Partial Differential Equations

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  1. MENO: Memory-Efficient Neural Operator

    Sep 23, 2026Shengyang Xu, Weijun Zhang, Jun Hu +1Neural Partial Differential Equation Solvers

  2. A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems

    Sep 23, 2026Tianhao Hu, Bangti Jin, Fengru Wang +1Boundary Value ProblemsNeural-Network Approximation

  3. Data-driven discrete-time deep recurrent neural network-based modeling for dissipative systems

    Sep 23, 2026Tuan Luong, Hyungpil MoonConventional Physics-Informed Neural Networks

  4. Learning Physics from an Imperfect Ancestor

    Sep 21, 2026S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas +1Conventional Physics-Informed Neural NetworksPartial Differential Equation Benchmarks

  5. Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers

    Sep 17, 2026Nilo Schwencke, Roland MaierBayesian QuadraturePartial Differential Equation Benchmarks

  6. Towards AI-enhanced control: a numerical technique for trajectory smoothing of a parallel robot for pancreatic surgery

    Sep 17, 2026Iosif Birlescu, Alexandru Pusca, Bogdan Gherman +4Trajectory PredictionClassical Numerical Solver

  7. Stringological sequence prediction III: layered ziplines and a tradeoff between efficiency and expressivity

    Sep 17, 2026Vanessa KosoySequence ModelingModel Complexity

  8. Amortizing Physics-Informed Neural Solvers via Graph Hypernetworks

    Sep 17, 2026Cheng Jing, Abhishek Verma, Kallol Bera +2Conventional Physics-Informed Neural NetworksNeural Solvers

  9. Physical knowledge on historical data matters more than enforcing physical constraints on the forecast

    Sep 17, 2026Etienne Lehembre, Pascal Audigane, Vincent Nguyen +2Conventional Physics-Informed Neural NetworksFundamental Hydrological Principles

  10. PhyRestore: Physics-Structured Latent-Factor Restoration

    Sep 17, 2026Ahmed Shafee, Chayan LahiriSoil Moisture EstimationRestoration

  11. Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Models

    Sep 17, 2026Yufeng Wang, Parivesh Priye, Lu Wei +1Counterfactual ReasoningWorld Models

  12. Fast Learning Rates for Physics-Informed Kernel Methods

    Sep 16, 2026Luc Brogat-Motte, Joachim Bona-Pellissier, Giacomo Meanti +1Physics-Informed Machine LearningKernel Method

  13. M3^3P-R1: Reinforcement Learning for Large Language Model Guided Multi-Modal Motion Planning via MIP Code Generation

    Sep 16, 2026Xingpeng Sun, Zherong Pan, Kai Cheng +3Robot PlanningMixed-Integer Programming

  14. HiLNO: A Hierarchical Latent Neural Operator with Multi-Scale Supervision for PDEs on General Geometries

    Sep 16, 2026Zhicheng Hu, Jiacheng Li, Min YangNeural OperatorsPartial Differential Equation Benchmarks

  15. Timely Activation of Safety Filters via One-Step Reachability Expansion

    Sep 15, 2026Javier BorquezSafety FiltersHamilton-Jacobi Reachability

  16. Lecture notes on Physics Informed Neural Networks, Neural Operators, and their applications

    Sep 15, 2026Alessandro BombiniConventional Physics-Informed Neural NetworksFourier Neural Operators

  17. Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction

    Sep 15, 2026Junyi Liao, Johann Guilleminot, Vahid TarokhLong-Horizon ForecastingNeural Partial Differential Equation Solvers

  18. Physics Informed Random Feature Neural Networks for Solving PDEs

    Sep 14, 2026Chi-An Chen, Chunyang Liao, Ming ZhongPartial Differential EquationsKernel Method

  19. Where to Compute and How to Interact: Operator-Readable Adaptation with Gauge-Aware Transport

    Sep 14, 2026Zixuan Shen, Quanxu Wan, Bingchuan Wang +2Neural OperatorsDiscretization

  20. Single-condition neural solvers encode transferable response spaces for parametric differential equations

    Sep 14, 2026Wenbo Cao, Weiwei ZhangNeural Partial Differential Equation SolversNeural Solvers

  21. Physics Informed Neural Network model for the dynamical study of Abdominal Aortic Aneurysm

    Sep 14, 2026Adrián Robles Arques, Martín Ruiz Fernandez, Javier Sanchis +2Conventional Physics-Informed Neural NetworksComputational Fluid Dynamic

