AI agents create specialized neural solvers for complex physics modeling
AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design
Computational Engineering, Finance, and ScienceArtificial Intelligence
Summary
Solving complex physical problems often requires specialized tools that take a long time to design. The authors introduce a new benchmark called AutoPDEBench to test AI systems that automatically design these tools, called neural PDE solvers, for different physical scenarios. They show that an AI system that iteratively improves solver designs works better than standard approaches. This makes it easier and faster to build solvers that handle tricky situations like changing parameters or fast flows.
What this means in practice
- •For engineering simulation teams: Design tailored neural PDE solvers for specific engineering problems without extensive manual tuning.
- •For software developers in computational physics: Integrate AI-driven automated solver design tools to speed up development of physics simulation software.
Authors
Ruoyan Li, Wei Wang, Yizhou Sun
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.