REVIEW 15 cited by
Geometry-Informed Neural Operator for Large-Scale 3D PDEs
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
Geometry-Informed Neural Operator for Large-Scale 3D PDEs
read the original abstract
We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and point-cloud representations of the input shape and neural operators based on graph and Fourier architectures to learn the solution operator. The graph neural operator handles irregular grids and transforms them into and from regular latent grids on which Fourier neural operator can be efficiently applied. GINO is discretization-convergent, meaning the trained model can be applied to arbitrary discretization of the continuous domain and it converges to the continuum operator as the discretization is refined. To empirically validate the performance of our method on large-scale simulation, we generate the industry-standard aerodynamics dataset of 3D vehicle geometries with Reynolds numbers as high as five million. For this large-scale 3D fluid simulation, numerical methods are expensive to compute surface pressure. We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points. The cost-accuracy experiments show a $26,000 \times$ speed-up compared to optimized GPU-based computational fluid dynamics (CFD) simulators on computing the drag coefficient. When tested on new combinations of geometries and boundary conditions (inlet velocities), GINO obtains a one-fourth reduction in error rate compared to deep neural network approaches.
Forward citations
Cited by 15 Pith papers
-
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 fi...
-
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,...
-
Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow
Learning only the Stokes boundary correction on an exact free-space core yields a 5–16× more data-efficient operator than black-box DeepONet, with geometric generalization controlled by descriptor invariance and train...
-
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
HS-FNO learns non-Markovian PDE dynamics on history-space states by predicting only the new future slice and using exact shift-append transport, cutting aggregate rollout error from 0.185-0.241 to 0.094 across benchma...
-
Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation
A physics-informed neural operator trained on the PSFD residual, not precomputed data, matches mask scattered-field predictions to MAE ~7e-3 and warms up the iterative solver to reach practical accuracy in ~2 minutes.
-
No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study
No single flow-surrogate architecture transfers from a boundary-driven Stokes film to a self-sustained Kármán wake; time treatment decides the winner and pointwise RMSE ranks the wrong models.
-
Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields
An attention graph neural network trained only against finite-volume residuals predicts coupled 3D thermo-fluid fields without labeled CFD data, matching or beating a supervised baseline on four benchmarks.
-
WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations
WLNO augments LNO with a parallel Haar wavelet branch and learnable gate to capture multi-scale spatial features, outperforming LNO on five PDE benchmarks especially those with sharp structures.
-
Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
Enforcing semi-group consistency on a time-conditioned secant velocity field via Symmetry Rupture improves rollout accuracy and efficiency when learning physical dynamics from discrete observations.
-
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 acce...
-
Physics-Informed Neural Operators for Cardiac Electrophysiology
Physics-informed neural operators accurately reproduce cardiac electrophysiology dynamics over long horizons, generalize to unseen conditions and higher resolutions, and run faster than traditional numerical solvers.
-
A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
-
Transolver: A Fast Transformer Solver for PDEs on General Geometries
Transolver learns intrinsic physical states from discretized meshes by adaptively splitting domains into flexible learnable slices and computing attention over physics-aware tokens, achieving state-of-the-art PDE solv...
-
Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction
LRFIO calibrates inertia operators from HEC-RAS trajectories for native-cell rollout, retaining adaptive complexity only when validated and reporting up to 27,500x speedup with 4.3% max regret.
-
A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction
GTF-Net combines triplane features, AFNO spectral mixing, CNN refinement, and explicit geometric encodings to reduce relative L2 error on vehicle pressure and shear stress prediction versus prior baselines.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.