{"total":171,"items":[{"citing_arxiv_id":"2605.23712","ref_index":22,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach","primary_cat":"cs.CE","submitted_at":"2026-05-22T14:56:05+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"A language model-based operator learning method reconstructs flow fields from under 10% sparse measurements on vortex street, US temperature, blood flow, and turbulent jet benchmarks with competitive accuracy.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.23282","ref_index":77,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring","primary_cat":"eess.IV","submitted_at":"2026-05-22T06:50:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"DGNO parameterizes integral kernels with discontinuous Galerkin elements for heterogeneous defocus deblurring in pathology images and reports superior performance over prior methods.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.23156","ref_index":14,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Any-Dimensional Invariant Universality","primary_cat":"cs.LG","submitted_at":"2026-05-22T02:07:27+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.22663","ref_index":22,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Therm-FM: Foundation Model is ALL YOU NEED for 3D-ICs Thermal Simulation","primary_cat":"cs.CE","submitted_at":"2026-05-21T16:03:48+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.22338","ref_index":28,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction","primary_cat":"cs.LG","submitted_at":"2026-05-21T11:24:48+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A generative solver separates data-driven prior learning from inference-time enforcement of conservation laws using martingale-regularized score matching and physics-informed sampling for stable field reconstruction.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.22182","ref_index":4,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"IKNO: Infinite-order Kernel Neural Operators","primary_cat":"cs.LG","submitted_at":"2026-05-21T08:52:36+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"IKNO replaces first-order kernel integrals in neural operators with infinite-order versions that have efficient closed-form approximations and reports SOTA accuracy on time-dependent and time-independent benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.21348","ref_index":6,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Data-Efficient Neural Operator Training via Physics-Based Active Learning","primary_cat":"cs.LG","submitted_at":"2026-05-20T16:13:53+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.20780","ref_index":8,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment","primary_cat":"cs.LG","submitted_at":"2026-05-20T06:22:44+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"REPA-P aligns intermediate representations in diffusion models with physical states using first-principles PDE residuals to accelerate convergence and boost out-of-distribution robustness on PDE tasks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.20532","ref_index":7,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Hybrid Edge-HPC Systems for Low-Latency Data-Driven Inference","primary_cat":"cs.DC","submitted_at":"2026-05-19T22:09:29+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"RBF is a hybrid edge-HPC architecture that decouples low-latency edge inference using surrogate models from asynchronous HPC-driven model updates for simulation-bounded cyber-physical systems.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.19867","ref_index":34,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning","primary_cat":"math.NA","submitted_at":"2026-05-19T13:58:31+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The Neural Green's Operator matches exact coarse-solve iteration counts in two-level preconditioners for diffusion and advection-diffusion problems when inputs are integrated against the output basis.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.19823","ref_index":2,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions","primary_cat":"cs.LG","submitted_at":"2026-05-19T13:17:59+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.19589","ref_index":65,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments","primary_cat":"cs.LG","submitted_at":"2026-05-19T09:31:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.19104","ref_index":19,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots","primary_cat":"cs.RO","submitted_at":"2026-05-18T20:44:41+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Develops four neural operator architectures to create generalizable surrogate models for tendon-driven continuum robot configurations across varying designs using simulation data.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.20250","ref_index":23,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Physics-informed convolutional neural networks for fluid flow through porous media","primary_cat":"cs.LG","submitted_at":"2026-05-18T08:02:28+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A physics-informed CNN predicts pore-scale velocity fields from geometry and serves as a warm-start to accelerate Lattice-Boltzmann solvers in over 90% of tested cases.