{"total":46,"items":[{"citing_arxiv_id":"2606.28600","ref_index":37,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Neuromorphic Energy-Aware Learning for Adaptive Deep Brain Stimulation","primary_cat":"cs.NE","submitted_at":"2026-06-26T20:48:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Energy-aware RL with a spiking Q-network in a brain circuit model cuts alpha-beta oscillations 45% and stimulation charge 80% vs continuous DBS, then deploys at 0.52 mW on neuromorphic hardware.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.28122","ref_index":40,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs","primary_cat":"cs.CE","submitted_at":"2026-06-26T14:22:30+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"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.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.18186","ref_index":1,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Kolmogorov Regression for Robust Diffusion Policies","primary_cat":"cs.LG","submitted_at":"2026-06-16T17:18:54+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Kolmogorov regression lifts diffusion policies to Cameron-Martin space via PDEs and a precision-weighted loss, yielding convergence guarantees and empirical gains on PushT and manufacturing benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.04366","ref_index":9,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers","primary_cat":"cs.LG","submitted_at":"2026-06-03T02:29:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"MeshTok uses AMR-inspired adaptive multiscale tokenization to improve the efficiency-accuracy trade-off of Transformer models for PDEs over uniform-grid baselines.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.25413","ref_index":25,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","primary_cat":"cs.LG","submitted_at":"2026-05-25T04:28:41+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"AFNO learns continuous-time dynamics in latent space via flow matching for time-dependent PDEs to reduce error accumulation in long-horizon forecasts.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.24651","ref_index":7,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains","primary_cat":"math.NA","submitted_at":"2026-05-23T16:35:08+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"WINO is a weak-form physics-informed neural operator for hyperelasticity on variable domains that uses phi-FEM for geometric flexibility and achieves accuracy below 0.04 while cutting computation time by 50-80% as warm starts for solvers.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.22663","ref_index":23,"ref_count":2,"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":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Therm-FM adapts a pretrained PDE foundation model using thermal-equivalent multi-fidelity training to achieve up to 10.6x lower error in 3D-IC thermal simulation with under 20% of typical training data and strong cross-design transfer.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.22338","ref_index":27,"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":"2605.16594","ref_index":16,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"fPINN-DeepONet: A Physics-Informed Operator Learning Framework for Multi-term Time-fractional Mixed Diffusion-wave Equations","primary_cat":"math.NA","submitted_at":"2026-05-15T19:57:17+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"fPINN-DeepONet integrates an L2 approximation for the Caputo derivative with DeepONet to solve multi-term time-fractional PDEs, including cases with space-time varying orders and noisy data.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15881","ref_index":3,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems","primary_cat":"math.DS","submitted_at":"2026-05-15T11:58:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Symplectic Neural Operators preserve symplectic structure for learning infinite-dimensional Hamiltonian PDEs and deliver improved long-term energy stability in theory and experiments.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15285","ref_index":83,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Universal Approximation of Nonlinear Operators and Their Derivatives","primary_cat":"cs.LG","submitted_at":"2026-05-14T18:00:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.","context_count":1,"top_context_role":"background","top_context_polarity":"unclear","context_text":"Springer-Verlag, Berlin ; London, 1996. [81] Pierre-Louis Lions. Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations.Journal of Functional Analysis, 86(1):1-18, 1989. [82] Pierre-Louis Lions. Mean-Field Games.Cours au Collège de France, 2007. [83] Lu Lu, Pengzhan Jin, and George Em Karniadakis. DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.arXiv preprint arXiv:1910.03193, 2020. [84] Dingcheng Luo, Thomas O'Leary-Roseberry, Peng Chen, and Omar Ghattas. Dimension reduction for derivative- informed operator learning: An analysis of approximation errors."},{"citing_arxiv_id":"2605.12754","ref_index":59,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling","primary_cat":"cs.LG","submitted_at":"2026-05-12T21:07:13+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Constraint-Aware Flow Matching integrates constraint projections into the flow matching training objective to align model dynamics with constrained sampling and reduce distributional shift.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.12301","ref_index":35,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Approximation of Maximally Monotone Operators : A Graph Convergence Perspective","primary_cat":"cs.LG","submitted_at":"2026-05-12T15:53:13+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Any maximally monotone operator can be approximated in local graph convergence by continuous encoder-decoder networks, with structure-preserving versions that retain maximal monotonicity via resolvent parameterizations.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"[33] Samuel Lanthaler, Siddhartha Mishra, and George E Karniadakis. Error estimates for deeponets: A deep learning framework in infinite dimensions.Transactions of Mathematics and its Applications, 6(1):tnac001, 2022. [34] Zichao Long, Yiping Lu, Xianzhong Ma, and Bin Dong. PDE-net: Learning PDEs from data. InInternational Conference on Machine Learning, pages 3208-3216. PMLR, July 2018. [35] Lu Lu, Pengzhan Jin, and George Em Karniadakis. Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv:1910.03193, 2019. [36] Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida. Spectral normalization for generative adversarial networks.arXiv:1802."},{"citing_arxiv_id":"2605.11691","ref_index":10,"ref_count":1,"confidence":0.9,"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":"solutions over time, while physics-informed frameworks (PINNs [5, 6], hPINN [7], PIKANs [8]) enabled unsupervised and semi-supervised recovery of single-instance solutions. The problem 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"},{"citing_arxiv_id":"2605.10792","ref_index":100,"ref_count":1,"confidence":0.9,"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":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A single-network implicit neural optimal transport method that solves the c-transform via proximal fixed-point iteration for stable, non-adversarial training.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.10451","ref_index":13,"ref_count":1,"confidence":0.9,"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":"Fourier neural operator for parametric partial differen- tial equations.arXiv preprint arXiv:2010.08895, 2020. 1, 7, 22 [12] 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. 2, 7 [13] Lu Lu, Pengzhan Jin, and George Em Karniadakis. Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv preprint arXiv:1910.03193, 2019. 1 [14] Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis. A comprehensive and fair comparison of two neural operators"},{"citing_arxiv_id":"2605.10154","ref_index":3,"ref_count":1,"confidence":0.9,"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":"References [1] E. De Bézenac, A. Pajot, and P. Gallinari, \"Deep learning for physical processes: Incorporating prior scientific knowledge,\"Journal of Statistical Mechanics: Theory and Experiment, vol. 2019, no. 12, p. 124009, 2019. [2] S. L. Brunton and J. N. Kutz, \"Machine learning for partial differential equations,\" arXiv preprint arXiv:2303.17078, 2023. [3] L. Lu, P. Jin, and G. E. Karniadakis, \"Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators,\"arXiv preprint arXiv:1910.03193, 2019. [4] N. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, and A. Anandkumar, \"Neural operator: Learning maps between function spaces with"},{"citing_arxiv_id":"2605.09016","ref_index":21,"ref_count":1,"confidence":0.9,"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":"development of learned surrogate solvers that trade a modest loss in accuracy for substantial gains ∗Corresponding author. Preprint. arXiv:2605.09016v1 [cs.AI] 9 May 2026 in computational efficiency. Unlike classical solvers, which typically solve each new PDE instance from scratch, learned surrogates amortize computation costs across many related problem settings. Neural operators [21, 28, 18, 30, 2, 5, 27, 4] have emerged as a promising data-driven alternative by learning mappings between function spaces directly from data. They enable fast inference and generalization across resolutions and have been successfully applied to weather forecasting [22, 13], medical imaging [9, 12], and scientific modeling [11, 33]. Transformer-based approaches"},{"citing_arxiv_id":"2605.08935","ref_index":14,"ref_count":4,"confidence":0.9,"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":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"PnP-Corrector decouples pre-trained physics engines from a correction agent to mitigate reciprocal error amplification in coupled spatiotemporal forecasting, cutting error by 28% on a 300-day ocean-atmosphere task.","context_count":2,"top_context_role":"background","top_context_polarity":"background","context_text":"Axially-Gated Block.The AGB is the fundamental build- ing block of DSLCast, designed to efficiently capture spatial dependencies via axial decomposition. For an input feature mapF in, its computation proceeds as follows: U=GN(F in)(10) Faxial =C 1×k dw (U) +C k×1 dw (U)(11) G=σ(C g(U))(12) F ′ res =F in +G⊙C mix(Faxial)(13) Fout =F ′ res +MLP C(GN(F ′ res))(14) where GN is Group Normalization, C 1×k dw and C k×1 dw are par- allel depthwise-separable axial convolutions, Cg and Cmix are 1×1 convolutions, σ is sigmoid, ⊙ denotes element- wise multiplication, and MLPC is a channel-wise MLP. Differentiable Semi-Lagrangian Advection Block.The DSL-Block introduces an inductive bias for advection. For an input Fin, it first extracts features Ff eat =F AGB(Fin)"},{"citing_arxiv_id":"2605.08915","ref_index":65,"ref_count":1,"confidence":0.9,"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":"2605.08539","ref_index":57,"ref_count":1,"confidence":0.9,"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":"2605.07444","ref_index":15,"ref_count":1,"confidence":0.9,"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":"2605.08232","ref_index":51,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Hierarchical Multi-Fidelity Learning for Predicting Three-Dimensional Flame Wrinkling and Turbulent Burning Velocity","primary_cat":"cs.LG","submitted_at":"2026-05-06T21:38:23+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"MuFiNNs integrates sparse experimental measurements with structured low-fidelity models via hierarchical construction and nonlinear correction to predict 3D flame wrinkling dynamics and turbulent mass burning velocity across fuels, pressures, and turbulence levels.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"nonlinear operators for identifying differential equa- tions based on the universal approximation theorem of operators, arXiv preprint arXiv:1910.03193 (2019). [50] G. Pang, M. D'Elia, M. Parks, G. E. Karniadakis, npinns: Nonlocal physics-informed neural networks for a parametrized nonlocal universal laplacian oper- ator, arXiv preprint arXiv:2004.04276 (2020). [51] D. Mangal, M. Saadat, S. Jamali, Learning a family of rheological constitutive models using neural operators, Journal of Rheology 69 (2) (2025) 55-67.doi:10. 