# AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing

arXiv: https://arxiv.org/abs/2602.17607 · HTML: https://mlsanity.com/paper/2602.17607/

## 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 17 of its 26 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 17 of 17)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [AIDE: AI-Driven Exploration in the Space of Code](https://mlsanity.com/paper/2502.13138/) (2025)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [CodePDE: An Inference Framework for LLM-driven PDE Solver Generation](https://mlsanity.com/paper/2505.08783/) (2025)
- [On the Benefits of Memory for Modeling Time-Dependent PDEs](https://mlsanity.com/paper/2409.02313/) (2024)
- [UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptation](https://mlsanity.com/paper/2403.07187/) (2024)
- [BioCoder: A Benchmark for Bioinformatics Code Generation with Large Language Models](https://mlsanity.com/paper/2308.16458/) (2023)
- [PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs](https://mlsanity.com/paper/2502.00963/) (2025)
- [AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learning](https://mlsanity.com/paper/2511.07262/) (2025)
- [PDE-Agent: A toolchain-augmented multi-agent framework for PDE solving](https://mlsanity.com/paper/2512.16214/) (2025)
- [Automated Code Development for PDE Solvers Using Large Language Models](https://mlsanity.com/paper/2509.25194/) (2025)

## Built on by (most cited first, 7 of 7)

- [GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2605.11117/) (2026)
- [PerspectiveGap: A Benchmark for Multi-Agent Orchestration Prompting](https://mlsanity.com/paper/2606.08878/) (2026)
- [AutoPDE: Reliable Agentic PDE Solving via Explicitly Represented Solver Strategies](https://mlsanity.com/paper/2606.10752/) (2026)
- [Bringing Agentic Search to Earth Observation Data Discovery](https://mlsanity.com/paper/2607.02387/) (2026)
- [A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS](https://mlsanity.com/paper/2606.10928/) (2026)
- [Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards](https://mlsanity.com/paper/2607.10474/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)

## Abstract (arXiv)

PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent neural network-based approaches improve flexibility but often demand high computational cost and suffer from limited interpretability. We introduce textttAutoNumerics, a multi-agent framework that autonomously designs, implements, debugs, and verifies numerical solvers for general PDEs directly from natural language descriptions. Unlike black-box neural solvers, our framework generates transparent solvers grounded in classical numerical analysis. We introduce a coarse-to-fine execution strategy and a residual-based self-verification mechanism. Experiments on 24 canonical and real-world PDE problems demonstrate that textttAutoNumerics achieves competitive or superior accuracy compared to existing neural and LLM-based baselines, and correctly selects numerical schemes based on PDE structural properties, suggesting its viability as an accessible paradigm for automated PDE solving.