001 Learning features from Newton's algorithm: a way to accelerate nonlinear parametrized PDE solvers arXiv Paper Rémy Vallot et al. Yesterday 002 Neural Network Approximation of Solutions to Fractional Parabolic Partial Differential Equations arXiv Paper Jae-Hwan Choi, Hyojae Lim et al. Yesterday 003 Reflected diffusion, no-flux continuity equations and confined Lagrangian flows in bounded domains arXiv Paper Rama Cont Yesterday 004 Adaptive Mamba Neural Operators arXiv Paper Zeyuan Song, Zheyu Jiang Jul 20 005 Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning arXiv Paper Ronald Katende Jul 17 006 Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limits arXiv Paper Trevor Teolis, Maarten V. de Hoop Jul 16 007 Approximation of solutions of parameter-dependent problems by residual neural networks arXiv Paper Ana Carpio Jul 15 008 Wasserstein gradient flows for Coulomb discrepancies arXiv Paper Antonin Chodron de Courcel, Matthew Rosenzweig Jul 14 009 A Formalization of the Mean-Field Derivation of the Vlasov Equation arXiv Paper Joseph K. Miller Jul 9 010 Avoiding unsafe sets when training with Langevin Dynamics arXiv Paper Adam M. Oberman Jul 8 011 LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems arXiv Paper Zihao Guo, Xin Li et al. Jul 4 012 Local Fokker--Planck Geometry for Score Estimation: Heat-Ball Mean-Value Representations and Exact High-Dimensional Sampling arXiv Paper Jiayao Bai et al. Jun 26 013 Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domains arXiv Paper Emmanuel E. Oguadimma, Victory C. Obieke et al. Jun 25 014 The Fractal Neural Operator: Overcoming Spectral Bias in Chaotic Attractors via Prime-Harmonic Weierstrass Encodings arXiv Paper Kanishk Awadhiya Jun 22 015 Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime arXiv Paper Weinan Wang, Bowen Gang et al. Jun 7 016 Quantifying Uncertainty In Wide Two-Layer Neural Networks: On The Law Of The Limiting Fluctuation Process arXiv Paper Arnaud Descours, A. Guillin et al. Jun 4 017 Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network arXiv Paper Antonin Chodron de Courcel Jun 3 018 Phase transitions for the noisy transformer model in arbitrary dimension arXiv Paper Kyunghoo Mun et al. Jun 3 019 Is Zero-Shot Super-Resolution Possible in Operator Learning? arXiv Paper Unique Subedi, Ambuj Tewari May 29 020 Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs arXiv Paper Chenyang An, Xiaoqian Xu May 20 021 Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions arXiv Paper Haohao Dang, Sebastian Schmidt et al. May 19 022 Propagation of Chaos in Contextual Flow Maps arXiv Paper Shi Chen, Zheng Lin et al. May 16 023 Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows arXiv Paper Alex Massucco, Leonardo Del Grande et al. May 15 024 Unified generalization analysis for physics informed neural networks arXiv Paper Yuka Hashimoto, Tomoharu Iwata May 13 025 Generalization Error Bounds for Picard-Type Operator Learning in Nonlinear Parabolic PDEs arXiv Paper K. Taniguchi, Sho Sonoda May 11 026 Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regime arXiv Paper A. Alcalde, Leon Bungert et al. May 11 027 Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow arXiv Paper L'enaic Chizat, Maria Colombo et al. May 10 028 Kinetic theory for Transformers and the lost-in-the-middle phenomenon arXiv Paper M. Duerinckx, Borjan Geshkovski et al. May 9 029 Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers arXiv Paper Noboru Isobe, Daisuke Inoue et al. May 8 030 Grokability in five inequalities arXiv Paper P. Ivanisvili, Xinyuan Xie May 6 031 Neural Discovery of Strichartz Extremizers