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

arXiv:2609.32245v1 Announce Type: cross Abstract: 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.

Abstract: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.

Computational Engineering, Finance, and Science (cs.CE); Artificial Intelligence (cs.AI)

arXiv:2609.32245 [cs.CE]

(or arXiv:2609.32245v1 [cs.CE] for this version)

https://doi.org/10.48550/arXiv.2609.32245 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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

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