Partial Differential Equations

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Period ending 2026-09-21

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  1. RECAST: A Machine-Learning Framework for Correction and Super-Resolution of Coarse-Grid PDE Solvers

    Aug 12, 2026Maryam Reza, Farbod FarajiPartial Differential EquationsArtifact Correction

  2. Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

    Aug 11, 2026Maciej J. Mikulski, Tadeusz UhlConventional Physics-Informed Neural NetworksAutomatic Differentiation

  3. Physics-Informed Implicit Neural Representations for Improved Myocardial Perfusion MRI Quantification

    Aug 11, 2026Christos Tsepas, Chang Yan, Maximilian Fuetterer +2Cardiac Magnetic Resonance ImagingConventional Physics-Informed Neural Networks

  4. Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws

    Aug 11, 2026Qi Gao, Kuang Huang, Xuan DiConventional Physics-Informed Neural Networks

  5. A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics

    Aug 10, 2026Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim TeweHamiltonian PhysicsHamiltonian

  6. The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics

    Aug 10, 2026Petr Badolia, Leonid Obukhov, Dmitry Bylinkin +1Partial Differential Equation BenchmarksPartial Differential Equations

  7. MoNo: Multiscale Optimal Transport Neural Operator for Solving PDEs on General Geometries

    Aug 10, 2026Zijiang Yang, Xiaomeng Wu, Dongmei FuNeural OperatorsPartial Differential Equations

  8. Physics-Informed Machine Learning in Prognostics and Health Management: A Systematic Literature Review

    Aug 10, 2026Christopher Braun, Julian Raible, Marco F. HuberPhysics-Informed Machine LearningPrognostics

  9. Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing

    Aug 10, 2026Konrad Kleinberg, Thomas KruseNeural-Network ApproximationStochastic Differential Equations

  10. Hierarchical rank-evolving representation for physics-informed neural networks

    Aug 10, 2026Ruoyang Su, Xi-Le Zhao, Kun Li +1Conventional Physics-Informed Neural NetworksFluid Dynamics

  11. Coordinate-Residual Physics-Driven Neural Network for Inverse Scattering Imaging

    Aug 10, 2026Yutong Du, Zicheng Liu, Bo Qi +2Ill-Posed Inverse ProblemConventional Physics-Informed Neural Networks

  12. Physics-Informed Learning for Robust Acoustic Localization with Calibrated Uncertainty

    Aug 9, 2026Jennifer N. Kampe, Changwoo J. Lee, Xin Shen +5Sound Source LocalizationCalibrated Uncertainty

  13. ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries

    Aug 9, 2026Roberto Nuca, Giovanni Testa, Luca Galimberti +1Fourier Neural OperatorsComputational Fluid Dynamic

  14. Stochastic Physics-Informed Neural Networks on Lie Groups for Learning Underwater Vehicle Dynamics

    Aug 8, 2026Evan F. Palmer, Ross L. Hatton, Geoffrey A. HollingerAutonomous Underwater VehiclesConventional Physics-Informed Neural Networks

  15. Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

    Aug 8, 2026Muhammad Akbar KhanConventional Physics-Informed Neural NetworksAdvection-Reaction-Diffusion

  16. Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains

    Aug 8, 2026Jeeeun Lee, Denis Korolev, Miro Duhovic +1Conventional Physics-Informed Neural NetworksProblem-Dependent Artificial Boundary Conditions

  17. Unsupervised Adaptation of PDE Foundation Models

    Aug 7, 2026Ziye Song, Zhao Wei, Xin Yu +2Neural Partial Differential Equation SolversPartial Differential Equation Benchmarks

  18. From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning

    Aug 7, 2026Zhentao Tan, Ruijie Quan, Yi YangPartial Differential Equation BenchmarksEdge

  19. Weak Adversarial Neural Pushforward Method for Boltzmann Equation

    Aug 7, 2026Jenia Fardousi Koly, Andrew Qing He, Wei CaiBoltzmann DistributionsBayesian Quadrature

  20. Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples

    Aug 7, 2026Xinliang Liu, Tong Mao, Jinchao XuNeural-Network ApproximationBayesian Quadrature

  21. Kastor: An efficient fine-tuning strategy for generative emulation of PDE simulations

    Aug 6, 2026Guillaume Couairon, Alexis Jacq, Yu-Han Wu +4EmulatorsAccurate Surrogate Models

