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PINNsAgent: Automated PDE Surrogation with Large Language Models
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Introduces PINNsAgent, an LLM-agent framework that automatically tunes PINN architectures and hyperparameters for PDEs using physics-guided retrieval of past configurations (PGKR) and MCTS-style memory tree search (MTRS).
Problem
Designing effective PINN architectures and hyperparameters requires expert knowledge and extensive manual trial-and-error, limiting non-expert use of PINNs for solving PDEs.
Approach
A multi-agent LLM framework (database, planner, programmer, code bank) that warm-starts PINN hyperparameter search by retrieving the best configurations of similar PDEs via weighted cosine similarity over PDE physics features, then explores the configuration space with a UCT-based memory tree guided by the LLM planner.
Key results
- PINNsAgent achieves the best MSE on 12 of 14 PDEs versus Random and Bayesian search, e.g., NS-C 8.50E-06 vs 4.02E-03 (random) and 5.12E-03 (Bayesian).
- Ablation on 12 PDEs shows removing PGKR and MTRS raises GS MSE from 4.31E-03 to 2.59E+08.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PINNsAgent instead of the strongest reported baseline | PINNsAgent · 14 PDEs in Table 1 | MSE | Mixed |
| Add PGKR to the framework (ablation) | PINNsAgent · Most of 12 PDEs in the ablation study | MSE | Helped |
| Add PGKR to the framework (ablation) | PINNsAgent · Wave-C and Wave-CG | MSE: 3.33E-02 -> 2.87E-02; 5.40E-02 -> 3.19E-02 | Hurt |
| Add MTRS alongside PGKR (ablation) | PINNsAgent · GS | MSE: 2.59E+08 -> 4.31E-03 | Helped |
| Add MTRS alongside PGKR (ablation) | PINNsAgent · Heat-CG | MSE: 6.97E-02 -> 1.80E-03 | Helped |
| Add PGKR and MTRS (ablation) | PINNsAgent · Wave-CG | MSE: 3.19E-02 -> 5.40E-02 | Hurt |
| Add PGKR and MTRS (ablation) | PINNsAgent · Poisson-ND | MSE: 2.43E-05 -> 2.09E-06 | Helped |
Surprising findings
- On Heat-ND, PINNsAgent reports MSE 3.51E-07 while the PINNacle reference is 8.52E+00, and on several PDEs the agent is worse than the PINNacle reference (e.g., Burgers-C, Poisson-MA).
Limitations
- Evaluated only on hyperparameter optimization task with a fixed search space; Config Generation mode for PDEs already in the code bank is the main focus.
- Only GPT-4 tested; results rely on a single LLM backbone and no other LLMs reported.
- Inconsistencies: text says 20 PDEs in database and 14 evaluated, ablation reports 12 PDEs, and the Table 1 Poisson-MA and Heat-ND results are weaker than the PINNacle reference in some cases.
Experimental setup
Datasets: PINNacle benchmark 3000 PINN experiment logs
Benchmarks: PINNacle benchmark (14 PDEs in Table 1)
Metrics: MSE standard deviation over 10 runs
Baselines: Random Search Bayesian Search PINNacle benchmark best results
Builds on: PINNs PINNacle Monte Carlo Tree Search UCT experience replay
Closest papers by meaning
- PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks (ICLR 2024 · similarity 0.90)
- PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs (NeurIPS 2024 · similarity 0.89)
- Sub-Sequential Physics-Informed Learning with State Space Model (ICML 2025 · similarity 0.89)
- RoPINN: Region Optimized Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.88)
- Efficient Error Certification for Physics-Informed Neural Networks (ICML 2024 · similarity 0.88)
- Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective (NeurIPS 2025 · similarity 0.88)
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