Partial Differential Equations

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  1. Physics-Informed Neural Networks for Discovering Periodic Orbits in the Gravitational Three-Body Problem

    Jul 26, 2026Nikolaos Kollias, Nikolaos MatzakosConventional Physics-Informed Neural NetworksNear-Earth Objects

  2. Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs

    Jul 26, 2026Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma +3Fourier Neural OperatorsNeural Operators

  3. Neural Representation of Minimal Surfaces

    Jul 26, 2026Jiayin Sun, Albert ChernImplicit Neural RepresentationsNeural Fields

  4. Learning Asymptotics with Convergence-Rate Guarantees using Linear Least Squares

    Jul 25, 2026Christos N. EfremAsymptoticsConvergence Analysis

  5. From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models

    Jul 25, 2026Jinshu Huang, Yiming Jiang, Chunlin WuScore-Based Diffusion ModelGenerative

  6. Data-Driven Diffusion Processes on Differential Forms via the Projected Ambient Connection Laplacian

    Jul 25, 2026Alvaro Almeida Gomez, Jorge Duque FrancoGraph LaplaciansStatistical Manifold

  7. PRIMS: Physics-guided Representation for Fluid Identification in Multimodal Sensing

    Jul 24, 2026Hai-Long Nguyen, Trung Thanh Nguyen, Lars Holm +2Multimodal TransformersFluid Dynamics

  8. Latent PDE mapping for efficient physics-informed learning across geometries with limited data

    Jul 24, 2026Ingvild Askim Adde, Mary M. Maleckar, Gabriel BalabanConventional Physics-Informed Neural NetworksPartial Differential Equation Benchmarks

  9. Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

    Jul 24, 2026Zhangyong Liang, Huanhuan GaoNeural Partial Differential Equation SolversRiemannian Optimization

  10. Generalized Neural Operator for Parametric and Boundary-Value Problems

    Jul 24, 2026Ruoyan Li, Yizhou Sun, Wei WangNeural OperatorsBoundary Value Problems

  11. Multilevel Graph Wavelet Compressed Sensing with Scale-Aware Neural Recovery

    Jul 23, 2026Amirhossein Nouranizadeh, Sarang Rajendra Patil, Alan John Varghese +3Discrete Wavelet TransformSparse Recovery

  12. PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

    Jul 22, 2026Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee +3Conventional Physics-Informed Neural NetworksBayesian Quadrature

  13. Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling

    Jul 22, 2026Somesh Pratap Singh, Govinda Anantha Padmanabha, Jingye Tan +4Conventional Physics-Informed Neural NetworksReliable Uncertainty Quantification

  14. PIER: Physics-Informed Environmental Retrieval for Time-Series Modeling

    Jul 22, 2026Shiyuan Luo, Runlong Yu, Chonghao Qiu +6Physics-Informed Machine LearningPhysics-Aware Models

  15. Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations

    Jul 21, 2026Jonathan Gallagher, Roberto GuglielmiModel Predictive ControlLatent Dynamics

  16. Thermodynamics-Informed Input Reparameterization for Neural Prediction of Real-Fluid Thermodynamic Properties in Supercritical Combustion

    Jul 21, 2026Haoze Zhang, Han Li, Ke Xiao +3Combustion ControlThermodynamics

  17. Boundary-Adapted PINNs for Elliptic Dirichlet Problems: H2(Ω)H^2(Ω) A Priori Error Bounds with Application to Mean Escape Time Computation

    Jul 21, 2026Nathanael Tepakbong, Jun Fan, Xiang Zhou +1Boundary Value ProblemsConventional Physics-Informed Neural Networks

  18. Neural network realization of binary refinement iterates via a two-chart atlas selector

    Jul 21, 2026Tsogtgerel GantumurRectified Linear Unit NetworksIterative Refinement

  19. Physics-Informed Super-Resolution of Atmospheric Data

    Jul 21, 2026Chang Xu, Gencer Sumbul, Hugo Porta +3Atmospheric DynamicsPhysics-Informed Machine Learning