  22. Alternating Levenberg-Marquardt Training of Physics-Informed Neural Networks with Fourier-Enhanced Features

    Aug 6, 2026Yulun Wu, Matthieu Barreau, Miguel Aguiar +1Conventional Physics-Informed Neural NetworksNewton

  23. Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations

    Aug 5, 2026Xujia Chen, Xinyue Hu, Letian Chen +2Conventional Physics-Informed Neural NetworksPartial Differential Equations

  24. Discretization and Statistical Consistency of Functional Flow Matching

    Aug 5, 2026Lennon J. ShikhmanConditional Flow MatchingIll-Posed Inverse Problem

  25. Improving Auto-Design of Neural PDE Solvers with a Domain-Specific Language

    Aug 5, 2026Shengxin Kong, Liwen Xu, Jingwen FuNeural Partial Differential Equation SolversNeural Architecture Search

  26. Transferable Dual-Stream Representations for Mesoscale-Preserving Sea Surface Temperature Downscaling

    Aug 4, 2026Parth Doshi, Priyanka Aravindan, Vaishnav Vaidheeswaran +2Dynamical DownscalingSea-Surface Temperature Data

  27. From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNs

    Aug 4, 2026Chenhao Si, Kang An, Shiqian Ma +1Conventional Physics-Informed Neural NetworksNewton

  28. A Physics-Flavored Transformer Network for Parametrizing Contraction Dynamics of Engineered Skeletal Muscle Tissues

    Aug 4, 2026Mattias Luber, Timo BetzConventional Physics-Informed Neural NetworksMuscle Anatomy

  29. Large language models for partial differential equation workflows

    Aug 4, 2026Han Wan, Rui Zhang, Hao SunNeural Partial Differential Equation SolversPartial Differential Equation Benchmarks

  30. Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models

    Aug 4, 2026Edgar Jaber, Rémy Vallot, Thibault Dairay +1Reduced-Order ModelsReliable Uncertainty Quantification

  31. A Physics-Informed Hybrid Neural Operator for Transient Magnetization Prediction in Power Magnetics

    Aug 3, 2026Yachao Zhu, Qiujie Huang, Sinan Li +3Magnetic Tunnel JunctionStress Fields

  32. Constrained Co-Design for Photonic Bayesian Neural Networks

    Aug 3, 2026Hendrik Borras, Xiao Wang, Bernhard Klein +4Bayesian Neural NetworksConventional Physics-Informed Neural Networks

  33. Physics-Informed Neural Networks for Complex Eigenfrequency Identification and Mode Structure Reconstruction of the Ground-State ITG Branch

    Aug 3, 2026Dengdi Sun, Bingbing Zhang, Xiao Wang +5Conventional Physics-Informed Neural NetworksPlasma Shape Control

  34. MBO Scheme for Local Chan--Vese Segmentation

    Aug 1, 2026Kevin Bui, Adina CiomagaRobust SegmentationClassical Numerical Solver

  35. Adaptive Quantum Physics-Informed Neural Networks for Differential Equations with Applications to Fluid Dynamics

    Aug 1, 2026Fabio Pereira dos Santos, Renato Portugal, Júlio de Castro Vargas Fernandes +1Conventional Physics-Informed Neural NetworksHybrid Quantum Neural Networks

  36. An Embedded RISC-V Evaluation of Kolmogorov--Arnold Networks in Hard-Constrained Recurrent Physics-Informed Models

    Aug 1, 2026Enzo Nicolas Spotorno, Josafat Leal FilhoKolmogorov-Arnold NetworksRisc-V

  37. Modeling Unknown Nonlocal PDE Systems via Flow Map Learning

    Aug 1, 2026Zhongshu Xu, Ying Li, Yanzhi Zhang +1Partial Differential EquationsFlow Map

  38. Localization in Spatiotemporal Fields via Environmental PDEs

    Jul 31, 2026Jose Fuentes, Abdullah Al Redwan Newaz, Ana Cavalcanti +1Robust LocalizationAdvection-Reaction-Diffusion

  39. A Physics-Chemistry-Informed Neural Network (PCINN) for Real-Time Spatial-ALD Coverage Prediction and Reliable Kinetics Inversion

    Jul 31, 2026Ning Hu, Chang Liu, Yunlei Jiang +1Conventional Physics-Informed Neural NetworksAdvection-Reaction-Diffusion

  40. Freeze, Then Select: Structured Field Adapters and Stability-Validated Weak Selection for PDE Discovery from Sparse Observations

