AutoPDE agent achieves 54.5% pass rate on PDE solving benchmark
AutoPDE is a code agent that explicitly represents solver strategies as inspectable objects before writing code, achieving a 54.5% pass rate on PDE Agent Bench — a 14.2 percentage point improvement over the strongest baseline.
Score breakdown
AutoPDE's explicit strategy representation closes a key gap in LLM-based PDE solvers, where numerical decisions previously remained hidden in code and were difficult to inspect or correct when solves failed.
- 01AutoPDE maintains a solver strategy as an explicit, inspectable object built before any code is written.
- 02When a solve fails, the strategy object — not just the code — can be revised using numerical evidence.
- 03The agent operates in three stages: PDE analysis, numerical method selection, and adaptive tuning.
Numerical solvers for partial differential equations (PDEs) are foundational tools in science and engineering, but building reliable ones requires careful decisions about discretization, stabilization, solver configuration, and resolution control. Recent LLM-based coding agents have reduced the programming burden by generating and debugging solver code, but they typically move directly from a PDE problem to implementation, leaving the solver strategy implicit. When a solve fails, feedback is routed back to code edits rather than to the underlying numerical strategy, making those decisions hard to inspect before code is written and hard to revise using numerical evidence after failure.
AutoPDE addresses this by maintaining the solver strategy as an explicitly represented, independent, inspectable object that is constructed before any code is written and can be revised whenever a solve fails.
AutoPDE addresses this by maintaining the solver strategy as an explicitly represented, independent, inspectable object that is constructed before any code is written and can be revised whenever a solve fails. The agent operates in three stages, all drawing from a library of reusable PDE-solving skills: PDE analysis identifies the equation type and algebraic structure; numerical method selection chooses a method matching that analysis and commits to a discretization, stabilization, and linear solver; and adaptive tuning runs low-cost pilot solves to calibrate resolution and tolerances within a prescribed accuracy and runtime budget.
Evaluated on PDE Agent Bench, AutoPDE achieves a pass rate of 54.5%, improving over the strongest baseline by 14.2 percentage points. The paper was authored by Huanshuo Dong, Keyao Zhang, and Hong Wang and published on ArXiv on June 9, 2026.
Key facts
- 01AutoPDE maintains a solver strategy as an explicit, inspectable object built before any code is written.
- 02When a solve fails, the strategy object — not just the code — can be revised using numerical evidence.
- 03The agent operates in three stages: PDE analysis, numerical method selection, and adaptive tuning.
- 04Adaptive tuning runs low-cost pilot solves to calibrate resolution and tolerances within a prescribed accuracy and runtime budget.
- 05All three stages draw from a library of reusable PDE-solving skills.
- 06AutoPDE achieves a 54.5% pass rate on PDE Agent Bench.
- 07This represents a 14.2 percentage point improvement over the strongest baseline.
Topics
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