{"total":14,"items":[{"citing_arxiv_id":"2606.18175","ref_index":53,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks","primary_cat":"math.NA","submitted_at":"2026-06-16T17:09:59+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.18032","ref_index":6,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities","primary_cat":"math.NA","submitted_at":"2026-06-16T15:06:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"INI-VPINN is a new weak-form PINN formulation that implicitly enforces Neumann and interface conditions for Poisson and Laplace problems in multi-material domains with geometric singularities.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.12735","ref_index":20,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Physics-Informed Neural Networks and Radial Basis Functions for PDEs with Dirac Delta Sources","primary_cat":"cs.LG","submitted_at":"2026-06-10T22:53:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"RBF-RLS outperforms PINNs on PDEs with Dirac deltas via weak-form integration, delivering consistent forward and inverse solutions for linear transport problems in porous media and rivers.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.10909","ref_index":67,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks","primary_cat":"cs.CE","submitted_at":"2026-06-09T14:20:39+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A coupled LSTM-GNN model reconstructs local elasto-plastic stress fields from macroscopic loading paths on a plate-with-hole microstructure, achieving 1000x speedup and mesh transferability with 1.9% error.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.10686","ref_index":30,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks","primary_cat":"physics.comp-ph","submitted_at":"2026-06-09T10:44:10+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"An adaptive KAN-based PINN framework for axisymmetric pulsar magnetosphere achieves O(1e-6) PDE residual errors, under-20-minute convergence, smaller stellar radii, and a correction to the flux-T-point equation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.26128","ref_index":35,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Physics-guided Convolutional Neural Network for Domain Growth Prediction in Systems with Conserved Kinetics","primary_cat":"cs.LG","submitted_at":"2026-06-09T10:16:50+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"An attention-based physics-guided CNN surrogate is trained to predict long-time microstructural evolution under the Cahn-Hilliard equation for both critical and off-critical mixtures while preserving composition and matching Lifshitz-Slyozov domain growth.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.04736","ref_index":44,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Curvature-aware dynamic precision approach for physics-informed neural networks","primary_cat":"cs.LG","submitted_at":"2026-06-03T11:19:53+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.24106","ref_index":25,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Overcoming \"Physics Shock\" in Earth Observation A Heteroscedastic Uncertainty Framework for PINN-based Flood Inference","primary_cat":"cs.LG","submitted_at":"2026-05-22T18:14:17+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A heteroscedastic uncertainty PINN with warm-start and deep ensembles for SAR flood inference claims 25% IoU gain by relaxing physics constraints in high-noise regions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.22115","ref_index":48,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Physics-Informed Neural Networks with Attention Feature Expansion for Monge-Amp\\`ere Equations","primary_cat":"math.NA","submitted_at":"2026-05-21T07:47:35+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"PINN-AFE uses multi-head attention and input convex networks to solve Monge-Ampère equations with claimed accuracy, efficiency, and extensions to image enhancement and medical registration.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.19856","ref_index":8,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"StableGrad: Backward Scale Control without Batch Normalization","primary_cat":"cs.LG","submitted_at":"2026-05-19T13:49:30+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"StableGrad applies scale correction to weight gradients after backpropagation to enable stable optimization of deep BatchNorm-free networks including PINNs.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.13268","ref_index":31,"ref_count":2,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Physics Guided Generative Optimization for Trotter Suzuki Decomposition","primary_cat":"quant-ph","submitted_at":"2026-05-13T09:48:33+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"P-GONE applies generative ML to optimize Trotter-Suzuki decompositions, reporting up to 19.4x circuit depth reduction at F >= 0.95 versus Qiskit baselines on structured Hamiltonians.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.00308","ref_index":52,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations","primary_cat":"math.NA","submitted_at":"2026-05-01T00:40:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"In:SIAM Journal on Scientific Computing, 43.5 (2021), A3055-A3081.doi:10.1137/20M1318043. eprint:https://doi.org/10.1137/20M1318043. [51] S. Wang, X. Yu, and P. Perdikaris. \"When and why PINNs fail to train: A neural tangent kernel perspective\". In:Journal of Computational Physics, 449, 110768 (2022).doi:https://doi.org/ 10.1016/j.jcp.2021.110768. [52] Z. Wang, X. Meng, X. Jiang, H. Xiang, and G. E. Karniadakis. \"Solution multiplicity and effects of data and eddy viscosity on Navier-Stokes solutions inferred by physics-informed neural networks\". In:arXiv pre-print repository(2023). Referred pre-print version - [v1]. arXiv: 2309 . 06010 [physics.flu-dyn].url:https://arxiv.org/abs/2309.06010. [53] C."},{"citing_arxiv_id":"2603.29184","ref_index":26,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Cell-induced densification and tether formation in fibrous extracellular matrices with biomimetic physics-informed neural networks","primary_cat":"cs.LG","submitted_at":"2026-03-31T02:50:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"https://doi.org/10.1038/s42254-021-00314-5 [25] Krishnapriyan, A.S., Gholami, A., Zhe, S., Kirby, R.M., Mahoney, M.W.: Charac- terizing possible failure modes in physics-informed neural networks. In: Advances in Neural Information Processing Systems, vol. 34, pp. 26548-26560 (2021). https://doi.org/10.48550/arXiv.2109.01050 .https://arxiv.org/abs/2109.01050 [26] Wang, S., Yu, X., Perdikaris, P.: When and why pinns fail to train: A neural tangent kernel perspective. Journal of Computational Physics449, 110768 (2022) https://doi.org/10.1016/j.jcp.2021.110768 [27] Daw, A., Bu, J., Wang, S., Perdikaris, P., Karpatne, A.: Mitigating propagation failures in physics-informed neural networks using retain-resample-release (R3)"},{"citing_arxiv_id":"2410.01990","ref_index":40,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Deep Learning Alternatives of the Kolmogorov Superposition Theorem","primary_cat":"cs.LG","submitted_at":"2024-10-02T19:53:14+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}