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16818","ref_index":26,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Observation-Aligned Mask Priors for Learning Physical Dynamics from Authentic Occlusions","primary_cat":"cs.CV","submitted_at":"2026-05-16T05:23:49+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A framework pretrained on authentic binary occlusion masks uses guided sampling and intersection-based partitioning to train diffusion models on incomplete physical observations without zero-query regions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16573","ref_index":47,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Wavelet Flow Matching for Multi-Scale Physics Emulation","primary_cat":"cs.LG","submitted_at":"2026-05-15T19:24:31+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Wavelet Flow Matching emulates multi-scale PDE-governed systems by transporting velocities directly in a hierarchical wavelet representation via U-Net, yielding improved long-horizon stability and spectral accuracy on fluid benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16078","ref_index":9,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"A numerical study into neural network surrogate model performance for uncertainty propagation","primary_cat":"stat.ML","submitted_at":"2026-05-15T15:39:52+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":3.0,"formal_verification":"none","one_line_summary":"Numerical study comparing feedforward NN and DeepONet with data-driven and physics-informed losses on stochastic heat equation, highlighting larger errors at distribution tails due to extrapolation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15754","ref_index":8,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs","primary_cat":"physics.comp-ph","submitted_at":"2026-05-15T09:15:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A spatiotemporally decoupled physics-informed Stone-Weierstrass neural operator for stable long-time prediction of time-dependent parametric PDEs.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15418","ref_index":80,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"A General Differentiable Ray-Wave Framework for Hybrid Refractive-Diffractive System Modeling and Optimization","primary_cat":"physics.optics","submitted_at":"2026-05-14T21:04:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A plug-and-play differentiable model bridging ray and wave optics for hybrid systems that enables end-to-end optimization of planar and conformal diffractive elements.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15407","ref_index":17,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Amortized Energy-Based Bayesian Inference","primary_cat":"math.NA","submitted_at":"2026-05-14T20:45:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Presents a likelihood-free transport map learned by minimizing an averaged energy-distance objective to amortize Bayesian inference for inverse problems, including PDE-constrained cases with neural operator representations.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.14546","ref_index":1,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Discovering Physical Directions in Weight Space: Composing Neural PDE Experts","primary_cat":"cs.LG","submitted_at":"2026-05-14T08:25:16+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.14332","ref_index":51,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems","primary_cat":"math.OC","submitted_at":"2026-05-14T03:55:39+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"PI-SONet trains a single structure-preserving operator network to deliver sub-second approximations to Pontryagin Maximum Principle solutions for parameterized multi-agent optimal control problems.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.13834","ref_index":6,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Topology-Preserving Neural Operator Learning via Hodge Decomposition","primary_cat":"cs.LG","submitted_at":"2026-05-13T17:56:23+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.13761","ref_index":15,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations","primary_cat":"cs.LG","submitted_at":"2026-05-13T16:41:14+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.12965","ref_index":12,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics","primary_cat":"cs.LG","submitted_at":"2026-05-13T04:00:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"U-HNO uses adaptive per-point routing in a U-shaped hybrid architecture to achieve state-of-the-art accuracy on PDE benchmarks with sharp localized features.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.12343","ref_index":15,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale","primary_cat":"cs.LG","submitted_at":"2026-05-12T16:20:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Local neural operators on 3x3x3 patches, composed via Schwarz iteration, solve large-scale nonlinear elasticity on arbitrary geometries without domain-specific retraining.