  22. Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems

    Sep 14, 2026Nima NouriComplex NetworksPhysics-Informed Machine Learning

  23. QuPAINT: Physics-Aware Multimodal Reasoning for Quantum Material Characterization

    Sep 14, 2026Sankalp Pandey, Xuan-Bac Nguyen, Hoang-Quan Nguyen +4Materials ScienceMicroscopy

  24. Physics-Informed Conformal Prediction: Embedding PDE Consistency into Distribution-Free Uncertainty Quantification for Neural Operators

    Sep 14, 2026Michael ChinConformal PredictionPartial Differential Equation Benchmarks

  25. Direct Topology Tracking in Continuous Implicit Models

    Sep 14, 2026Guanqun Ma, David Lenz, Kaiyuan Tang +4Implicit Neural RepresentationsTopological Data Analysis

  26. Linearized PINN with pretrained nonlinear layers

    Sep 14, 2026Wenhao Chen, Alexandre M. TartakovskyConventional Physics-Informed Neural NetworksPartial Differential Equation Benchmarks

  27. An explicit solution of the five-expert prediction PDE and the exact optimality set of COMB

    Sep 14, 2026Jeff Calder, Nadejda DrenskaInequalitiesOptimality

  28. Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradients

    Sep 13, 2026Sidharth S. Menon, Irina Tezaur, Ameya D. JagtapConventional Physics-Informed Neural NetworksGradient Surgery

  29. Physics-Informed Neural Networks to Infer the Perpendicular Energy Conductivity in the Scrape-Off Layer of Stellarator Devices

    Sep 12, 2026J. Gallego (Departamento de Tecnología, CIEMAT, Spain) +23Conventional Physics-Informed Neural NetworksPlasma Shape Control

  30. Toward Reliable Railway-Bogie Response Prediction Using Multifidelity TDNN and Physics-Informed Residual Learning

    Sep 10, 2026Gyeolhee Lee, Moosun Kim, Taewook Kwon +3Dynamics ModelsPhysics-Informed Machine Learning

  31. A variational physics-informed graph neural network for heterogeneous solid mechanics

    Sep 10, 2026Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar AnnabattulaConventional Physics-Informed Neural NetworksFinite Element Method

  32. Physics-Informed Multi-Task Surrogate Model for the Martian Nightside Thermosphere

    Sep 9, 2026Sergey NikiforovAtmospheric DynamicsLunar Surface

  33. Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics

    Sep 8, 2026Will Houser, Vanja Dukic, David M. BortzSystem IdentificationNonlinear Dynamics

  34. MLIP Detective: Active Failure Mode Discovery Beyond Benchmark Scores for Machine-Learning Interatomic Potentials

    Sep 8, 2026Ryuhei Okuno, Nontawat Charoenphakdee, Kaoru Hisama +1Interatomic PotentialsFailure Mechanism

  35. Learning Metamaterial Eigenmodes with Wavelet-Encoded Fourier Neural Operators

    Sep 8, 2026Han Zhang, Alexander Ogren, Cynthia Rudin +2Fourier Neural OperatorsMetamaterials

  36. Two-Scale Localized PCA-Net: Coarse-Global and Local-Residual Representations for Artifact-Reduced PDE Operator Learning

    Sep 7, 2026Mrigank Dhingra, Jordan Stout, Omer SanPartial Differential EquationsTemporal Convolutional Networks

  37. Solving the Elastic Wave Equation with Physics-Informed Neural Networks: A Robust and Critical Assessment

    Sep 7, 2026Davide Staub, Ben MoseleyConventional Physics-Informed Neural NetworksFull Waveform Inversion

  38. Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics

    Sep 7, 2026Hanwen Wang, Paris PerdikarisConventional Physics-Informed Neural NetworksPartial Differential Equations

  39. Local gradient neural operator

    Sep 7, 2026Baiming Zhang, Jinsong Tang, Ying Xu +2Partial Differential Equation Benchmarks

  40. A Systematic Analysis of Automatic Differentiation versus Discretization-based Constraints for Physics-Informed PDE Solvers

    Sep 7, 2026Xing Guo, Hongwei Tang, Zewei Meng +3Neural Partial Differential Equation SolversDiscretization

  41. Prospective Coding Improves Learning in Deep Continuous-Time Recurrent Networks

    Sep 3, 2026Shivang Rawat, Mirko Morello, Flaviano Morone +1Recurrent Neural NetworksRecurrent Model

