{"total":13,"items":[{"citing_arxiv_id":"2606.20916","ref_index":35,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Physics-Guided Dual-Stream Heterogeneous Graph Neural Network for Predicting Full-Field Structural Response of Stiffened Panels","primary_cat":"cs.LG","submitted_at":"2026-06-18T20:12:18+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"DS-HGNN achieves lower RMSE for stress and displacement prediction on stiffened panels than six benchmark GNN models and matches top accuracy with 19-38% fewer training samples.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.18200","ref_index":12,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A Diagnostic Software Suite for Auditing Learned PDE Simulators","primary_cat":"cs.MS","submitted_at":"2026-06-16T17:30:25+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.08448","ref_index":28,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Multiscale Fourier Neural Operator for Inverse Wave Scattering in Highly Oscillatory Media","primary_cat":"math.NA","submitted_at":"2026-06-07T04:36:49+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"MscaleFNO learns mappings from oscillatory media to wavefields for Helmholtz inverse problems and pairs it with diffusion regularization for partial-aperture 2D reconstructions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.00937","ref_index":28,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs","primary_cat":"cs.LG","submitted_at":"2026-05-31T00:49:25+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.25786","ref_index":22,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","primary_cat":"cs.LG","submitted_at":"2026-05-25T12:33:52+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"NPSolver trains neural Poisson solvers label-free by supervising with a small number of preconditioned conjugate gradient steps and adds Boundary-Aware Transolver for mixed boundaries, outperforming baselines on 2D/3D irregular geometries.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.20514","ref_index":47,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data","primary_cat":"cs.LG","submitted_at":"2026-05-19T21:34:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"FLASH-MAX embeds exact Maxwell solutions as neurons in a neural network to reconstruct homogeneous EM fields from sparse data with guaranteed zero PDE residual and proven universal approximation on arbitrary domains.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.13761","ref_index":17,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"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":"2605.12343","ref_index":16,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"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":"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 constraints during training [16]. These methods have significantly expanded the scope of learned PDE solvers, but they typically learn a global operator associated with a prescribed problem family. In particular, the training distribution usually fixes or strongly constrains the domain class, boundary representation, coefficient statistics, and input-output structure. As a result, changing the geometry or"},{"citing_arxiv_id":"2605.07365","ref_index":9,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Solving Convolution-type Integral Equations using Preconditioned Neural Operators","primary_cat":"math.NA","submitted_at":"2026-05-08T07:21:53+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.04307","ref_index":12,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation","primary_cat":"physics.plasm-ph","submitted_at":"2026-05-05T21:14:13+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Specifically, the macroscopic electron particle flux jz(z) and electron energy flux jez(z) are obtained by taking the moments of f1(z,U) as jz(z) = 1 3 r 2 me Z ∞ 0 U f1(z,U)dU, (10) jez(z) = 1 3 r 2 me Z ∞ 0 U 2 f1(z,U)dU. (11) The transport properties such as mobility b(z) and diffusion coefficient D(z) are given by b(z) = −e0 3 r 2 me Z ∞ 0 U NQΣ(U) ∂ ∂U \u0012 f0(z,U) ne(z) \u0013 dU, (12) D(z) = 1 3 r 2 me Z ∞ 0 U NQΣ(U) f0(z,U) ne(z) dU, (13) and the rate coefficient for a k-type inelastic collision process is calculated as kk(z) = 1 ne(z) r 2 me Z ∞ 0 UQ in k (U) f0(z,U)dU. (14) It is well established from experiments and kinetic studies that these properties are nonlocal in conditions when λε ≥ Λ, meaning the electron energy relaxation length equals or ex-"},{"citing_arxiv_id":"2604.26621","ref_index":26,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence","primary_cat":"physics.flu-dyn","submitted_at":"2026-04-29T12:46:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"their outputs depend on the data provided at the specified temporal resolution. The physics-informed neural operator (PINO) improves operator learning models by penalizing deviations from governing equations. Such new machine learning models include, but are not limited to, the physics-informed Deep- ONets [61], physics-informed Transformer [62], and physics-informed Fourier neural operator [26]. PINO has demon- strated the ability to produce highly accurate results across various classical linear and non-linear PDEs [63-68]. Most recently, Jiao et al. [69] evaluated the effectiveness of physics-informed DeepONets in solving both forward and in- verse problems of PDEs on unknown manifolds. Chen et al. [70] presented a novel physics-enhanced neural operator"},{"citing_arxiv_id":"2602.16000","ref_index":27,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Imaging-Derived Coronary Fractional Flow Reserve: Advances in Physics-Based, Machine Learning, and Physics-Informed Methods","primary_cat":"physics.med-ph","submitted_at":"2026-02-17T20:46:25+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"The review summarizes progress toward faster, automated imaging-derived FFR using ML/DL and physics-informed approaches like PINNs and PINOs, while noting challenges in generalizability and the need for clinical validation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2407.17182","ref_index":57,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results","primary_cat":"cs.LG","submitted_at":"2024-07-24T11:34:24+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}