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"less like task-specific predictors and more like reusable computational building blocks. 2 Related Work Neural operators for parametric PDEs.Operator learning has emerged as a central paradigm for scientific machine learning, aiming to approximate mappings between infinite-dimensional function spaces rather than finite-dimensional input-output pairs. Early architectures such as DeepONet [14] and the Fourier Neural Operator (FNO) [15] demonstrated that neural networks can learn solution operators for families of parametric PDEs, enabling fast inference after training. Subsequent work developed a broader theory of neural operators, including universal approximation and discretization- invariance results [11], as well as physics-informed variants that incorporate PDE residuals or physical"},{"citing_arxiv_id":"2605.12025","ref_index":8,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Approximation Theory of Laplacian-Based Neural Operators for Reaction-Diffusion System","primary_cat":"cs.LG","submitted_at":"2026-05-12T12:13:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Laplacian eigenfunction-based neural operators approximate the solution operator of the generalized Gierer-Meinhardt reaction-diffusion system with error bounds that imply only polynomial growth in parameters as accuracy improves.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.11691","ref_index":11,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Compositional Neural Operators for Multi-Dimensional Fluid Dynamics","primary_cat":"cs.LG","submitted_at":"2026-05-12T07:48:03+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Compositional Neural Operators decompose multi-dimensional fluid PDEs into a library of pretrained elementary physics blocks assembled via an aggregator that minimizes data and physics residuals.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"with these neural solvers is their limited ability to handle discretization effectively as well as their dependency on system configuration. Other continuous frameworks like neural operators [9] and DeepONet [10] can learn mappings between function spaces by approximating operators instead of data distribution. DeepONet [10] employs a dual network design to map infinite- dimensional functions, while the Fourier Neural Operator (FNO) [11] leverages the fast Fourier transform to achieve discretization invariance. Some extensions, like GINO [12], were proposed to adapt it to complex geometries, while other work, such as PI-DeepONet [13] and PFNO [14], were trying to enhance the performance of neural operators, but they still face challenges related to limited generalization abilities."},{"citing_arxiv_id":"2605.11280","ref_index":5,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Discovery of Interpretable Surrogates via Agentic AI: Application to Gravitational Waves","primary_cat":"gr-qc","submitted_at":"2026-05-11T22:09:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"GWAgent agentic workflow produces analytic surrogates for eccentric BBH waveforms with 6.9e-4 median mismatch and 8.4x speedup, outperforming baselines, and infers eccentricity for GW200129.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"M¨ uller, SchNet - A deep learning architecture for molecules and materials.The Journal of chemical physics148 24, 241722 (2017),https://api.semanticscholar.org/CorpusID: 4897444. [4] Z.-Y. Li,et al., Fourier Neural Operator for Parametric Partial Differential Equations.ArXivabs/2010.08895(2020),https: //api.semanticscholar.org/CorpusID:224705257. [5] M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.J. Comput. Phys.378, 686-707 (2019), https://api.semanticscholar.org/CorpusID:57379996. [6] A. S. Mancini, D. Piras, J. Alsing, B. Joachimi, M. P. Hobson, COSMOPOWER: emulating cosmological power spectra for"},{"citing_arxiv_id":"2605.11111","ref_index":37,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"ShardTensor: Domain Parallelism for Scientific Machine Learning","primary_cat":"cs.DC","submitted_at":"2026-05-11T18:20:10+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"ShardTensor is a domain-parallelism system for SciML that enables flexible scaling of extreme-resolution spatial datasets by removing the constraint of batch size one per device.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"namic range in model outputs for surrogate simulations, and computationally reduced precision offers only modest memory savings - typically a factor of 2x when using half precision. •Spatial Downsamplingis perhaps the most obvious and simplest path towards reducing the memory cost of intermediate activations in training a scientific ML model. Many problems, especially neural operators [31]-[33], [37], [38] are trained very successfully at reduced spatial sampling, though some evidence [39], [40] indicates higher spatial resolution during training can in fact lead to better convergence of operator models. Other problems, especially imaging problems, inherently suffer lack of information when downsampling and can not be trivially downsampled without more sophisticated algorithmic im-"},{"citing_arxiv_id":"2605.10792","ref_index":99,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Implicit Neural Optimal Transport via Fixed-Point Optimization","primary_cat":"math.OC","submitted_at":"2026-05-11T16:22:06+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.10645","ref_index":84,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"GenMed: A Pairwise Generative Reformulation of Medical Diagnostic Tasks","primary_cat":"cs.CV","submitted_at":"2026-05-11T14:32:09+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"GenMed uses diffusion models to capture P(X,Y) for medical tasks and performs inference via gradient-based test-time optimization, supporting arbitrary observation combinations without retraining.