{"total":12,"items":[{"citing_arxiv_id":"2605.15959","ref_index":5,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective","primary_cat":"cs.LG","submitted_at":"2026-05-15T13:54:03+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Adversarial training improves PINNs by using the discriminator to mitigate spectral bias and stiffness, with a new NTK-based framework providing theoretical grounding and a practical algorithm.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.15254","ref_index":8,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"Curriculum Learning of Physics-Informed Neural Networks based on Spatial Correlation","primary_cat":"cs.LG","submitted_at":"2026-05-14T17:16:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A spatially correlated curriculum learning framework for PINNs using causal weights, low-frequency bridges, and adaptive reweighting to reduce training failures on spatially coupled BVPs.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.09975","ref_index":14,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"Chebyshev Center-Based Direction Selection for Multi-Objective Optimization and Training PINNs","primary_cat":"cs.LG","submitted_at":"2026-05-11T04:30:39+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Update direction selection for PINN training is cast as a Chebyshev-center problem in the dual cone, yielding an efficient dual formulation with nonconvex convergence guarantees and automatic recovery of scale robustness and simultaneous descent.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"their practical success depends critically on how effectively they can be trained [3, 4]. Training PINNs is challenging in practice, as their performance can be highly sensitive to data sampling, model design, and training dynamics [5-7]. These challenges have motivated a broad 1 arXiv:2605.09975v1 [cs.LG] 11 May 2026 literature on sampling strategies [8-10], network design [11-13], and optimization [14, 15]. In this work, we focus on the optimization aspect of PINN training, where multiple loss terms induced by PDE residuals, boundary conditions, and initial conditions must be optimized simultaneously. This multi-loss structure can produce imbalanced gradient magnitudes across objectives, while also creating conflicts among their preferred update directions [16, 17]."},{"citing_arxiv_id":"2605.09288","ref_index":37,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving","primary_cat":"cs.LG","submitted_at":"2026-05-10T03:32:46+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"MC² corrects low-budget Monte Carlo solutions for elliptic PDEs with a single-pass neural network to match the accuracy of 1000× more Monte Carlo samples while outperforming classical and learned baselines.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"DiffusionPDE conditions a diffusion model on sparse observations to jointly recover coeffi- cients and solutions while CoCoGen augments score-based sampling with PDE-residual guidance to improve physical consistency [16, 17]. Transformer-based architectures have further enabled fast inference and some degree of cross-PDE generalization. However, neural solvers face non-convex loss landscapes, spectral bias [37, 29], and distribution-shift fragility, producing biased solutions that degrade on out-of-distribution problems [23, 7]. Hybrid Monte Carlo-Neural Network Methods:Recent work combines neural networks with Monte Carlo solvers to retain unbiasedness while reducing variance. Li et al. [23] train a neural field to approximate the PDE solution, then use it as a control-variate cache during WoS sampling."},{"citing_arxiv_id":"2605.03542","ref_index":67,"ref_count":1,"confidence":0.55,"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":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Proves H^{-1} norm equivalence to expectation over random test functions and introduces SV-PINNs that outperform standard PINNs on eight elliptic problems.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.14562","ref_index":22,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"Material-Agnostic Zero-Shot Thermal Inference for Metal Additive Manufacturing via a Parametric PINN Framework","primary_cat":"cs.LG","submitted_at":"2026-04-16T02:45:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A decoupled parametric PINN with conditional modulation and Rosenthal-derived output scaling achieves zero-shot thermal inference across arbitrary metal alloys in laser powder bed fusion.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.09289","ref_index":3,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"Meta-Learned Basis Adaptation for Parametric Linear PDEs","primary_cat":"cs.LG","submitted_at":"2026-04-10T13:00:03+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A meta-network learns to adapt Gaussian basis geometry across parametric PDE families, which a physics-informed least-squares corrector then refines for improved accuracy.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.05587","ref_index":31,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"ResearchEVO: An End-to-End Framework for Automated Scientific Discovery and Documentation","primary_cat":"cs.AI","submitted_at":"2026-04-07T08:29:41+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"ResearchEVO automates the discover-then-explain cycle by evolving algorithms via fitness-driven LLM co-evolution and generating grounded, anti-hallucination research papers through sentence-level RAG.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2603.12676","ref_index":57,"ref_count":1,"confidence":0.55,"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":"2602.17776","ref_index":14,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method","primary_cat":"math.NA","submitted_at":"2026-02-19T19:17:55+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2512.07755","ref_index":38,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations","primary_cat":"stat.ML","submitted_at":"2025-12-08T17:38:49+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2505.16786","ref_index":55,"ref_count":1,"confidence":0.55,"is_internal_anchor":false,"paper_title":"FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting","primary_cat":"cs.LG","submitted_at":"2025-05-22T15:28:47+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A single-layer architecture called FlowMixer uses constrained matrix operations and a semi-group property to enable depth-agnostic, interpretable spatiotemporal forecasting with direct eigenmode extraction.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}