arXiv Machine Learning
Aug 12
The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics
arXiv:2608. 10234v1 Announce Type: cross Abstract: Operator learning is a rapidly advancing area of computational science.
Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs
arXiv:2607. 23466v1 Announce Type: new Abstract: Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited.
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arXiv Machine Learning
Aug 3
Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators
arXiv:2607. 28762v1 Announce Type: new Abstract: This work embeds feature interaction modules derived from factorization machines (FMs) into physics-informed neural networks (PINNs) and neural operator learning, to enhance model expressiveness for solution manifolds of parameterized partial differential equations (PDEs).
arXiv AI
Jun 29
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
arXiv:2606. 28122v1 Announce Type: cross Abstract: Neural operators provide deep neural networks for learning mappings between function spaces.
arXiv Machine Learning
Jul 17
Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables
arXiv:2607. 14855v1 Announce Type: cross Abstract: We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations.
arXiv Machine Learning
Aug 24
Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries
The paper introduces a method for selecting the best neural‑operator model during deployment without needing high‑fidelity reference solutions. By using a squared Hilbert‑space loss, the authors show that ranking a finite library of models depends only on the low‑dimensional span of candidate differences, enabling simultaneous scoring of all models with a single anchor‑based linearized response of the governing equation. This shared physical diagnostic accurately recovered over 99.6% of pairwise preferences and 99.0% of optimal checkpoints across diverse Fourier and convolutional operator libraries for fluid, reaction‑diffusion, and wave dynamics, and often outperformed the best individual candidates.
arXiv Machine Learning
Jun 19
Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
arXiv Machine Learning
Jun 16
The Machine Learning Approach to Moment Closure Relations for Plasma: A Review
arXiv:2511. 22486v3 Announce Type: replace-cross Abstract: The requirement for large-scale global simulations of plasma is an ongoing challenge in both space and laboratory plasma physics.
arXiv Machine Learning
Aug 19
Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements
The paper introduces Neptune, a method that uses independent coordinate neural networks to infer parameter fields in multi-physics PDEs from sparse measurements. Neptune can accurately estimate parameters with nonlinear, spatiotemporal variations, outperforming existing techniques by reducing estimation errors by up to two orders of magnitude and improving dynamic response predictions by a factor of ten. It also demonstrates strong physical extrapolation, enabling reliable predictions beyond the training data.
arXiv Machine Learning
Jun 3
Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter
arXiv:2602. 06842v2 Announce Type: replace-cross Abstract: Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate convergence.
arXiv Machine Learning
Sep 18
Hypernetwork-Parameterized Spatially Adaptive Neural Operators for PDE Learning
The paper introduces Hypernetwork-Parameterized Spatially Adaptive Neural Operators (SANO) for learning partial differential equations (PDEs) with spatial heterogeneity. SANO replaces spatially shared parameterization with a continuous field of location-dependent operator parameters, generated by a coordinate-conditioned hypernetwork and interpolated via a Hyper-Neural Element mechanism. Experiments on 1‑, 2‑, and 3‑dimensional PDEs and perforated-domain elliptic benchmarks demonstrate that SANO consistently outperforms existing neural‑operator, hypernetwork‑based, and physics‑informed baselines.
arXiv Machine Learning
Jun 18
TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
arXiv:2601. 20361v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time.
arXiv AI
Jul 29
COMPOL: A Unified Neural Operator Framework for Scalable Multi-Physics Simulations
arXiv:2501. 17296v4 Announce Type: replace-cross Abstract: Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved computational efficiency they often fail to effectively capture intricate correlations inherent in coupled physical processes To address this limitation we introduce COMPOL a novel coupled multiphysics operator learning framework COMPOL extends conventional operator architectures by incorporating sophisticated recurrent and attentionbased aggregation mechanisms effectively modeling interdependencies among interacting physical processes within latent feature spaces Our approach is architectureagnostic and seamlessly integrates into various neural operator frameworks that involve latent space transformations Extensive experiments on diverse benchmarksincluding biological reactiondiffusion systems patternforming chemical reactions multiphase geological flows and thermohydromechanical processes demonstrate that COMPOL consistently achieves superior predictive accuracy compared to stateoftheart methods.