    Jul 31, 2026Juncheng Zhong, Chenghuang Shen, Jianfeng Liu +5Neural Partial Differential Equation Solvers

  41. Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction

    Jul 31, 2026Jiaquan Zhang, Shuxu Chen, Haifan Meng +6Long-Horizon ForecastingPartial Differential Equations

  42. Dynamics-aware identification of governing equations from sparse and noisy data

    Jul 31, 2026Pongpisit Thanasutives, Yoshinobu KawaharaSystem IdentificationPartial Differential Equations

  43. Feature Interaction Modeling for Neural Operators

    Jul 30, 2026Quan Gu, Xiaoduo Li, Hongxia LiuConventional Physics-Informed Neural NetworksPartial Differential Equations

  44. A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem

    Jul 30, 2026Tancredi Schettini GherardiniConventional Physics-Informed Neural NetworksBoundary Value Problems

  45. Learning features from Newton's algorithm: a way to accelerate nonlinear parametrized PDE solvers

    Jul 30, 2026Rémy Vallot, Florian de Vuyst, Thibault Dairay +1NewtonPartial Differential Equation Benchmarks

  46. Neural Network Approximation of Solutions to Fractional Parabolic Partial Differential Equations

    Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural-Network ApproximationPartial Differential Equations

  47. Event-Structured Physics-Informed Neural Networks for Differentiable Critical Clearing Boundaries

    Jul 30, 2026Baoli Hao, Chenxi Hu, Ming Zhong +1Conventional Physics-Informed Neural NetworksPower Systems

  48. Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem

    Jul 29, 2026Anton Myshak, Md Rezwan Bin Mizan, Ilya TimofeyevConventional Physics-Informed Neural NetworksMulti-Material Shock Physics

  49. PIKS: Universal Physics-Informed Kernel Methods

    Jul 29, 2026Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria +1Physics-Informed Machine LearningKernel Method

  50. EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks

    Jul 29, 2026Peng Yin, Kai Li, Yifan Zhang +1Conventional Physics-Informed Neural NetworksPartial Differential Equation Benchmarks

  51. Where Physics Meets Privacy: Federated PINNs for Privacy-Preserving Brain Tumor Biomechanical Modeling

    Jul 28, 2026Mahmuda Akter Sristy, Md Al-Mahfuz Chowdhury, Momota Ahsana Meem +2Conventional Physics-Informed Neural NetworksDeep Learning

  52. A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates

    Jul 28, 2026Muhammad Akbar Khan, Fahim Raees, Ubaida FatimaConventional Physics-Informed Neural NetworksThermal Imaging

  53. Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

    Jul 28, 2026Pinki Khatun, M. Sajid, Abhinav Jha +1Conventional Physics-Informed Neural NetworksPhysics-Informed Machine Learning

  54. Fourier Feature Physics-Informed Neural Networks for Elasto-Plastic Analysis of Geomaterials with a Non-Associative Mohr-Coulomb Model

    Jul 27, 2026Apisit Robjanghvad, Sompote YouwaiFinite Element MethodConventional Physics-Informed Neural Networks

  55. Physics-Informed CNN-LSTM for Street-Scale Urban Flood Prediction: Reconciling Aggregate Accuracy and Street-Level Plausibility

    Jul 27, 2026Luc DCosta, Yidi Wang, Jonathan L. Goodall +1Accurate Flood PredictionSen1Floods11

  56. Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs

    Jul 27, 2026Justin Sirignano, Konstantinos Spiliopoulos, Samuel CohenPartial Differential Equation BenchmarksPartial Differential Equations

  57. Physics Transformer: Tailoring Transformer for General PDE Prediction

    Jul 27, 2026Guoze Sun, Rui Zhang, Jiankai Tang +4Partial Differential EquationsUnified Transformer

  58. Perturbative-NeuSA: A Structured Spectral Framework for Time-Dependent PDEs

    Jul 27, 2026Xianli Zhu, Jia YinNeural Partial Differential Equation SolversPartial Differential Equations

  59. Variational Boosting for Physics-Informed Neural Networks

    Jul 27, 2026Pavlos Protopapas, Kaylee VoConventional Physics-Informed Neural NetworksZeroth-Order Optimization

  60. On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

    Jul 26, 2026Baptiste Mathevon, Farah Cherfaoui, Amaury Habrard +1Partial Differential EquationsEvaluation Metrics