Problem
Research questions and friction points this paper is trying to address.
Partial Differential Equations
Neural PDE Solvers
Automated Research
LLM Agents
Architecture Design
AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design
🤖 AI Summary
This study addresses the challenge that architectural design for neural PDE solvers heavily relies on expert knowledge and is highly time-consuming. To overcome this, we propose leveraging a multi-agent collaborative system based on large language models (LLMs) to automatically synthesize specialized solvers. Methodologically, we construct the first LLM-based automated research benchmark dedicated to PDE solver design and introduce an iterative multi-agent pipeline grounded in Transformers and graph neural networks as a baseline. Experimental results demonstrate that this iterative automated research system significantly outperforms general-purpose baselines. These findings validate the feasibility of employing AI agents in scientific discovery and establish a novel paradigm for automated research.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
AutoPDEBench
LLM-driven automated research
Neural PDE solvers
Multi-agent system
Autonomous AI research agents
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