{"total":16,"items":[{"citing_arxiv_id":"2606.23251","ref_index":29,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids","primary_cat":"cs.CE","submitted_at":"2026-06-22T12:33:55+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Self-attention mechanisms are used to build mesh-preserving neural surrogates that approximate PFEM dynamics for free-surface flows, delivering accurate transient predictions and improved scalability on 2D and 3D benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15793","ref_index":25,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training","primary_cat":"cs.LG","submitted_at":"2026-05-15T09:50:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"AOT-POT adaptively reshapes complex PDE solution operators via input-dependent transformations and parallel stream mixing to enable effective large-scale pre-training, yielding SOTA results on 12 benchmarks with minimal added parameters.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.09523","ref_index":34,"ref_count":2,"confidence":0.9,"is_internal_anchor":false,"paper_title":"HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations","primary_cat":"cs.LG","submitted_at":"2026-05-10T13:14:59+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":8.0,"formal_verification":"none","one_line_summary":"HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.","context_count":1,"top_context_role":"dataset","top_context_polarity":"use_dataset","context_text":"Derivative-informed neural operators (DINO) show that adding derivative information can improve operator and Jacobian approximation in high-dimensional parametric settings, a JCP example of using problem structure to strengthen neural-operator surrogates [37]. Benchmarks such as PDEBench have standardized evaluation across equations, parameters, and initial conditions [38]. Most time-dependent neural-operator benchmarks are Markovian: the learned map is from u(t,·) to u(t+ ∆t,·) . DPDEs break this setup because the same current field can correspond to multiple valid futures. HS-FNO keeps the FNO backbone but changes the domain of the learned evolution from instantaneous fields to lifted history fields. History-aware predictionThe use of history for prediction has a deep mathematical foundation."},{"citing_arxiv_id":"2605.09016","ref_index":14,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"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":"Transformer-Based Neural Operators.Due to the fact that self-attention can be viewed as a learnable nonlocal integral operator, transformers have been an essential stride into neural PDE solving. Specific techniques like the Galerkin Transformer [ 3], which implemented kernels in a linear attention without softmax, and models such as HT-Net [20], OFormer [14], GNOT [10], ONO [31], and FactFormer [15] used hierarchical, linear, orthogonal, or factorized approaches to provide a better trade-off between accurate long-range interaction modeling while maintaining computational efficiency. These approaches showed that attention-based architectures can be successful in learning PDE solution operators. SAOT [ 32] combines Fourier attention for global patterns with Wavelet"},{"citing_arxiv_id":"2605.07375","ref_index":22,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"QuadNorm: Resolution-Robust Normalization for Neural Operators","primary_cat":"cs.LG","submitted_at":"2026-05-08T07:30:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"QuadNorm uses quadrature-based moments instead of uniform averaging in normalization layers, achieving O(h²) consistency across resolutions and better cross-resolution transfer in neural operators.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Neural operators are designed to approximate maps between infinite-dimensional function spaces from finite-dimensional discretizations [ 17, 18, 25, 32]. A defining appeal of this paradigm is discretization invariance: A model trained on one grid should generalize to different resolutions without retraining, a goal that also motivates physics-informed, factorized, and transformer-based operator variants [22, 26, 44, 48]. Accordingly, cross-resolution evaluation, where models are trained on one discretization and evaluated on other discretizations, such as 322 →64 2 or 322 →128 2, is a common generalization setting in neural operators. In practice, however, several components of neural operator architectures are not resolution-invariant. Normalization layers are a critical yet under-examined example."},{"citing_arxiv_id":"2605.00062","ref_index":4,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics","primary_cat":"eess.IV","submitted_at":"2026-04-30T06:43:30+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"RETO achieves relative L2 errors of 0.063 on ShapeNet and 0.089/0.097 on DrivAerML surface pressure/velocity, outperforming Transolver and other baselines.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.25985","ref_index":47,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Learning Neural Operator Surrogates for the Black Hole Accretion Code","primary_cat":"astro-ph.HE","submitted_at":"2026-04-28T17:08:25+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"However, heuristic token pruning and discrete tree formulations often restrict models from acting as true resolution-invariant continuous operators. To maintain AMR-native resolution without the smoothing effects of regular-grid proxies while scaling to massive token sequences, linear attention mechanisms show the greatest potential. By utilizing a Galerkin-style linear attention [46], OFormer [47] avoids the quadratic Softmax(·) memory bottleneck while remaining compatible with disparate input and query grids. Based on these considerations and the failures of hybrid models observed in our preliminary work, we present OFormer as a viable AMR-native model and demonstrate its effectiveness on a custom relativistic jet dataset governed by SRMHD."},{"citing_arxiv_id":"2604.11403","ref_index":11,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions","primary_cat":"cs.CE","submitted_at":"2026-04-13T12:44:04+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Scale-autoregressive modeling (SAR) samples fluid flow distributions hierarchically from coarse to fine resolutions on meshes, achieving lower distributional error and 2-7x faster runtime than diffusion or flow-matching baselines.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2603.21210","ref_index":24,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows","primary_cat":"cs.LG","submitted_at":"2026-03-22T13:08:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"WinDiNet repurposes a 2B-parameter video diffusion model as a differentiable surrogate that generates 112-frame urban wind flow rollouts in under one second and enables direct gradient optimization of building positions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2602.11626","ref_index":27,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning","primary_cat":"cs.LG","submitted_at":"2026-02-12T06:22:59+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"ArGEnT adds self-, cross-, and hybrid-attention transformers to DeepONet to learn geometry-dependent operators from point-cloud inputs, yielding higher accuracy than standard DeepONet on fluid, solid, and electrochemical benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2602.11229","ref_index":23,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Latent Generative Solvers for Generalizable Long-Term Physics Simulation","primary_cat":"cs.AI","submitted_at":"2026-02-11T15:34:52+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2510.22068","ref_index":5,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Deep Gaussian Processes for Functional Maps","primary_cat":"cs.LG","submitted_at":"2025-10-24T23:05:48+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"DGPFM stacks GP-based linear and nonlinear transformations in function space via kernel integrals and inducing-point variational learning for function-on-function regression.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2510.00233","ref_index":30,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling","primary_cat":"cs.LG","submitted_at":"2025-09-30T19:57:52+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"DIANO builds coarse-grid latent spaces for fluid dynamics data via neural operator encoding and decoding while integrating a differentiable PDE solver directly in the latent space for end-to-end physics-constrained training.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2509.18611","ref_index":35,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Flow marching for a generative PDE foundation model","primary_cat":"cs.LG","submitted_at":"2025-09-23T04:00:41+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Flow Marching jointly samples noise and physical time to learn a velocity field for generative PDE modeling, paired with a latent autoencoder and efficient transformer for large-scale pretraining on 2.5M trajectories.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2509.12344","ref_index":43,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning","primary_cat":"cs.LG","submitted_at":"2025-09-15T18:13:28+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2412.07010","ref_index":48,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems","primary_cat":"cs.LG","submitted_at":"2024-12-09T21:36:42+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"TAE combines Tikhonov regularization with autoencoders and a data randomization strategy to learn forward and inverse surrogates from one sample, with linear error bounds and tests on heat inversion and Navier-Stokes reconstruction.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}