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"686-707, 2019. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0021999118307125 [83] N. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stu- art, and A. Anandkumar, \"Neural operator: Learning maps between function spaces with applications to pdes,\"Journal of Machine Learning Research, vol. 24, no. 89, pp. 1-97, 2023. [84] Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, \"Fourier neural operator for parametric partial differential equations,\" 2021. [Online]. Available: https://arxiv.org/abs/2010.08895 [85] B. Raoni 'c, R. Molinaro, T. De Ryck, and G. E. Karniadakis, \"Convolu- tional neural operators for robust and accurate learning of pdes,\"arXiv"},{"citing_arxiv_id":"2605.10451","ref_index":12,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs","primary_cat":"cs.LG","submitted_at":"2026-05-11T12:20:57+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"ABLE learns a spatially adaptive Parseval frame from data via an ancillary density to replace fixed bases in spectral neural operators for PDEs.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"and not necessarily translation-invariant kernels with inherently endowed nonlinearity. We demonstrate the effectiveness of ABLE on several challenging PDE benchmarks, including Burgers', Darcy, and Navier-Stokes equations, with consistent improvements in regimes exhibiting strong multiscale and localized phenomena. 2 Related Work Fixed-basis Spectral Neural Operators.The Fourier Neural Operator (FNO) [ 12] represents the current state of practice for learning PDE solution operators. By assuming translation invariance, FNO diagonalises convolution kernels in the Fourier domain, achieving O(NlogN) complexity via the Fast Fourier Transform. The Fourier basis is orthonormal, self-dual, and satisfies Parseval's identity, which guarantees energy preservation."},{"citing_arxiv_id":"2605.10159","ref_index":6,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"jNO: A JAX Library for Neural Operator and Foundation Model Training","primary_cat":"cs.LG","submitted_at":"2026-05-11T08:05:54+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.10154","ref_index":5,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators","primary_cat":"cs.LG","submitted_at":"2026-05-11T08:00:42+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A latent Structured Spectral Propagator enables stable autoregressive PDE forecasting by decoupling spatial details from recurrent modal dynamics.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"temporal and spatial derivative orders. The operatorF may contain both linear and nonlinear differential terms. The equation is equipped with initial conditions∂j tu(x, 0) = uj(x)for j= 0,...,s t−1, and boundary conditionsB[u](x,t) =g(x,t)on∂Ω×(0,Tmax]. Neural operators as finite-time propagators.Let U andV be Banach spaces of input and solution functions. Operator learning [5, 25-30] aims to approximate a ground-truth operatorG :U →Vby a neural operatorˆG :U →V. For time-dependent PDEs, this operator is typically learned through finite-time prediction between solution snapshots or short temporal windows [21]. Long-horizon forecasting then requires recursively composing the learned propagator to approximate the global evolution induced byG."},{"citing_arxiv_id":"2605.09870","ref_index":200,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions","primary_cat":"cs.LG","submitted_at":"2026-05-11T01:54:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"SVAR-FM uses simulator clamping to produce interventional distributions and flow matching to identify time series causal structures, with an error bound that predicts sign reversal of causal effects below a simulator accuracy threshold.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.09360","ref_index":17,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Your Simulation Runs but Solves the Wrong Physics: PDE-Grounded Intent Verification for LLM-Generated Multiphysics Simulation Code","primary_cat":"cs.LG","submitted_at":"2026-05-10T06:19:47+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A new Intent Fidelity Score and refinement loop verify that LLM-generated simulation code matches the intended PDEs, improving performance on a 220-case benchmark where execution alone fails to ensure correctness.