REVIEW 20 cited by
Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries
read the original abstract
Although deep models have been widely explored in solving partial differential equations (PDEs), previous works are primarily limited to data only with up to tens of thousands of mesh points, far from the million-point scale required by industrial simulations that involve complex geometries. In the spirit of advancing neural PDE solvers to real industrial applications, we present Transolver++, a highly parallel and efficient neural solver that can accurately solve PDEs on million-scale geometries. Building upon previous advancements in solving PDEs by learning physical states via Transolver, Transolver++ is further equipped with an extremely optimized parallelism framework and a local adaptive mechanism to efficiently capture eidetic physical states from massive mesh points, successfully tackling the thorny challenges in computation and physics learning when scaling up input mesh size. Transolver++ increases the single-GPU input capacity to million-scale points for the first time and is capable of continuously scaling input size in linear complexity by increasing GPUs. Experimentally, Transolver++ yields 13% relative promotion across six standard PDE benchmarks and achieves over 20% performance gain in million-scale high-fidelity industrial simulations, whose sizes are 100$\times$ larger than previous benchmarks, covering car and 3D aircraft designs.
Forward citations
Cited by 20 Pith papers
-
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.
-
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.
-
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.
-
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 th...
-
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-matchi...
-
Adaptive Mamba Neural Operators
AMO builds adaptive Takenaka-Malmquist bases inside a Mamba state-space model for PDE operator learning, but the claimed equivalence to adaptive Fourier decomposition is not supported by the implemented recurrence.
-
Evaluation of State-of-the-Art Deep Learning Architectures for Aerodynamical Predictions
Benchmarking four neural operators for airfoil and NASA CRM pressure prediction: Transolver best on 2D, BSMS-GNN best on 3D; UPT and GAOT lag.
-
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.
-
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.
-
Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation
Mask-Morph Graph U-Net morphs coarse graph hierarchies with barycentric parameterization and applies masked supervised pretraining to improve generalizability of hierarchical GNN surrogates for crashworthiness predict...
-
Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation
MMGUNet morphs coarse graph hierarchies with feature-aligned barycentric mapping and uses masked pretraining plus frozen edge layers to improve generalisability of mesh surrogates for crashworthiness prediction under ...
-
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.
-
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.
-
Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systems
APT, a mesh-agnostic neural operator fusing graph-based local features with global attention, is claimed to be the first architecture trained directly on adaptive-mesh-refinement simulations and outperforms state-of-t...
-
Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs
A geometry-conditioned Whitney-form neural network that solves a learned discrete conservation law improves out-of-distribution geometry generalization for steady-state PDEs compared with regression-based neural operators.
-
Data-free neural PDE solvers based on Graph Neural Networks and weak forms
A graph-neural-network PDE solver trained on the weak-form force residual — no simulation data — reports residual convergence below 1% on unseen load cases and one modified geometry, with residual-based test-time refinement.
-
LEIA: Learned Environment for Interactive Architected Materials
LEIA is a world model for autoregressive 3D simulation of architected materials under interactive loading, benchmarked on MicroPlate and applied to surrogate-guided de novo design search with finite-element validation.
-
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-sc...
-
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 an...
-
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.