  42. Residual neural networks overcome the curse of dimensionality for semilinear heat equations

    Sep 3, 2026Ilkhom Mukhammadiev, Diyora SalimovaNeural-Network ApproximationResidual Connections

  43. Equation Recast for Canonical Operator Learning Across Parametric PDEs

    Sep 2, 2026Qiyun Cheng, Valentin Duruisseaux, Cesar F. Clauser +7Probabilistic Operator LearningNeural Partial Differential Equation Solvers

  44. Physics-Informed Neural Network Surrogate for Oxygen Vacancy Dynamics in epitaxial SrTiO3\mathrm{SrTiO_3} on Si memristors via Dynamic Spectral Optimization

    Sep 2, 2026Rodion Podorozhny, Nikoleta Theodoropoulou, Jelena TešićResistive Random Access MemoryConventional Physics-Informed Neural Networks

  45. Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks

    Sep 1, 2026Jing Xiao, Xinhai Chen, Qinglin Wang +5Conventional Physics-Informed Neural NetworksNewton

  46. Predicting Subsurface Abnormalities Growth using Physics-Informed Neural Networks

    Sep 1, 2026Mehrdad Shafiei Dizaji, Hoda AzariConventional Physics-Informed Neural NetworksSub-Surface Mineral Prospectivity Modelling

  47. iPINN for Broadband CARS Phase Retrieval: A Framework for Function Approximation and Inverse Modeling Problems in Nonlinear Spectroscopy

    Sep 1, 2026Ravi Teja Vulchi, Carl Messerschmidt, Mohammadsadegh Vafaeinezhad +4Conventional Physics-Informed Neural NetworksIll-Posed Inverse Problem

  48. Conditional Flow Matching for ML-Based Inverse Design Problems

    Sep 1, 2026Juliana Felder, Milad Habibi, Soheyl Massoudi +1Generative Inverse DesignConditional Flow Matching

  49. Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains

    Aug 31, 2026Zi Wang, Minghui Xu, Tapan MukerjiGeometry-Aware Foundation ModelPartial Differential Equations

  50. Learning the Geometry of Admissible Hypotheses through Inductive Bias in Training Distributions

    Aug 31, 2026James Crowley, Faez Ahmed, Anton van BeekPartial Differential EquationsUnified Inductive Bias

  51. DiffPDE: Masked Diffusion Language Models as PDE Solver

    Aug 31, 2026Wenxuan Guo, Yuyang Hong, Lubin Fan +4Partial Differential Equation BenchmarksPartial Differential Equations

  52. Learning PDE Time-Stepping with Neural Cellular Automata

    Aug 31, 2026Esha Saha, Hao WangNeural Partial Differential Equation SolversPartial Differential Equation Benchmarks

  53. Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

    Aug 30, 2026Abdolmehdi Behroozi, Chaopeng ShenNeural OperatorsPartial Differential Equation Benchmarks

  54. Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems

    Aug 30, 2026Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer +1Neural OperatorsPartial Differential Equations

  55. Reference-free logged energy-oracle recovery for neural approximations of symmetric coercive variational problems: conforming Riesz reconstruction and archive-level selection

    Aug 17, 2026Karim Bounja, Lahcen Laayouni, Boujemaa Achchab +1Neural-Network ApproximationNeural Partial Differential Equation Solvers

  56. The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity

    Aug 13, 2026Martin J. WainwrightDiffusion SamplingDiscretization

  57. Physics-informed distribution of relaxation times estimation and latent-space condition monitoring of solid oxide fuel and electrolysis cells from electrochemical impedance spectroscopy

    Aug 13, 2026Žan Gorenc, Žiga Gradišar, Felix Mütter +2Parallel Liquid-Inspired Temporal RelaxationHydrogen Multi-Energy Systems

  58. Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection

    Aug 13, 2026Pongpisit Thanasutives, Yoshinobu KawaharaAdvection-Reaction-DiffusionBayesian Quadrature

  59. Distillation of Foundation Models for Time-dependent PDEs

    Aug 12, 2026Daniel Musekamp, Boshra Ariguib, Andrei Manolache +1Knowledge DistillationPartial Differential Equations

  60. Kernel Methods for Learning Operators with Multiple Inputs and Outputs

    Aug 12, 2026Adrien Weihs, Chunyang Liao, Jingmin Sun +1Probabilistic Operator LearningKernel Method