  20. Image Editing Models are Numerical Solvers

    Jul 21, 2026Ulysse MizrahiImage EditingClassical Numerical Solver

  21. Adaptive Mamba Neural Operators

    Jul 20, 2026Zeyuan Song, Zheyu JiangNeural OperatorsPartial Differential Equation Benchmarks

  22. FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

    Jul 20, 2026Peiyu Zang, Bosen Xie, Ruoxiang Xu +1Neural Partial Differential Equation SolversPartial Differential Equation Benchmarks

  23. Bridging battery design and health assessment through virtual sensing and physics-informed learning

    Jul 18, 2026Wendi Guo, Søren Byg Vilsen, Daniel Ioan Stroe +4Lithium-Ion BatteriesPhysics-Informed Machine Learning

  24. Spatial Transport of Integration Error in Generative ODEs

    Jul 17, 2026Songheng YinTraining-Inference MismatchClassical Numerical Solver

  25. From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

    Jul 17, 2026Zhiheng Zhou, Mengyao Zhou, Yancheng Chen +3HypergraphsNeural Network

  26. Trainable Spline Representations for Physics-Informed Learning

    Jul 17, 2026Giovanni Canali, Nicola Demo, Gianluigi RozzaConventional Physics-Informed Neural NetworksB-Spline

  27. Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning

    Jul 17, 2026Ronald KatendeVariationalMultiscale Dynamics

  28. Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design

    Jul 17, 2026Xu Yang, Mingyang Yu, Jing Xu +1Conventional Physics-Informed Neural NetworksPhysics-Aware Models

  29. Delocalization of bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin

    Jul 16, 2026Yifan Chen, Xiaoou Cheng, Jonathan Niles-Weed +1Hamiltonian Monte CarloLangevin Dynamics

  30. Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data

    Jul 16, 2026Tatthapong Srikitrungruang, Jaesung LeeDisplacement FieldsConventional Physics-Informed Neural Networks

  31. Adaptive Runge-Kutta Step Control Buys Training Loss, Not Generalization: An Honest Compute-Matched Study of RK-Adam Optimizers

    Jul 16, 2026Akhilesh GogikarAdamLearning Rates

  32. LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

    Jul 15, 2026Nilay Anurag, Shital Adhikari, Taniya Kapoor +1Conventional Physics-Informed Neural NetworksPartial Differential Equations

  33. Approximation of solutions of parameter-dependent problems by residual neural networks

    Jul 15, 2026Ana CarpioNeural-Network ApproximationNeural Network

  34. Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

    Jul 15, 2026Tianchi Yu, Ivan OseledetsPartial Differential EquationsNeural Network

  35. Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems

    Jul 14, 2026Marc Haltmayer, Jaemin Seo, Yuseung Lee +3Multiscale DynamicsBoundary Value Problems

  36. Mechanical Analysis of Parachute Suspension Line Deployment with Binding Tapes Using PINN

    Jul 14, 2026Xiang Zhao, Ronghui Quan, Yaqi Xiao +1Conventional Physics-Informed Neural NetworksFlight Performance

  37. A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground

    Jul 14, 2026Moke Rao, Thomas Hamacher, Smajil HalilovicConventional Physics-Informed Neural NetworksSub-Surface Mineral Prospectivity Modelling

  38. Velocity Scheduled Flow Matching

    Jul 13, 2026Vitalii BondarConditional VelocityClassical Numerical Solver

  39. SPARC-Net: A Spectral, Causality-Aware, and Hard-Constrained Physics-Informed Architecture for Stiff and Shock-Dominated Partial Differential Equations

    Jul 13, 2026Divyavardhan Singh, Dimple Sonone, Hammad Mohammad +1Partial Differential Equation BenchmarksPartial Differential Equations

  40. Multi-dimensional training-priority weighting based on physical information propagation paths: a unified residual-weighting framework for physics-informed neural networks

    Jul 13, 2026Zhangyi Lian, Xinda Dong, Wenxuan Huo +3Conventional Physics-Informed Neural NetworksNeural Network

