arXiv AI
Jul 10
LLT: Local Linear Transformer for PDE Operator Learning
arXiv:2607. 07718v1 Announce Type: cross Abstract: Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations.
Learnable Hodge-Laplacian Driven Mixture of Experts for Steady-PDE Surrogates on Coarse Unstructured Meshes
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arXiv Machine Learning
Sep 30
Learning Spectrally Optimised Mesh-Free Discretisations
The paper introduces Spectrally Optimised Neural Discretisations (SpeND), a mesh‑free framework that learns discretisation weights from local stencil geometry on unstructured point clouds. By embedding discrete moment conditions into the network architecture, SpeND guarantees polynomial consistency and allows the weights to be optimised for spectral accuracy over a chosen wavenumber band, using an unsupervised Fourier‑mode loss. The resulting operators are PDE‑agnostic, perform well on Poisson, Burgers, and Navier–Stokes equations, and can reduce wall‑clock time by 3–20× compared to existing mesh‑free methods at the same accuracy.
arXiv Machine Learning
Sep 10
ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows
arXiv:2609.08947v1 Announce Type: cross Abstract: Graph-based surrogate models offer a promising route to accelerate computational fluid dynamics (CFD) simulations on unstructured meshes. However, th...
arXiv Machine Learning
Oct 27
CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes
arXiv:2610.32299v1 Announce Type: cross Abstract: High-fidelity Reynolds-averaged Navier--Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured...
arXiv Statistics ML
Oct 1
Warm-starting PDE solvers with any-dimensional machine learning
arXiv:2609.38916v1 Announce Type: new Abstract: Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and...
arXiv Machine Learning
Aug 21
CarBench: A Comprehensive Benchmark for Neural Surrogates on High-Fidelity 3D Car Aerodynamics
arXiv:2512. 07847v2 Announce Type: replace Abstract: Benchmarking has been the cornerstone of progress in computer vision, natural language processing, and the broader deep learning domain, driving algorithmic innovation through standardized datasets and reproducible evaluation protocols.
arXiv AI
Jul 15
Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
arXiv Machine Learning
Oct 2
Airfoil2Vec: Spectral Geometry-Conditioned Neural Surrogate Models for Airfoil Aerodynamics and a Downforce-Generating CFD Dataset
The paper presents a dataset of roughly 10,000 RANS simulations of steady, incompressible, two‑dimensional subsonic flow around downforce‑generating NACA 4‑digit airfoils, aimed at automotive and motorsport regimes. It explores geometry‑conditioned neural surrogates—comparing neural fields, neural ODEs, MLPs, graph models, and spectral conditioning—and introduces Airfoil2Vec, a spectral geometry encoder that fuses joint contour, camber, and thickness spectra to predict continuous pressure and velocity fields. The surrogate models are evaluated on angle‑of‑attack interpolation, unseen NACA geometries, and non‑NACA airfoils, achieving accurate aerodynamic predictions with orders‑of‑magnitude speedups over traditional CFD.
arXiv Machine Learning
Oct 2
SHIFT-Truck: A High-Fidelity Aerodynamics Dataset and Benchmark for Pickup Trucks
SHIFT‑Truck is the first high‑fidelity aerodynamics dataset and benchmark specifically for pickup trucks, comprising 1,000 Spalart‑Allmaras delayed detached‑eddy simulations of a reference truck geometry morphed across 17 shape parameters. Each simulation uses a ~100‑million‑cell mesh at a Reynolds number of 1.4×10⁷ and provides time‑averaged surface pressure, wall shear stress, volumetric pressure, and velocity data, verified by grid refinement, repeated runs, and wind‑tunnel measurements. The benchmark defines geometry‑grouped splits and evaluates four neural surrogates—DoMINO, GeoTransolver, AB‑UPT, and SMART—on surface and volume tracks, while also introducing controlled distribution shifts in operating point, surface discretization, and vehicle archetype to test generalization.
arXiv Machine Learning
Sep 4
Learnable composition for neural operators
The paper introduces LatentDDM, a neural operator framework that first pretrains on small subdomains and then adapts to new settings by training only a lightweight composition module. Experiments on steady Darcy flow and unsteady airfoil flow show that this approach reduces error by 36‑56% on larger domains and improves 20‑step rollouts, outperforming capacity‑matched full‑domain models. The study highlights co‑designed local pretraining and composition‑level transfer as a promising design principle for physical foundation models.
arXiv Machine Learning
Oct 22
Machine-learned spectral PDE solvers for fluids and plasmas
The paper introduces Weak-form Anchored Rollout for PDEs (WARP), a method that learns PDE solvers by differentiating through multistep rollouts anchored at observed states. WARP addresses noise sensitivity and data consistency issues of sparse regression approaches, producing numerically stable rollouts and improved coefficient recovery across eight fluid and plasma benchmarks, including high‑dimensional turbulent simulations. The method is tailored to systems solvable by spectral Galerkin techniques and outperforms a single‑step weak‑form SINDy baseline in rollout accuracy and statistical metrics.
arXiv Machine Learning
Aug 6
TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning
arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.