiv preprint arXiv:2505.18781
14 Pith papers cite this work. Polarity classification is still indexing.
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MEEC equips point clouds with a discrete exterior calculus that satisfies exact conservation and is differentiable in point positions, allowing a single trained kernel to produce compatible physics on unseen geometries and parameters.
Hybrid exact-learned equivariant operator for incompressible Stokes flow fixes the known core kernel exactly and learns only the boundary correction as a second-kind operator, achieving high accuracy, data efficiency, and cross-shape generalization.
M³ partitions space by physical variation using multi-scale Morton ordering to balance training measures, yielding up to 4.7× lower error on industrial volumetric datasets and outperforming higher-resolution training even after aggressive subsampling.
QuadNorm uses quadrature-based moments instead of uniform averaging in normalization layers, achieving O(h²) consistency across resolutions and better cross-resolution transfer in neural operators.
Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
A graph-based neural operator trained on expert-validated race-car CFD data reaches accuracy levels usable for early-stage interactive aerodynamic design exploration.
Scale-autoregressive modeling (SAR) samples fluid flow distributions hierarchically from coarse to fine resolutions on meshes, achieving lower distributional error and 2-7x faster runtime than diffusion or flow-matching baselines.
Courant is a state-adaptive Perceiver encoder-processor-decoder surrogate trained with L2 loss that yields interpretable, multiscale, locally supported latent features acting as time-evolving spatial basis functions.
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.
Neural and spectral operators can approximate shape-to-solution maps for families of elliptic and parabolic PDEs and BIEs with provable uniform error bounds derived from parametric holomorphy on a reference domain.
A 10.9M-parameter self-supervised model pretrained on 61k CAD meshes achieves R²=0.729 reconstruction and 98.1% top-1 retrieval on held-out data via masked normalized geometry reconstruction and multi-resolution contrastive learning.
GeoPT pre-trains on over one million geometry samples augmented with synthetic dynamics to improve neural physics simulators on fluid and solid mechanics benchmarks while reducing labeled data needs by 20-60% and accelerating convergence by 2x.
ArGEnT adds self-, cross-, and hybrid-attention transformers to DeepONet to learn geometry-dependent operators from point-cloud inputs, yielding higher accuracy than standard DeepONet on fluid, solid, and electrochemical 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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A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds
MEEC equips point clouds with a discrete exterior calculus that satisfies exact conservation and is differentiable in point positions, allowing a single trained kernel to produce compatible physics on unseen geometries and parameters.
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Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow
Hybrid exact-learned equivariant operator for incompressible Stokes flow fixes the known core kernel exactly and learns only the boundary correction as a second-kind operator, achieving high accuracy, data efficiency, and cross-shape generalization.
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M$^3$: Reframing Training Measures for Discretized Physical Simulations
M³ partitions space by physical variation using multi-scale Morton ordering to balance training measures, yielding up to 4.7× lower error on industrial volumetric datasets and outperforming higher-resolution training even after aggressive subsampling.
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QuadNorm: Resolution-Robust Normalization for Neural Operators
QuadNorm uses quadrature-based moments instead of uniform averaging in normalization layers, achieving O(h²) consistency across resolutions and better cross-resolution transfer in neural operators.
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Learning Neural Operator Surrogates for the Black Hole Accretion Code
Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
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Faster by Design: Interactive Aerodynamics via Neural Surrogates Trained on Expert-Validated CFD
A graph-based neural operator trained on expert-validated race-car CFD data reaches accuracy levels usable for early-stage interactive aerodynamic design exploration.
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One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions
Scale-autoregressive modeling (SAR) samples fluid flow distributions hierarchically from coarse to fine resolutions on meshes, achieving lower distributional error and 2-7x faster runtime than diffusion or flow-matching baselines.
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Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition
Courant is a state-adaptive Perceiver encoder-processor-decoder surrogate trained with L2 loss that yields interpretable, multiscale, locally supported latent features acting as time-evolving spatial basis functions.
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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.
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Neural Shape Operator Surrogates -- Expression Rate Bounds
Neural and spectral operators can approximate shape-to-solution maps for families of elliptic and parabolic PDEs and BIEs with provable uniform error bounds derived from parametric holomorphy on a reference domain.
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Shape: A Self-Supervised 3D Geometry Foundation Model for Industrial CAD Analysis
A 10.9M-parameter self-supervised model pretrained on 61k CAD meshes achieves R²=0.729 reconstruction and 98.1% top-1 retrieval on held-out data via masked normalized geometry reconstruction and multi-resolution contrastive learning.
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GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training
GeoPT pre-trains on over one million geometry samples augmented with synthetic dynamics to improve neural physics simulators on fluid and solid mechanics benchmarks while reducing labeled data needs by 20-60% and accelerating convergence by 2x.
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ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning
ArGEnT adds self-, cross-, and hybrid-attention transformers to DeepONet to learn geometry-dependent operators from point-cloud inputs, yielding higher accuracy than standard DeepONet on fluid, solid, and electrochemical benchmarks.