  41. Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

    Jul 13, 2026Zixuan Shen, Bingchuan Wang, Zhi Wang +1Neural Partial Differential Equation SolversDiscretization

  42. Hierarchical Bayesian Quadrature

    Jul 12, 2026Tim Weiland, Toni Karvonen, Philipp HennigBayesian QuadratureBayesian

  43. Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards

    Jul 11, 2026Pengfei Cai, Utkarsh Utkarsh, Alan Edelman +2Reinforcement Learning With Verifiable RewardPartial Differential Equation Benchmarks

  44. Co4ICF: Co-evolving Physics-Informed Surrogate and RL-based Pulse Optimizer for Inertial Confinement Fusion

    Jul 11, 2026Jiatong Zhao, Tengyue Zhang, Yuhan Wang +2Inertial Confinement FusionPhysics-Informed Machine Learning

  45. A Hyperbolic Neural Closure for M1 Radiation Transfer

    Jul 11, 2026Bongseok Kim, Jiahao Zhang, Johannes Krotz +3JacobianClassical Numerical Solver

  46. The Differential Neural Tangent Kernel and Its Positivity

    Jul 11, 2026Bangti Jin, Longjun WuNeural Tangent KernelConventional Physics-Informed Neural Networks

  47. Residual Physics-Informed Neural Networks for High-Fidelity BLDC Motor Modeling

    Jul 10, 2026Haitham El-HussienyConventional Physics-Informed Neural NetworksDynamics Models

  48. Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling

    Jul 9, 2026Yiwei ZhouDiffusion SamplingClassical Numerical Solver

  49. PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations

    Jul 9, 2026Weiheng Zhong, Jing Bi, Victor Oancea +1Neural Partial Differential Equation SolversNeural Operators

  50. Physics-Informed Machine Learning Under Small-Data Constraints: Lessons from Abrasive Waterjet Milling

    Jul 8, 2026Sarah Grewe, Jörg FrochtePhysics-Informed Machine LearningHyperparameter Optimization

  51. A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems

    Jul 7, 2026Sonal Ankush Chibire, Jenn-Terng Gau, Bo ZhangConventional Physics-Informed Neural NetworksFinite Element Method

  52. Physics-Informed Neural Embeddings of PDE Solution Families

    Jul 7, 2026Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas +3Partial Differential Equation BenchmarksPhase Space

  53. Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension

    Jul 7, 2026Rüdiger KempfProbabilistic Operator LearningPhysics-Informed Machine Learning

  54. Self-Supervised Implicit CEST Reconstruction via Physics-Informed Lorentz Encoding

    Jul 7, 2026Dexuan Li, Yupeng Wu, Chenglong Wang +4Magnetic Resonance Imaging ReconstructionImplicit Neural Representations

  55. Level-Crossing Density as a Mesh-Free High-Frequency Auxiliary Loss for Implicit Neural Representations

    Jul 7, 2026Gunner Levi HoweNeural FieldsDiscretization

  56. Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks

    Jul 6, 2026Tancredi Schettini Gherardini, Edward Hirst, Alexander George StapletonBinary Black Hole MergersConventional Physics-Informed Neural Networks

  57. Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach

    Jul 6, 2026Qian Hu, Bin Fan, Yao Xiao +2Conventional Physics-Informed Neural NetworksAdvection-Reaction-Diffusion

  58. MeGA-MP: Metric Graph Advection Message Passing -- A Physics-Informed Message Passing Operator for Advection-Dominated Metric Graphs

    Jul 6, 2026Janine Strotherm, Luca Hermes, André Artelt +1Message Passing Neural NetworksAdvection-Reaction-Diffusion

  59. PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference

    Jul 6, 2026Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas +1Neural Partial Differential Equation SolversNeural Operators

  60. Physics-Informed Structure Anchoring With Capture-Aware Prototype Calibration for Cross-Environment RF Fingerprinting

    Jul 6, 2026Fengchong Yao, Jianbing Li, Qing Liu +4Radio FrequencyReconfigurable Intelligent Surfaces