{"total":15,"items":[{"citing_arxiv_id":"2606.03838","ref_index":131,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Uncovering Turbulent Dynamics in Stenotic Flows from 4D-flow MRI Measurements via Resolvent Analysis and Data Assimilation","primary_cat":"physics.flu-dyn","submitted_at":"2026-06-02T16:19:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A hybrid MRI-PINN-resolvent framework extracts mean fields from stenotic flow measurements and identifies stationary eigenmodes in the recirculation bubble plus broadband pseudo-resonance in the shear layer.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.01179","ref_index":13,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Physics-Informed Deep Learning for Entropy Prediction in Heterogeneous Systems: Thermodynamic and Information-Theoretic Case Studies","primary_cat":"cs.LG","submitted_at":"2026-05-31T11:38:52+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"A PIDL framework with shared-encoder architecture and Softplus constraints solves CSTR ODEs and financial inverse Fokker-Planck PDEs, claiming zero Second-Law violations and over 90% accuracy with 30% training data.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.25949","ref_index":46,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers","primary_cat":"cs.LG","submitted_at":"2026-05-25T15:27:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"WaveLiT combines wavelet tokenization, linear attention, and multiscale pyramids to produce parameter-efficient neural PDE solvers that match much larger models on TheWell benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.25057","ref_index":67,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Random Neural Network Expressivity for Non-Linear Partial Differential Equations","primary_cat":"math.NA","submitted_at":"2026-05-24T13:08:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.12368","ref_index":42,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions","primary_cat":"cs.LG","submitted_at":"2026-05-12T16:36:12+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"MetaColloc meta-learns a universal set of neural basis functions offline so that new PDEs can be solved at test time with a single linear solve instead of per-equation neural-network optimization.","context_count":1,"top_context_role":"background","top_context_polarity":"support","context_text":"1 Physics-Informed Neural Networks Physics-Informed Neural Networks (PINNs) [34] encode PDE constraints directly into a loss function. They solve equations using gradient descent. Many studies improve this baseline. Researchers balance loss terms during training [40, 19, 24], analyze gradients with Neural Tangent Kernels [41], and enforce causality [42]. Other works design new optimization techniques [7, 39, 47, 4] or propose new architectures like Kolmogorov-Arnold Networks [25]. To solve high-frequency problems, some 2 methods use random Fourier features [41] or dynamic meshes [20]. However, these methods remain very sensitive to hyper-parameters. All these approaches share a core limitation. They perform per-instance optimization."},{"citing_arxiv_id":"2605.11316","ref_index":60,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Error whitening: Why Gauss-Newton outperforms Newton","primary_cat":"cs.LG","submitted_at":"2026-05-11T23:07:25+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Gauss-Newton descent whitens errors by projecting Newton directions or gradients onto the tangent space, replacing JJ^T with the identity and removing parameterization distortions that affect Newton descent.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"[58] Sifan Wang, Ananyae Kumar Bhartari, Bowen Li, and Paris Perdikaris. Gradient alignment in physics-informed neural networks: A second-order optimization perspective.arXiv preprint arXiv:2502.00604, 2025. [59] Sifan Wang, Bowen Li, Yuhan Chen, and Paris Perdikaris. Piratenets: Physics-informed deep learning with residual adaptive networks.Journal of Machine Learning Research, 25(402):1-51, 2024. [60] Sifan Wang, Shyam Sankaran, and Paris Perdikaris. Respecting causality is all you need for training physics-informed neural networks.arXiv preprint arXiv:2203.07404, 2022. [61] Sifan Wang, Shyam Sankaran, Hanwen Wang, and Paris Perdikaris. An expert's guide to training physics-informed neural networks.arXiv preprint arXiv:2308.08468, 2023. [62] Sifan Wang, Yujun Teng, and Paris Perdikaris."},{"citing_arxiv_id":"2605.10136","ref_index":42,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks","primary_cat":"cs.LG","submitted_at":"2026-05-11T07:46:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"PINN gradient conflicts occur in distinct regimes (persistent directional, magnitude imbalance, or low/transient) that each favor different fixes, with per-loss adapters plus reweighting improving results on forward and multi-physics problems.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T. Barron, and Ren Ng. Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains. InNeurIPS, 2020. [41] Sifan Wang, Yujun Teng, and Paris Perdikaris. Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks.SIAM J. Sci. Comput., 43(5):A3055-A3081, 2021. [42] Sifan Wang, Shyam Sankaran, and Paris Perdikaris. Respecting causality is all you need for training physics-informed neural networks.CoRR, abs/2203.07404, 2022. [43] Sifan Wang, Xinling Yu, and Paris Perdikaris. When and why PINNs fail to train: A neural tangent kernel perspective.J. Comput. Phys., 449:110768, 2022. [44] Sifan Wang, Shyam Sankaran, Hanwen Wang, and Paris Perdikaris."},{"citing_arxiv_id":"2605.09495","ref_index":175,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Enabling Structure-Only Initialization and Out-of-Distribution Generalization in GNN-based Molecular Dynamics Simulators","primary_cat":"physics.chem-ph","submitted_at":"2026-05-10T12:00:21+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"GNN-based MD simulators achieve stable structure-only initialization and reliable OOD generalization through inference-time physics optimization and a GNN barostat on elastic network compression tasks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.04708","ref_index":12,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems","primary_cat":"cs.LG","submitted_at":"2026-05-06T09:59:05+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A differentiable chemistry solver is added to PINNs along with parameterized network architecture and stiffness-tailored residual weighting to solve initial/boundary value problems, inverse parameter identification, and parameterized PDEs for hydrogen combustion.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.03542","ref_index":64,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks","primary_cat":"math.NA","submitted_at":"2026-05-05T09:14:38+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":"2605.02681","ref_index":53,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"The Design and Composition of Structural Causal Decision Processes","primary_cat":"cs.CE","submitted_at":"2026-05-04T15:00:32+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"SCDMs and SCDPs are composable causal decision models that are strictly more expressive than POMDPs by allowing endogenous memory formation and variable discounting without rational belief assumptions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.15645","ref_index":67,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs","primary_cat":"cs.LG","submitted_at":"2026-04-17T02:42:08+00:00","verdict":"ACCEPT","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"PINNACLE is an open-source framework for classical and quantum PINNs that supplies modular training methods and benchmarks showing high sensitivity to architecture choices plus parameter-efficiency gains in some hybrid quantum regimes.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.13723","ref_index":21,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Physics-Informed Neural Networks for Solving Derivative-Constrained PDEs","primary_cat":"cs.LG","submitted_at":"2026-04-15T10:57:22+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"DC-PINNs embed derivative constraints into PINN optimization using a minimum principle and adaptive balancing, reducing violations and improving fidelity on heat, finance, and fluid benchmarks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2603.12676","ref_index":54,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs","primary_cat":"cs.LG","submitted_at":"2026-03-13T05:46:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"DLDMF disentangles latent dynamics for parameterized PDEs by feeding parameters into a latent embedding that initializes a parameter-conditioned Neural ODE, then uses dynamic manifold fusion with a shared decoder to reconstruct spatiotemporal fields for better generalization and extrapolation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2602.02779","ref_index":7,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Comparison of Trefftz-Based PINNs and Standard PINNs Focusing on Structure Preservation","primary_cat":"math.NA","submitted_at":"2026-02-02T20:34:51+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Trefftz-PINNs preserve the global topology of magnetic field lines and velocity streamlines more reliably than standard PINNs even when mean squared errors are matched.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}