mlsanityData to 7 Oct 2026

ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

arXiv 2512.03476 ↗First posted 3 Dec 2025cs.LG cs.AI cs.MAcited by 7

On the map: LLM agents and tool use → Web, search, and research agents

Abstract (arXiv)

Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a major bottleneck. Although large language models can generate isolated code fragments, they lack the structured reasoning required to design, verify, and iteratively refine complete scientific pipelines. Here we introduce ATHENA, an agentic framework explicitly designed to emulate scientific research modeled as a knowledge-driven contextual bandit process. Its core loop separates conceptual policy from numerical realization through expert-derived conceptual scaffolding, enabling principled diagnosis, reformulation, and repair of computational strategies. Across scientific computing and scientific machine learning tasks, ATHENA autonomously derives and correctly applies exact analytical solutions, constructs stable numerical solvers, diagnoses ill-posed formulations, and orchestrates hybrid symbolic-numeric workflows. Quantitatively, ATHENA matches and frequently surpasses the accuracy of expert-authored reference solutions reported in the literature on canonical benchmarks. By reframing computation as an object of agentic reasoning, our framework enables autonomous orchestration of heterogeneous algorithms across scientific domains.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use. Builds on 42 of its 76 references that are in the map. First posted on arXiv 3 Dec 2025.

Builds on

42 of 76 references.

References · 42

  1. 2023Lost in the Middle: How Language Models Use Long Contextscited by 3,383
  2. 2024The AI Scientist: Towards Fully Automated Open-Ended Scientific Discoverycited by 1,002
  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  4. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
  5. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  6. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  7. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
  8. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  9. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
  10. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  11. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  12. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
30 more
  1. 2023Residual-based attention in physics-informed neural networkscited by 72
  2. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
  3. 2025Mathematical exploration and discovery at scalecited by 66
  4. 2022Failure-informed adaptive sampling for PINNscited by 64
  5. 2025Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspectivecited by 55
  6. 2025An AI system to help scientists write expert-level empirical softwarecited by 52
  7. 2020DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolationcited by 45
  8. 2025Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networkscited by 41
  9. 2023On the training and generalization of deep operator networkscited by 31
  10. 2024Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be?cited by 31
  11. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  12. 2019Multi-scale Deep Neural Networks for Solving High Dimensional PDEscited by 24
  13. 2024Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networkscited by 20
  14. 2025PINNsAgent: Automated PDE Surrogation with Large Language Modelscited by 17
  15. 2025Defining Foundation Models for Computational Science: A Call for Clarity and Rigorcited by 16
  16. 2025A multi-agentic framework for real-time, autonomous freeform metasurface designcited by 14
  17. 2023Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulationcited by 13
  18. 2024Learning in PINNs: Phase transition, diffusion equilibrium, and generalizationcited by 13
  19. 2024KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamicscited by 13
  20. 2025AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learningcited by 13
  21. 2025DeepSeek vs. ChatGPT vs. Claude: A Comparative Study for Scientific Computing and Scientific Machine Learning Taskscited by 12
  22. 2025Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacologycited by 10
  23. 2025High precision PINNs in unbounded domains: application to singularity formulation in PDEscited by 6
  24. 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learningcited by 6
  25. 2025Self-adaptive weighting and sampling for physics-informed neural networkscited by 6
  26. 2023GPT vs Human for Scientific Reviews: A Dual Source Review on Applications of ChatGPT in Sciencecited by 5
  27. 2025Toward Autonomous Engineering Design: A Knowledge-Guided Multi-Agent Frameworkcited by 5
  28. 2025FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor designcited by 2
  29. 2025An Agentic AI Workflow to Simplify Parameter Estimation of Complex Differential Equation Systemscited by 1
  30. 2025Flexible Swarm Learning May Outpace Foundation Models in Essential Taskscited by 1

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Citing papers per year: 2026: 7.

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