Awesome Math & Equations

Key papers

• An AI system to help scientists write expert-level empirical software (2025)
  Eser Ayg\"un et al.
  12.64
• 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.
  10.30
• 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
• Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study (2025)
  Jassem Abbasi et al.
  8.84
• 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
  8.56
• Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble (2025)
  Zongren Zou et al.
  8.18
• Learning Hidden Physics and System Parameters with Deep Operator Networks (2024)
  Dibakar Roy Sarkar et al.
  7.77
• QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs (2025)
  Afrah Farea et al.
  7.40
• Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks (2025)
  Elham Kiyani 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
• AlphaEvolve: A coding agent for scientific and algorithmic discovery (2025)
  Alexander Novikov et al.
  6.88
• Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs (2025)
  Salah A. Faroughi and Farinaz Mostajeran
  6.39
• 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
• 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.
  6.23
• Adaptive Physics-informed Neural Networks: A Survey (2025)
  Edgar Torres et al.
  6.23
• LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks (2025)
  Ze Tao et al.
  6.23
• Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony (2025)
  James Bagrow and Josh Bongard
  6.12
• Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks (2025)
  Zewen Liu et al.
  5.96
• Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations (2023)
  Abhishek Setty et al.
  5.86
• Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs (2025)
  Sidharth S. Menon et al.
  5.76
• Differentiable Programming for Differential Equations: A Review (2024)
  Facundo Sapienza et al.
  5.73
• A Physics-informed Multi-resolution Neural Operator (2025)
  Sumanta Roy et al.
  5.68
• 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
• RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion (2025)
  Siming Shan et al.
  5.63
• Hamiltonian Neural Networks approach to fuzzball geodesics (2025)
  Andrea Cipriani et al.
  5.59
• QCBench: Evaluating Large Language Models on Domain-Specific Quantitative Chemistry (2025)
  Jiaqing Xie et al.
  5.57
• Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discovery (2025)
  Jiaqi Liu et al.
  5.57
• An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks (2025)
  Jiaqi Luo et al.
  5.54
• An efficient wavelet-based physics-informed neural network for multiscale problems (2024)
  Himanshu Pandey et al.
  5.35
• On learning functions over biological sequence space: relating Gaussian process priors, regularization, and gauge fixing (2025)
  Samantha Petti et al.
  5.35
• From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing (2025)
  Prashant K. Jha
  5.29
• Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networks (2025)
  D. Veerababu et al.
  5.29
• Sharp-PINNs: staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion (2025)
  Nanxi Chen et al.
  5.24
• Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields (2025)
  Mohammad Mahdi Abedi 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
• RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations (2025)
  Weihang Ouyang et al.
  5.21
• An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulence (2025)
  Karan Jakhar et al.
  5.21
• GRAPPA -- A Hybrid Graph Neural Network for Predicting Pure Component Vapor Pressures (2025)
  Marco Hoffmann et al.
  5.18
• Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms (2025)
  Yahong Yang and Juncai He
  5.15
• Causal Climate Emulation with Bayesian Filtering (2025)
  Sebastian Hickman et al.
  5.04
• Why dimensional analysis works: general classification of self-similarity based on scale-invariance (2026)
  Hirokazu Maruoka
  5.01
• Feynman Kac Reweighted Schr\"odinger Bridge Matching for Surface-Based Tau PET Harmonization (2026)
  Jianwei Zhang et al.
  5.01
• When Volumetric Growth Selects Surface Growth (2026)
  Rohn Abeyaratne et al.
  5.01
• Dual-Balancing for Physics-Informed Neural Networks (2025)
  Chenhong Zhou et al.
  4.98
• Fast and Flexible Quantum-Inspired Differential Equation Solvers with Data Integration (2025)
  Lucas Arenstein et al.
  4.98
• Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations (2025)
  Giovanni Catalani et al.
  4.93
• GENEOnet: Statistical analysis supporting explainability and trustworthiness (2025)
  Giovanni Bocchi and Patrizio Frosini and Alessandra Micheletti and Alessandro Pedretti and Carmen Gratteri and Filippo Lunghini and Andrea Rosario Beccari and Carmine Talarico
  4.87
• Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training (2025)
  Amin Totounferoush et al.
  4.87
• Introduction to Symbolic Regression in the Physical Sciences (2025)
  Deaglan J. Bartlett et al.
  4.86
• Language-Based Bayesian Optimization Research Assistant (BORA) (2025)
  Abdoulatif Ciss\'e et al.
  4.76
• Training Deep Physics-Informed Kolmogorov-Arnold Networks (2025)
  Spyros Rigas et al.
  4.75
• Spectral functions in Minkowski quantum electrodynamics from neural reconstruction: Benchmarking against dispersive Dyson--Schwinger integral equations (2025)
  Rodrigo Carmo Terin
  4.75
• Accurate and scalable deep Maxwell solvers using multilevel iterative methods (2025)
  Chenkai Mao et al.
  4.69
• Bayesian Physics Informed Neural Networks for Reliable Transformer Prognostics (2025)
  Ibai Ramirez et al.
  4.69
• The Ubiquitous Sparse Matrix-Matrix Products (2025)
  Ayd{\i}n Bulu\c{c}
  4.64