1122/8.0000908. [52] M. Saberi, A. B. Farimani, S. Jamali, Rheoformer: A generative transformer model for simulation of com- plex fluids and flows, arXiv preprint arXiv:2510.01365 (2025).doi:10."},{"citing_arxiv_id":"2605.04474","ref_index":10,"ref_count":3,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Geometry-Aware Neural Optimizer for Shape Optimization and Inversion","primary_cat":"cs.LG","submitted_at":"2026-05-06T03:51:22+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":7.0,"formal_verification":"none","one_line_summary":"GANO is an end-to-end differentiable latent-space optimizer that unifies shape encoding, surrogate prediction, and controllable geometry updates for PDE-governed shape optimization and inversion.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"anism, making the predicted fields explicitly differentiable with respect tozproduced by STABLESDF. Given a slice token tg ∈R D and latent code z∈R d, we first project z to token dimension D, then compute a gate vector and use it to modulate the latent code, after which the modulatedzis injected through a residual update: gg =σ(W 2 SiLU (W1tg))∈(0,1) D,(9) ∆tg =g g ⊙W zz, ˆtg ←t g + ∆tg.(10) Importantly, the injection in Eqs. 9-10 is fully differentiable, enabling the information from optimization target to be passed tozefficiently, i.e.,∂ zJ= ∂J ∂ˆu ∂ˆu ∂z . 3.4. Differentiable Optimization with GANO We performgradient-basedgeometry optimization or inver- sion in latent space by iteratively updating the latent code z, freezing the geometry decoder sθ and the forward sur-"},{"citing_arxiv_id":"2605.00062","ref_index":6,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"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":"2604.20372","ref_index":32,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"AI models of unstable flow exhibit hallucination","primary_cat":"physics.flu-dyn","submitted_at":"2026-04-22T09:12:23+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"AI models of viscous fingering exhibit hallucinations from spectral bias; DeepFingers combines FNO and DeepONet with time-contrast conditioning to predict accurate finger dynamics while preserving mixing metrics.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.18261","ref_index":25,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splitting","primary_cat":"math.AP","submitted_at":"2026-04-20T13:34:50+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A DeepRitzSplit neural operator trained on energy-split variational forms enforces dissipation in phase-field models and outperforms data-driven training in generalization while running faster than Fourier spectral methods on Allen-Cahn and dendritic growth cases.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.16721","ref_index":5,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Late Fusion Neural Operators for Extrapolation Across Parameter Space in Partial Differential Equations","primary_cat":"cs.LG","submitted_at":"2026-04-17T21:52:37+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Late Fusion Neural Operators disentangle state and parameter learning to outperform FNO and CAPE-FNO on advection, Burgers, and reaction-diffusion PDEs with 72% average RMSE reduction in and out of domain.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.11375","ref_index":34,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"DiLO: Decoupling Generative Priors and Neural Operators via Diffusion Latent Optimization for Inverse Problems","primary_cat":"math.NA","submitted_at":"2026-04-13T12:15:48+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"DiLO turns diffusion sampling into deterministic latent optimization to satisfy the manifold consistency requirement for neural operators in inverse problem solving.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.06497","ref_index":85,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Hyperfastrl: Hypernetwork-based reinforcement learning for unified control of parametric chaotic PDEs","primary_cat":"cs.CE","submitted_at":"2026-04-07T21:58:09+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Hypernetworks map a forcing parameter directly to policy weights in an RL framework, enabling unified stabilization of the Kuramoto-Sivashinsky equation across regimes with KAN architectures showing strongest extrapolation.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Deep learning alternatives of the kolmogorov superposition theorem.arXiv preprint arXiv:2410.01990, 2024. [84] Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. InInternational Conference on Learning Representations (ICLR), 2021. [85] Lu Lu, Pengzhan Jin, and George Em Karniadakis. Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.arXiv preprint arXiv:1910.03193, 2019. [86] Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida. 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Q. J. Xu, \"Multi-scale deep neural networks for solving high dimensional PDEs,\" arXiv preprint arXiv:1910.11710, 2019. [155] L. Lu, P. Jin, and G. E. Karniadakis, \"DeepONet: Learning non linear operators for identifying differential equations based on the universal approximation theor em of operators,\" arXiv preprint arXiv:1910.03193, 2019. [156] A. D. Jagtap, K. Kawaguchi, and G. E. Karniadakis, \"Locally ad aptive activation functions with slope recovery for deep and physics-informed neural networks,\" Proceedings of the Royal Society A , vol. 476, no. 2239, p. 20200334, 2020. [157] L. Yang, X. Meng, and G. E. Karniadakis, \"B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data,\" Journal of Computational Physics , vol."},{"citing_arxiv_id":"2510.21804","ref_index":26,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"XRePIT: A deep learning-computational fluid dynamics hybrid framework implemented in OpenFOAM for fast, robust, and scalable unsteady simulations","primary_cat":"cs.LG","submitted_at":"2025-10-21T02:29:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"XRePIT automates residual-guided switching between neural surrogates and OpenFOAM to enable stable, up to 2.91x faster 3D unsteady flow simulations with L2 errors around 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