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"[15] Jae Ryong Lee and Han Young Yoon. Multi-physics simulation of nuclear reactor core by coupled simulation using cupid/master.International Journal of Heat and Mass Transfer, 115: 1020-1032, 2017. [16] Mengnan Li, Jason Miller, Zachary Prince, Alexander Lindsay, and Cody Permann. Moosenger- a domain-specific ai agent for the moose ecosystem.arXiv preprint arXiv:2603.04756, 2026. [17] Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations.CoRR, abs/2010.08895, 2020. URL https://arxiv.org/abs/2010. 08895. [18] Yulong Liu and Chloé Arson. Physics-informed neural network surrogate modeling of pressur-"},{"citing_arxiv_id":"2605.09275","ref_index":32,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"DiffATS: Diffusion in Aligned Tensor Space","primary_cat":"cs.LG","submitted_at":"2026-05-10T02:53:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"DiffATS trains diffusion models directly on aligned Tucker tensor primitives that are proven to be homeomorphisms, delivering efficient unconditional and conditional generation across images, videos, and PDE data with high compression.","context_count":1,"top_context_role":"baseline","top_context_polarity":"baseline","context_text":"tensor (or matrix) to its TGP (or MGP) and trains DMs in the aligned primitive space. During inference, the generated primitive is mapped back to the original data space through the multilinear reconstruction map. We conduct experiments on images, videos, and PDE solutions, with representative samples shown in Fig. 1. Across all settings, DiffATS outperforms DCTDiff [39], SDIFT [4], FNO [32], and average pooling (AvgPool) in generation quality, despite using compression ratios that match or exceed those of the baselines. 2 n2 n1 n3 ∈ℝn1×n2×n3 Input tensor1 U1 U2 U3 U2 U3 Tucker decomposition2 ˜U2 ˜U3 n1×r2×r3 Tucker Grassmannian primitive 3 n1×r2×r3 n2×r2 n2×r2 n3×r3n3×r3 Generative training 4 Diffusion model ∇logpθ Train Sampling5"},{"citing_arxiv_id":"2605.09016","ref_index":17,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"CATO: Charted Attention for Neural PDE Operators","primary_cat":"cs.AI","submitted_at":"2026-05-09T15:55:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Early deep learning approaches, such as Physics-Informed Neural Networks (PINNs) [1], incorporate PDE residuals directly into the loss, enabling unsupervised training but often suffering from training instability and spectral bias. Operator learning offers an alternative paradigm: learn a mapping between function spaces directly from paired data. DeepONet [ 21] first demonstrated this idea. FNO [ 17] introduced global convolution in the spectral domain, achieving resolution invariance. Subsequent works improved expressivity and efficiency: U-FNO [28] and U-NO [23] added multi-scale paths; Geo-FNO [16] learned deformations to handle irregular geometries; GINO [18] extended to 3D point clouds; LSM [29] leveraged latent spectral representations; WMT [8] used"},{"citing_arxiv_id":"2605.08935","ref_index":97,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecasting","primary_cat":"cs.AI","submitted_at":"2026-05-09T13:12:33+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.08915","ref_index":59,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow","primary_cat":"cs.LG","submitted_at":"2026-05-09T12:29:10+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Spatio-Temporal MeanFlow adapts MeanFlow to PDEs by replacing the generative velocity field with the physical operator and extending the integral constraint to the spatio-temporal domain, yielding a unified solver for time-dependent and stationary equations with improved accuracy and generalization.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.08856","ref_index":6,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Controlling Transient Amplification Improves Long-horizon Rollouts","primary_cat":"cs.LG","submitted_at":"2026-05-09T10:10:30+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Commutativity regularization mitigates transient error amplification in autoregressive neural simulators by penalizing non-normality and non-commutativity of Jacobians, yielding stable long-horizon rollouts.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.08539","ref_index":56,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Continuity Laws for Sequential Models","primary_cat":"cs.LG","submitted_at":"2026-05-08T22:55:45+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"S4 models exhibit stable time-continuity unlike sensitive S6 models, with task continuity predicting performance and enabling temporal subsampling for better efficiency.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.07738","ref_index":7,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics","primary_cat":"physics.comp-ph","submitted_at":"2026-05-08T13:46:28+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"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.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Anandkumar, Neural operator: Learning maps between function spaces, arXiv preprint arXiv:2108.08481 (2023). doi:10.48550/arXiv.2108.08481. [6] L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, Nat. Mach. Intell. 