Most Influential ArXiv (Numerical Analysis) Papers (2026-04 Version)

2026-04-06 · Source: Resources | Paper Digest · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning, Engineering & Applied Sciences · Depth: Expert, extended

Summary

Paper Digest Team has released the April 2026 version of its "Most Influential ArXiv (Numerical Analysis) Papers" list, identifying top research from 2010 to 2025. This curated list, updated frequently, ranks papers based on citations from both research publications and granted patents. The Numerical Analysis field on arXiv encompasses algorithms for problems in analysis, algebra, and scientific computation. The list highlights key advancements across various sub-fields, including physics-informed neural networks (PINNs) for solving PDEs, finite element methods (FEM), model order reduction, and numerical schemes for fractional differential equations. Notable papers from 2025 include "A Note on Eigenvalues of Perturbed Hermitian Matrices" and "An Approximate Lax-Wendroff-Type Procedure for High Order Accurate Schemes for Hyperbolic Conservation Laws," both with an Influence Factor (IF) of 3. The most influential paper overall, from 2017, is "Solving High-dimensional Partial Differential Equations Using Deep Learning" with an IF of 8.

Key takeaway

For AI Scientists and Research Scientists seeking to identify impactful research in numerical analysis, you should consult this list to pinpoint foundational and emerging methods. Focus on the highly cited papers, especially those integrating deep learning with traditional numerical techniques, such as Physics-Informed Neural Networks (PINNs) and operator learning. Your research strategy could benefit from exploring these influential works to inform new algorithm development or to understand the current landscape of computational challenges and solutions.

Key insights

Citation-based ranking reveals key trends and influential papers in numerical analysis, particularly in scientific machine learning and PDE solvers.

Principles

• Influence is measured by citations from papers and patents.
• Deep learning methods are increasingly prominent in numerical analysis.
• Robustness and stability are critical for numerical schemes.

Method

Paper Digest automatically ranks papers using a proprietary algorithm that considers citations from both academic research and granted patents, with frequent updates to reflect current influence.

In practice

• Explore top-ranked papers for foundational knowledge in specific numerical analysis sub-fields.
• Investigate scientific machine learning techniques for solving complex PDEs.
• Consider adaptive sampling and multi-fidelity approaches for computational efficiency.

Topics

• Physics-Informed Neural Networks
• Finite Element Methods
• Partial Differential Equations
• Model Order Reduction
• Inverse Problems

Code references

• odinn-sciml/diffeqsensitivity-review
• tamaragrossmann/fem-vs-pinns
• mtezzele/digital-twin-shm
• fpichi/gca-rom
• benmoseley/fbpinns

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Resources | Paper Digest.