HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
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Optimizing training data via a differentiable SCM yields climate emulators that outperform those trained on six standard ScenarioMIP pathways while using less data and isolating distinct forcing responses.
HAMNO introduces adaptive gating between local and global operators in a hierarchical setup, with PI-HAMNO adding PDE residual constraints, demonstrating better performance on Allen-Cahn, Cahn-Hilliard, and Swift-Hohenberg equations.
Stable size extrapolation in local score models requires the receptive field to cover the quasi-locality range of the Gaussian-smoothed score, formalized via a size-uniform comparison theorem and validated on the new FDLF benchmark.
APIC applies Neural Processes in a two-branch latent model to amortize Kennedy-O'Hagan-style calibration, separating instance-specific parameters from shared structural discrepancies for fast inference on new realizations.
Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.
FLASH-MAX embeds exact Maxwell solutions as neurons in a neural network to reconstruct homogeneous EM fields from sparse data with guaranteed zero PDE residual and proven universal approximation on arbitrary domains.
Shock-centered scaling of DSMC fields in micro-nozzles reveals low-rank density structure, enabling DeepONet surrogates with mean errors reduced to 4.51% on hardest test cases.
Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.
A multilinear operator learned on PCA coefficients maps time-since-ignition inputs to smoke outputs, matching Monte Carlo accuracy with half the model calls and outperforming prior classifiers on holdout data.
Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
DeepOPiraKAN learns parameter-to-spectrum mappings via operator learning and achieves relative errors of O(10^{-6}) to O(10^{-4}) for Kerr black hole quasinormal modes up to n=7 when benchmarked against Leaver's method.
A finite element-guided physics-informed operator learning framework learns solution operators for coupled multiphysics PDEs, enabling discretization-independent predictions on arbitrary domains without labeled data.
Symbolic rational-function networks recover an admissible PDE from noiseless complete measurements and select the regularization-minimizing parameterization within the architecture.
LJ-DSMC with VED collision selection from Chapman-Enskog viscosity matching and DeepONet scattering prediction is validated on shocks, Couette flows, and cylinders with 36% wall-time reduction.
Mamba-based neural operators predict stiff chemical kinetics evolution with high fidelity from initial states on Syngas and GRI-Mech 3.0 mechanisms.
A machine learning model called neural quantum propagator is introduced to efficiently solve non-Markovian quantum dynamics described by HEOM and applied to simulate spectra of the FMO complex.
SS-POD augments standard POD-Galerkin with a spectral-subspace partition and local POD to achieve lower out-of-sample error than either plain POD or pure spectral-Galerkin when only a handful of snapshots are available.
Mosaic is a benchmark suite evaluating 14 differentiable PDE solvers across fluids, structures, and heat transfer, showing large variations in cost and conditioning but similar convergence behavior.
A physics-informed Fourier-wavelet transformer model reports the lowest normalized mean-squared error on cylinder-wake and fluid-structure interaction velocity-field benchmarks compared with spectral, transformer, operator-learning, and PINN baselines.
A data-driven ABL flux parameterization using convolution operators on mean profiles, trained and tested on LES, improves on standard K-profile closures while remaining interpretable.
Neural Operator Processes (NOPs) unify neural-process conditioning with neural-operator decoding for probabilistic full-field prediction from sparse joint input-output observations.
A two-level overlapping Schwarz domain decomposition constructs a hierarchical attention operator that trains faster and approximates the inverse of a discretized 1D diffusion operator more accurately than global low-rank attention while using fewer parameters.
Spectral deflation anchored to a single reference Schur complement reduces CG iterations 55-98% across diffusion, convection-diffusion, and heat-transfer benchmarks by restricting low eigenmodes to varying inactive sets.
citing papers explorer
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Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.
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Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments
ELGIN is a graph-based physics-informed surrogate model that predicts carrier flow and polydisperse particle motion in dental aerosol scenarios, achieving lower tracking errors and 37x speedup versus full OpenFOAM CFD in a preliminary single-case test.