Key papers

• Physics-Informed Diffusion Models (2024)
  Jan-Hendrik Bastek et al.
  10.79
• DeepSeek vs. ChatGPT vs. Claude: A Comparative Study for Scientific Computing and Scientific Machine Learning Tasks (2025)
  Qile Jiang et al.
  10.19
• Multi-Objective Loss Balancing for Physics-Informed Deep Learning (2021)
  Rafael Bischof et al.
  9.39
• Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning (2024)
  Luis Mandl et al.
  9.22
• Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks (2025)
  Elham Kiyani et al.
  8.78
• Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study (2025)
  Jassem Abbasi et al.
  8.73
• A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder (2020)
  Youngkyu Kim et al.
  8.66
• Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning (2025)
  Alfio Quarteroni and Paola Gervasio and Francesco Regazzoni
  8.45
• Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble (2025)
  Zongren Zou et al.
  8.07
• Learning Hidden Physics and System Parameters with Deep Operator Networks (2024)
  Dibakar Roy Sarkar et al.
  7.77
• AlphaEvolve: A coding agent for scientific and algorithmic discovery (2025)
  Alexander Novikov et al.
  7.35
• Mathematics of Data Science (2026)
  Afonso S. Bandeira et al.
  7.34
• QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs (2025)
  Afrah Farea et al.
  7.29
• Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML (2023)
  Hrishikesh Viswanath et al.
  7.16
• Physics-Informed Neural Networks for microflows: Rarefied Gas Dynamics in Cylinder Arrays (2025)
  Jean-Michel Tucny et al.
  7.02
• Physics-informed machine learning as a kernel method (2024)
  Nathan Doum\`eche (LPSM (UMR\_8001) et al.
  6.35
• FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation (2022)
  Adarsh Ganeshram et al.
  6.34
• LT-PINN: Lagrangian Topology-conscious Physics-informed Neural Network for Boundary-focused Engineering Optimization (2025)
  Yuanye Zhou et al.
  6.28
• Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs (2025)
  Salah A. Faroughi and Farinaz Mostajeran
  6.28
• An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks (2025)
  Jiaqi Luo et al.
  6.25
• Data-Efficient Inference of Neural Fluid Fields via SciML Foundation Model (2024)
  Yuqiu Liu et al.
  6.24
• Curriculum Learning-Driven PIELMs for Fluid Flow Simulations (2025)
  Vikas Dwivedi et al.
  6.12
• Adaptive Physics-informed Neural Networks: A Survey (2025)
  Edgar Torres et al.
  6.12
• Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks (2025)
  Zewen Liu et al.
  6.12
• LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks (2025)
  Ze Tao et al.
  6.12
• Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony (2025)
  James Bagrow and Josh Bongard
  6.01
• Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations (2023)
  Abhishek Setty et al.
  5.86
• Differentiable Programming for Differential Equations: A Review (2024)
  Facundo Sapienza et al.
  5.73
• Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs (2025)
  Sidharth S. Menon et al.
  5.65
• Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification (2023)
  Jun Liu and Yiming Meng and Maxwell Fitzsimmons and Ruikun Zhou
  5.64
• A Physics-informed Multi-resolution Neural Operator (2025)
  Sumanta Roy et al.
  5.57
• RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion (2025)
  Siming Shan et al.
  5.52
• Hamiltonian Neural Networks approach to fuzzball geodesics (2025)
  Andrea Cipriani et al.
  5.48
• QCBench: Evaluating Large Language Models on Domain-Specific Quantitative Chemistry (2025)
  Jiaqing Xie et al.
  5.46
• Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discovery (2025)
  Jiaqi Liu et al.
  5.46
• A novel Trunk Branch-net PINN for flow and heat transfer prediction in porous medium (2025)
  Haoyun Xing et al.
  5.43
• An efficient wavelet-based physics-informed neural network for multiscale problems (2024)
  Himanshu Pandey et al.
  5.35
• Scientific machine learning in Hydrology: a unified perspective (2025)
  Adoubi Vincent De Paul Adombi
  5.35
• Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modeling (2025)
  Wei Wang et al.
  5.24
• On learning functions over biological sequence space: relating Gaussian process priors, regularization, and gauge fixing (2025)
  Samantha Petti et al.
  5.24
• Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics (2024)
  Boyang Chen et al.
  5.23
• From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing (2025)
  Prashant K. Jha
  5.18
• Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networks (2025)
  D. Veerababu et al.
  5.18
• Sharp-PINNs: staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion (2025)
  Nanxi Chen et al.
  5.13
• Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields (2025)
  Mohammad Mahdi Abedi et al.
  5.13
• RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations (2025)
  Weihang Ouyang et al.
  5.10
• An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulence (2025)
  Karan Jakhar et al.
  5.10
• Explainable autoencoder for neutron star dense matter parameter estimation (2025)
  Francesco Di Clemente et al.
  5.07
• Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms (2025)
  Yahong Yang and Juncai He
  5.04
• An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks (2026)
  Joseph Webb et al.
  4.95
• Causal Climate Emulation with Bayesian Filtering (2025)
  Sebastian Hickman et al.
  4.93
• Nothing from Something: Can a Language Model Discover 0? (2026)
  Phoebe Zeng et al.
  4.90
• An Introduction to Variational Quantum Eigensolver Applied to Chemistry (2025)
  Matheus da S. Fonseca et al.
  4.87
• Dual-Balancing for Physics-Informed Neural Networks (2025)
  Chenhong Zhou et al.
  4.87
• Fast and Flexible Quantum-Inspired Differential Equation Solvers with Data Integration (2025)
  Lucas Arenstein et al.
  4.87
• PINNs for Solving Unsteady Maxwell's Equations: Convergence Issues and Comparative Assessment with Compact Schemes (2025)
  Gal G. Shaviner et al.
  4.82
• A discrete physics-informed training for projection-based reduced order models with neural networks (2025)
  N. Sibuet et al.
  4.82
• Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations (2025)
  Giovanni Catalani et al.
  4.82
• Weighted balanced truncation method for approximating kernel functions by exponentials (2025)
  Yuanshen Lin et al.
  4.76
• PIED: Physics-Informed Experimental Design for Inverse Problems (2025)
  Apivich Hemachandra et al.
  4.76