arXiv Paper Nicol'as Valenzuela, R. Freire et al. May 6 032 Provable imitation learning for control of instability in partially-observed Vlasov--Poisson equations arXiv Paper Xiaofan Xia, Qin Li et al. May 6 033 QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems arXiv Paper Chenyang An, Qihao Ye et al. Apr 27 034 Partition-of-Unity Gaussian Kolmogorov-Arnold Networks arXiv Paper A. Noorizadegan Apr 26 035 A Topology fixated Shape Gradient Framework for Non Simple Boundary Extraction for CIE Lab color images with Repulsive Energy arXiv Paper Shafeequdheen Palengara et al. Apr 25 036 Scale-Parameter Selection in Gaussian Kolmogorov-Arnold Networks arXiv Paper A. Noorizadegan, Sifan Wang Apr 23 037 DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splitting arXiv Paper Chih-Kang Huang, L. Gagnon et al. Apr 20 038 Duality for the Adversarial Total Variation arXiv Paper Leon Bungert, Lucas Schmitt Apr 20 039 Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches arXiv Paper Yixuan Wang Apr 18 040 Phase transitions in Doi-Onsager, Noisy Transformer, and other multimodal models arXiv Paper Kyunghoo Mun et al. Apr 17 041 Lectures on AI for Mathematics arXiv Paper Xiaoyan Chen Apr 13 042 On the continuum limit of t-SNE for data visualization arXiv Paper Jeff Calder, Zhonggan Huang et al. Apr 13 043 Score Shocks: The Burgers Equation Structure of Diffusion Generative Models arXiv Paper Krisanu Sarkar Apr 8 044 General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations arXiv Paper G. Ma, Ting Luo et al. Apr 2 045 A Neural Score-Based Particle Method for the Vlasov-Maxwell-Landau System arXiv Paper V. Ilin, Jingwei Hu Mar 26 046 Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning arXiv Paper Salah A. Faroughi, Farinaz Mostajeran et al. Mar 25 047 Double Coupling Architecture and Training Method for Optimization Problems of Differential Algebraic Equations with Parameters arXiv Paper Wenqiang Yang, Wenyuan Wu et al. Mar 24 048 Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations arXiv Paper Sebastien Andre-Sloan, Dibyakanti Kumar et al. Mar 24 049 Regularity of Solutions to Beckmann's Parametric Optimal Transport arXiv Paper Hanno Gottschalk et al. Mar 20 050 Two-Time-Scale Learning Dynamics: A Population View of Neural Network Training arXiv Paper G. Borghi, Hyesung Im et al. Mar 20 051 Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control arXiv Paper Samuel N. Cohen, Filippo de Feo et al. Mar 19 052 Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees arXiv Paper Amartya Mukherjee, Maxwell Fitzsimmons et al. Mar 19 053 Mathematical Modeling of Cancer-Bacterial Therapy: Analysis and Numerical Simulation via Physics-Informed Neural Networks arXiv Paper Ayoub Farkane, David Lassounon Mar 18 054 Physics-informed fine-tuning of foundation models for partial differential equations arXiv Paper V. Medvedev, Leon Armbruster et al. Mar 16 055 Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium arXiv Paper V. Ilin Mar 16 056 Learning embeddings of non-linear PDEs: the Burgers' equation arXiv Paper Pedro Tarancón-Álvarez et al. Mar 8 057 Partial Differential Equations in the Age of Machine Learning: A Critical Synthesis of Classical, Machine Learning, and Hybrid Methods arXiv Paper M. Nooraiepour, J. Both et al. Mar 8 058 Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs arXiv Paper Akshay Govind Srinivasan et al. Mar 6 059 Quantitative Convergence of Wasserstein Gradient Flows of Kernel Mean Discrepancies arXiv Paper Lénaïc Chizat et al. Mar 2 060 Solving Inverse PDE Problems using Minimization Methods and AI arXiv Paper Noura Al Helwani et al. Mar 2