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.
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.
Operator Boosting constructs compact neural-operator PDE surrogates by sequential residual learning with validation-selected shrinkage, yielding 72-95% parameter reduction and accuracy gains on 21 of 30 dataset-architecture pairs.
citing papers explorer
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Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
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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Optimal scenario design for climate emulation
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: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems
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.
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When Do Local Score Models Extrapolate Across Size? A Diagnostic Theory and Benchmark
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.
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APIC: Amortized Physics-Informed Calibration using Neural Processes
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.
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Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
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.
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Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
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 Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows
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.
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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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Enabling Real-Time Training of a Wildfire-to-Smoke Map with Multilinear Operators
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.
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Hybrid Fourier Neural Operator-Lattice Boltzmann Method
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.
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Physics informed operator learning of parameter dependent spectra
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.
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Tackling multiphysics problems via finite element-guided physics-informed operator learning
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.
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Symbolic recovery of PDEs from measurement data
Symbolic rational-function networks recover an admissible PDE from noiseless complete measurements and select the regularization-minimizing parameterization within the architecture.
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Resolving Cryogenic and Hypersonic Rarefied Flows via Deep Learning-Accelerated Lennard-Jones DSMC
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.
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Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kinetics
Mamba-based neural operators predict stiff chemical kinetics evolution with high fidelity from initial states on Syngas and GRI-Mech 3.0 mechanisms.
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Non-markovian neural quantum propagator and its application to the simulation of ultrafast nonlinear spectra
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.
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Mosaic: A Benchmark Suite for Differentiable Physics Solvers
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.
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A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling
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.
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Data-Driven Flux Parameterization for the Atmospheric Boundary Layer
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.
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Neural Operator Processes for Probabilistic Operator Learning under Partial Observations
Neural Operator Processes (NOPs) unify neural-process conditioning with neural-operator decoding for probabilistic full-field prediction from sparse joint input-output observations.
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Hierarchical Attention via Domain Decomposition
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.
-
Online Spectral Deflation for State Constrained Optimal Control Problems
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.
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Operator Boosting Produces Pareto-Efficient PDE Surrogates
Operator Boosting constructs compact neural-operator PDE surrogates by sequential residual learning with validation-selected shrinkage, yielding 72-95% parameter reduction and accuracy gains on 21 of 30 dataset-architecture pairs.
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Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation
Dmsh is a new multi-agent RL framework that formulates mesh generation as an MDP and uses three coordinated agents plus curriculum learning to produce globally conforming all-quad meshes without post-processing.
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Will Accurate Fields Mislead Photonic Design? FromGlobal Accuracy to Port Readout
PaNO neural operator improves port-power readout fidelity in photonic design surrogates over global-field baselines on a 3x3 MMI benchmark.
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Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers
Oscillatory state-space models with PDE-aware spectral bases are introduced as inductive biases for PINNs, yielding improved accuracy and lower memory on forward, inverse, and up to 100D PDE tasks.
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Semigroup Consistency as a Diagnostic for Learned Physics Simulators
Normalized semigroup error is introduced as a diagnostic for learned simulators on 1D heat and Burgers equations; it correlates with rollout degradation (Spearman ρ=0.635) while regularization shows mixed results.
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Data-Efficient Neural Operator Training via Physics-Based Active Learning
Physics-based active learning using PDE residuals improves data efficiency for neural operator training on Burgers and Navier-Stokes equations while adding a physics inductive bias.
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Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions
Cut-DeepONet uses a lifting strategy and an auxiliary network to predict discontinuity locations, enabling a neural operator to learn smooth components in partitioned regions and outperforming prior methods on benchmark PDEs with fewer parameters even on low-resolution data.
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Mechanism Learning: Prototype-Anchored Mechanism Inference for Scientific Forecasting
Mechanism learning infers active local evolution rules via prototype-anchored descriptors to achieve more robust forecasting than direct state prediction on benchmarks like Burgers, WeatherBench2, and Lorenz96.
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Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations
CLDNet is a conditional latent dynamics network surrogate for the shallow water equations that delivers 115x faster 96-hour flood forecasts on irregular metropolitan basins while maintaining usable accuracy against gauge data.
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MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions
MetaColloc meta-learns a universal set of neural basis functions offline so that new PDEs can be solved at test time with a single linear solve instead of per-equation neural-network optimization.
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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.
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NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
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Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics
EquiNO with Q-DEIM creates reduced-order physics-informed surrogates for 3D hyperelastic RVEs that enforce equilibrium and periodicity by construction, achieve 10^3 speedups, and accurately interpolate and extrapolate stresses from few snapshots.
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Do Neural Operators Forget Geometry? The Forgetting Hypothesis in Deep Operator Learning
Neural operators progressively forget domain geometry with depth due to Markovian layers and global mixing; a geometry memory injection mechanism mitigates this forgetting.
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A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
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Conditional Neural Field based Reduced Order Model for Dynamic Ditching Load Prediction
Conditional neural fields combined with LSTM networks predict aircraft ditching loads accurately across heterogeneous spatial discretizations using fewer parameters than convolutional autoencoders.
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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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FlowForge: A Staged Local Rollout Engine for Flow-Field Prediction
FlowForge predicts flow fields via staged local updates with a shared lightweight predictor, matching or exceeding baselines in accuracy while improving robustness to noise and reducing latency.
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Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks
A hybrid FEM and ELM framework for parameter-dependent PDEs derives existence, uniqueness, regularity, and error estimates for inverse problems in photoacoustic tomography.
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AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kinetics
AMORE develops an adaptive multi-output DeepONet with custom losses, partition-of-unity trunk, and invertible/softmax mass-fraction maps to surrogate stiff kinetics on syngas (12 states) and GRI-Mech (24 states).
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MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration
MD-PNOP recasts parameter-induced operator differences as source terms to enable single-configuration neural operator training for extrapolation and acceleration of parametric PDE solvers.
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A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
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Striding Across Reynolds Numbers: Representation Geometry in Neural PDE Generalisation
ConvAE-Relay retrieval via source-trained autoencoder latent matching achieves 38.34+/-0.07% relative L2 error on 10x Re shift using only source database, with U-Net at 34.72% and matching quality identified as dominant factor.
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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.
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Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs
A spatiotemporally decoupled physics-informed Stone-Weierstrass neural operator for stable long-time prediction of time-dependent parametric PDEs.
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From Perception to Autonomous Computational Modeling: A Multi-Agent Approach
A multi-agent LLM framework autonomously completes the full computational mechanics pipeline from a photograph to a code-compliant engineering report on a steel L-bracket example.
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Physics Priors Offer Useful Accuracy-Carbon Trade-Offs in Spatio-Temporal Forecasting
Stronger physics priors in neural networks for spatio-temporal shear flow forecasting yield substantially lower training carbon footprints than weak or no priors, though inference savings are less consistent.