3 (2021) 218-229. doi:10.1038/s42256-021-00302-5. [7] Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, A. Anandkumar, Fourier neural operator for parametric partial differential equations, arXiv preprint arXiv:2010.08895 (2020). doi:https://doi.org/10.48550/arXiv. 2010.08895. [8] L. Lu, X. Meng, S. Cai, Z. Mao, S. Goswami, Z. Zhang, G. E. Karniadakis, A comprehensive and fair comparison of two"},{"citing_arxiv_id":"2605.07522","ref_index":75,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"WeatherSyn: An Instruction Tuning MLLM For Weather Forecasting Report Generation","primary_cat":"cs.CL","submitted_at":"2026-05-08T09:53:33+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"WeatherSyn is the first instruction-tuned MLLM for weather forecasting report generation, outperforming closed-source models on a new dataset of 31 US cities across 8 weather aspects.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.07485","ref_index":15,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Excluding the Target Domain Improves Extrapolation: Deconfounded Hierarchical Physics Constraints","primary_cat":"cs.LG","submitted_at":"2026-05-08T09:27:21+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Deconfounded Hierarchical Gate with counterfactual estimation and hierarchical constraints achieves 46% better RMSE on out-of-distribution battery temperature extrapolation, with excluding target data from pretraining outperforming inclusion.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"0 ◦C, we achieve RMSE = 0.215, a 46% improvement over the unconst rained baseline (Pure CFM RMSE: 0.397), demonstrating that physic s-guided generation with causal deconfounding substantially outperforms unconstr ained flow matching. 2 Related Work Neural Operators and Their V ariants. Neural Operators learn mappings between function spaces [6], with FNO [15] parameterizing the integral kerne l in Fourier space for efficient PDE solving. V ariants include GNO [16], DeepONet [19], WNO [31] , U-FNO [33], and VINO [9]. PINO [17] combines FNO with PDE residual losses, but its \"hie rarchy\" refers to multi-scale resolu- tion, not the priority ordering of physical laws addressed h ere; we apply constraints in a Coarse-to-"},{"citing_arxiv_id":"2605.07444","ref_index":14,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Accelerated and data-efficient flow prediction in stirred tanks via physics-informed learning","primary_cat":"cs.CE","submitted_at":"2026-05-08T08:49:40+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Physics-informed constraints on implicit neural representations yield more accurate and stable predictions of stirred-tank flows than purely data-driven models when training data is scarce, with diminishing returns at larger dataset sizes.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.06929","ref_index":27,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Physics-Based Flow Matching for Full-Field Prediction of Silicon Photonic Devices","primary_cat":"physics.optics","submitted_at":"2026-05-07T20:40:24+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"PIC-Flow applies conditional flow matching with a real-valued U-Net and interface-masked Helmholtz residual loss to predict electromagnetic fields in photonic devices, generalizing to held-out device classes beyond its training set.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.05862","ref_index":8,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Do Neural Operators Forget Geometry? The Forgetting Hypothesis in Deep Operator Learning","primary_cat":"cs.LG","submitted_at":"2026-05-07T08:31:33+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Neural operators progressively forget domain geometry with depth due to Markovian layers and global mixing; a geometry memory injection mechanism mitigates this forgetting.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.05299","ref_index":51,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Universal Neural Propagator: Learning Time Evolution in Many-Body Quantum Systems","primary_cat":"quant-ph","submitted_at":"2026-05-06T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The Universal Neural Propagator is a single neural model trained self-supervised to predict time evolution in driven quantum many-body systems across arbitrary protocols and initial states.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"parameter vector, but a function of time. Neural oper- ators are precisely designed for this setting: rather than learning maps between finite-dimensional spaces, they learn mappings between function spaces [49, 50]. In par- ticular, the FNO architecture is a natural choice, because it parameterizes the operator through learnable convolu- tion in the frequency domain [51]. FNO-based models have been successfully applied across a range of scientific problems, including many-body quantum systems [24- 26, 52]. Concretely, the driving protocolH(t) is first lifted into a higher-dimensional latent representation. Each FNO layer then transforms this temporal representation to the frequency domain, applies a learnable spectral convolu-"}],"limit":50,"offset":0}