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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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
21 Pith papers cite this work, alongside 2,447 external citations. Polarity classification is still indexing.
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cs.LG 11 physics.flu-dyn 3 physics.comp-ph 2 cs.CE 1 gr-qc 1 math.NA 1 physics.chem-ph 1 physics.plasm-ph 1years
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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.
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.
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.
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.
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.
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.
Neural operators progressively forget domain geometry with depth due to Markovian layers and global mixing; a geometry memory injection mechanism mitigates this forgetting.
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
A quantum ensemble method reduces operator inference to linear complexity and supplies distribution-free uncertainty bounds for high-dimensional dynamical systems.
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.
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.
LASER trains a reinforcement learning policy inside a latent dynamics model to choose sensor placements that improve reconstruction of continuum fields under sparsity.
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.
jNO introduces a unified JAX tracing system for data-driven and physics-informed neural operator training that compiles domains, residuals, losses, and diagnostics into one pipeline.
A replay-based continual learning strategy for physics-informed neural operators mitigates catastrophic forgetting on prior physical problems while enabling efficient adaptation to new data using only physical constraints.
DeepONet surrogate model accurately predicts wave-induced radiation stress and wave heights in steady-state simulations as a replacement for the SWAN numerical model.
A critical review of AI surrogate models for multiscale combustion that compares supervised, unsupervised, and physics-guided methods, identifies transferability and consistency challenges, and outlines future opportunities.
citing papers explorer
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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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
Conformalized Quantum DeepONet Ensembles for Scalable Operator Learning with Distribution-Free Uncertainty
A quantum ensemble method reduces operator inference to linear complexity and supplies distribution-free uncertainty bounds for high-dimensional dynamical systems.
-
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.
-
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.
-
LASER: Learning Active Sensing for Continuum Field Reconstruction
LASER trains a reinforcement learning policy inside a latent dynamics model to choose sensor placements that improve reconstruction of continuum fields under sparsity.
-
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.
-
jNO: A JAX Library for Neural Operator and Foundation Model Training
jNO introduces a unified JAX tracing system for data-driven and physics-informed neural operator training that compiles domains, residuals, losses, and diagnostics into one pipeline.
-
Replay-Based Continual Learning for Physics-Informed Neural Operators
A replay-based continual learning strategy for physics-informed neural operators mitigates catastrophic forgetting on prior physical problems while enabling efficient adaptation to new data using only physical constraints.
-
Operator Learning for Surrogate Modeling of Wave-Induced Forces from Sea Surface Waves
DeepONet surrogate model accurately predicts wave-induced radiation stress and wave heights in steady-state simulations as a replacement for the SWAN numerical model.
-
AI-Powered Surrogate Modelling for Multiscale Combustion: A Critical Review and Opportunities
A critical review of AI surrogate models for multiscale combustion that compares supervised, unsupervised, and physics-guided methods, identifies transferability and consistency challenges, and outlines future opportunities.