Key papers

• A brief review of the Deep BSDE method for solving high-dimensional partial differential equations (2025)
  Jiequn Han et al.
  6.53
• Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications (2024)
  Youngkyu Lee and Alena Kopani\v{c}\'akov\'a and George Em Karniadakis
  5.15
• Multi-Level Monte Carlo Training of Neural Operators (2025)
  James Rowbottom et al.
  4.93
• Representing Flow Fields with Divergence-Free Kernels for Reconstruction (2025)
  Xingyu Ni et al.
  4.87
• Level-Crossing Density as a Mesh-Free High-Frequency Auxiliary Loss for Implicit Neural Representations (2026)
  Gunner Levi Howe
  4.39
• SplineNet: An Isogeometric Deep Learning Method for Complex Shells (2026)
  Shizhou Luo et al.
  4.39
• Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative (2026)
  Yongjin Choi et al.
  4.33
• Modularity-Free Conflict-Averse Training for Generalized PINNs (2026)
  Heejo Kong et al.
  4.33
• Accelerating Bayesian inverse design in computational fluid dynamics using neural operators (2026)
  Bipin Tiwari et al.
  4.27
• Two-Parameter Flows for Learning Population Dynamics of Physical Systems (2026)
  Paul Schwerdtner et al.
  4.27
• Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation (2025)
  Hanfei Zhou and Lei Shi
  3.97
• ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance (2025)
  Haolan Zheng et al.
  3.97
• Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning (2025)
  Hector Vargas Alvarez et al.
  3.92
• UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss (2025)
  Zhichao Wang et al.
  3.92
• Dimension reduction for derivative-informed operator learning: An analysis of approximation errors (2025)
  Dingcheng Luo et al.
  3.70
• Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators (2024)
  Zekun Shi et al.
  3.53
• Hybrid Two-Level Transport Method with Solution Decomposition in Macro and Micro Components (2026)
  Caleb A. Shaw et al.
  3.51
• Regional climate risk assessment from climate models using probabilistic machine learning (2024)
  Zhong Yi Wan et al.
  3.26
• Learning from Linear Algebra: A Graph Neural Network Approach to Preconditioner Design for Conjugate Gradient Solvers (2024)
  Vladislav Trifonov et al.
  3.14
• Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-based Matrix Inversion (2025)
  Anton Lebedev and Won Kyung Lee et al.
  3.04
• Kourkoutas-Beta: A Sunspike-Driven Adam Optimizer with Desert Flair (2025)
  Stavros C. Kassinos
  2.99
• Deep Uzawa for Kinetic Transport with Lagrange-Enforced Boundaries (2025)
  Charalambos Makridakis and Aaron Pim and Tristan Pryer and Nikolaos Rekatsinas
  2.93
• Dimer-Enhanced Optimization: A First-Order Approach to Escaping Saddle Points in Neural Network Training (2025)
  Yue Hu and Zanxia Cao and Yingchao Liu
  2.93
• Jacobian-Enhanced Neural Networks (2024)
  Steven H. Berguin
  2.92
• Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints (2025)
  Utkarsh Utkarsh et al.
  2.87
• DUE: A Deep Learning Framework and Library for Modeling Unknown Equations (2025)
  Junfeng Chen et al.
  2.76
• An analysis of the derivative-free loss method for solving PDEs (2023)
  Jihun Han et al.
  2.70
• Optimal Transport-inspired Deep Learning Framework for Slow-Decaying Kolmogorov n-width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel (2023)
  Moaad Khamlich and Federico Pichi and Gianluigi Rozza
  2.64
• Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups (2024)
  Zakhar Shumaylov et al.
  2.49
• A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations (2024)
  Shu Liu et al.
  2.45
• Neural empirical interpolation method for nonlinear model reduction (2024)
  Max Hirsch et al.
  2.26
• Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows (2024)
  Shuhao Cao et al.
  2.21
• Automated Derivation of Lattice Boltzmann Methods for Systems of Conservation Laws (2026)
  Adrian Kummerl\"ander et al.
  2.00
• A Tuning-Free Variational Framework for Muscle Redundancy Resolution: Torque Fiber Proximal Dynamics with Active-Set Switching and EMG-Validated Activation Prediction (2026)
  Morteza Ganji
  2.00
• Automated Numerical Stability Analysis of Deep Learning Operators (2026)
  Xinye Chen
  2.00
• Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks (2026)
  Pengcheng Cheng
  2.00
• Learning Orthonormal Bases for Function Spaces (2026)
  Hamidreza Kamkari et al.
  1.94
• When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains (2026)
  Brandon Yee et al.
  1.89
• Convolutional Surrogate for 3D Discrete Fracture-Matrix Tensor Upscaling (2026)
  Martin \v{S}petl\'ik and Jan B\v{r}ezina
  1.83
• Kinetic-based regularization: Learning spatial derivatives and PDE applications (2026)
  Abhisek Ganguly et al.
  1.78
• Model Order Reduction of Cerebrovascular Hemodynamics Using POD_Galerkin and Reservoir Computing_based Approach (2026)
  Rahul Halder et al.
  1.78
• Learning Mesh-Free Discrete Differential Operators with Self-Supervised Graph Neural Networks (2026)
  Lucas Gerken Starepravo et al.
  1.78
• Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNs (2026)
  Zhangyong Liang et al.
  1.78
• Generative Neural Operators through Diffusion Last Layer (2026)
  Sungwon Park et al.
  1.72
• Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter (2026)
  Yuhan Wu et al.
  1.72
• Distribution-Free Robust Predict-Then-Optimize in Function Spaces (2026)
  Yash Patel et al.
  1.72
• Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition (2026)
  Changhong Mou et al.
  1.72
• Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver (2026)
  Pietro Sittoni et al.
  1.72
• From Basis to Basis: Gaussian Particle Representation for Interpretable PDE Operators (2026)
  Zhihao Li et al.
  1.72
• Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference (2026)
  Shane A. McQuarrie et al.
  1.67
• An adjoint method for training data-driven reduced-order models (2026)
  Donglin Liu et al.
  1.67
• Multi-Preconditioned LBFGS for Training Finite-Basis PINNs (2026)
  Marc Salvad\'o-Benasco et al.
  1.67
• Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs (2026)
  Lorenzo Tomada et al.
  1.67
• ProFlow: Zero-Shot Physics-Consistent Sampling via Proximal Flow Guidance (2026)
  Zichao Yu et al.
  1.67
• Enforcing governing equation constraints in neural PDE solvers via training-free projections (2025)
  Omer Rochman and Gilles Louppe
  1.56
• Adaptive Mesh-Quantization for Neural PDE Solvers (2025)
  Winfried van den Dool et al.
  1.56
• Weights initialization of neural networks for function approximation (2025)
  Xinwen Hu et al.
  1.50
• SPIKE: Stable Physics-Informed Kernel Evolution Method for Solving Hyperbolic Conservation Laws (2025)
  Hua Su et al.
  1.50
• Interpolative separable density fitting on adaptive real space grids (2025)
  Hai Zhu et al.
  1.50
• Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks (2025)
  Zhi-Feng Wei et al.
  1.44