Functional Attention replaces pairwise softmax attention with structured linear operators inspired by geometric functional maps to produce compact, resolution-invariant representations for operator learning.
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Transolver++: An accurate neural solver for pdes on million-scale geometries.arXiv preprint arXiv:2502.02414
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Proposes residual-based physics-informed coarsening in multigrid GNNs to allocate capacity to high-activity regions for more stable solid mechanics surrogates.
Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
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.
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.
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.
ShardTensor is a domain-parallelism system for SciML that enables flexible scaling of extreme-resolution spatial datasets by removing the constraint of batch size one per device.
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.
LoRA adapters enable a 61.47M-parameter aerodynamics Transformer pretrained on four vehicle families to adapt to a held-out fifth family with 20 samples, reaching R²=0.85 and outperforming full fine-tuning and from-scratch training with 3x more data.
DDS-PINN uses localized neural networks plus a unified global loss to model multiscale fluid flows with long-range dependencies, achieving CFD-comparable accuracy on laminar backward-facing step flow with zero data and O(10^-4) error on turbulent flow with only 500 supervision points.
RETO achieves relative L2 errors of 0.063 on ShapeNet and 0.089/0.097 on DrivAerML surface pressure/velocity, outperforming Transolver and other baselines.
citing papers explorer
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Functional Attention: From Pairwise Affinities to Functional Correspondences
Functional Attention replaces pairwise softmax attention with structured linear operators inspired by geometric functional maps to produce compact, resolution-invariant representations for operator learning.
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Physics-Informed Coarsening for Multigrid Graph Neural Surrogates
Proposes residual-based physics-informed coarsening in multigrid GNNs to allocate capacity to high-activity regions for more stable solid mechanics surrogates.
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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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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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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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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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ShardTensor: Domain Parallelism for Scientific Machine Learning
ShardTensor is a domain-parallelism system for SciML that enables flexible scaling of extreme-resolution spatial datasets by removing the constraint of batch size one per device.
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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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Adapting Automotive Aerodynamics Surrogates to New Vehicle Families via Transfer Learning
LoRA adapters enable a 61.47M-parameter aerodynamics Transformer pretrained on four vehicle families to adapt to a held-out fifth family with 20 samples, reaching R²=0.85 and outperforming full fine-tuning and from-scratch training with 3x more data.
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Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies
DDS-PINN uses localized neural networks plus a unified global loss to model multiscale fluid flows with long-range dependencies, achieving CFD-comparable accuracy on laminar backward-facing step flow with zero data and O(10^-4) error on turbulent flow with only 500 supervision points.
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RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics
RETO achieves relative L2 errors of 0.063 on ShapeNet and 0.089/0.097 on DrivAerML surface pressure/velocity, outperforming Transolver and other baselines.
- Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation