# AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design

arXiv: https://arxiv.org/abs/2609.32245 · HTML: https://mlsanity.com/paper/2609.32245/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 92 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Agent Laboratory: Using LLM Agents as Research Assistants](https://mlsanity.com/paper/2501.04227/) (2025)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Language agents achieve superhuman synthesis of scientific knowledge](https://mlsanity.com/paper/2409.13740/) (2024)
- [AI-Researcher: Autonomous Scientific Innovation](https://mlsanity.com/paper/2505.18705/) (2025)
- [Kosmos: An AI Scientist for Autonomous Discovery](https://mlsanity.com/paper/2511.02824/) (2025)
- [Neural Inverse Operators for Solving PDE Inverse Problems](https://mlsanity.com/paper/2301.11167/) (2023)
- [LitLLM: A Toolkit for Scientific Literature Review](https://mlsanity.com/paper/2402.01788/) (2024)
- [Robin: A multi-agent system for automating scientific discovery](https://mlsanity.com/paper/2505.13400/) (2025)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [AI Idea Bench 2025: AI Research Idea Generation Benchmark](https://mlsanity.com/paper/2504.14191/) (2025)
- [Learning Physical Dynamics with Subequivariant Graph Neural Networks](https://mlsanity.com/paper/2210.06876/) (2022)
- [CodePDE: An Inference Framework for LLM-driven PDE Solver Generation](https://mlsanity.com/paper/2505.08783/) (2025)
- [Learning Neural PDE Solvers with Parameter-Guided Channel Attention](https://mlsanity.com/paper/2304.14118/) (2023)
- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries](https://mlsanity.com/paper/2411.15178/) (2024)
- [Can LLMs Beat Classical Hyperparameter Optimization Algorithms? A Study on autoresearch](https://mlsanity.com/paper/2603.24647/) (2026)
- [Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2510.25803/) (2025)
- [Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics](https://mlsanity.com/paper/2402.06275/) (2024)
- [From Papers to Panoramas: Building Hierarchies of Scientific Literature at Scale](https://mlsanity.com/paper/2504.13834/) (2025)
- [PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation](https://mlsanity.com/paper/2605.09636/) (2026)
- [Automated Code Development for PDE Solvers Using Large Language Models](https://mlsanity.com/paper/2509.25194/) (2025)
- [M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation](https://mlsanity.com/paper/2412.04134/) (2024)
- [FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation](https://mlsanity.com/paper/2505.20349/) (2025)

## Abstract (arXiv)

Partial differential equations (PDEs) are essential for modeling complex physical systems, and neural solvers have recently emerged as powerful data-driven tools for numerically solving them. However, existing neural solvers struggle with domain-specific challenges, such as varying parameters and high-speed flows, necessitating specialized architectures. Manually designing these specialized solver architectures is a highly iterative, time-consuming process requiring deep expertise, creating a significant bottleneck in scientific discovery. We propose leveraging autonomous AI research agents to automate the synthesis of specialized solvers. To support this, we introduce AutoPDEBench, a benchmark dedicated to LLM-driven automated research for PDE solver design. The benchmark includes 25 challenging datasets featuring both novel and actively studied physical scenarios. We evaluate a suite of general-purpose models (transformer, ROM, and graph-based) alongside a multi-agent instantiation of the iterative automated research pipeline, which serves as an agentic baseline. Empirical results show that the iterative automated research system significantly outperforms the general-purpose neural solver baselines. Our findings demonstrate the viability of using AI agents to automatically design neural solvers for complex physical systems. AutoPDEBench provides a foundational testbed to accelerate agent-driven scientific discovery in physics and engineering.