dolq-ode-discovery-llm

# DoLQ: LLM-Based ODE Discovery with Qualitative & Quantitative Evaluation > Multi-agent symbolic regression framework that combines LLM-based qualitative evaluation with quantitative metrics to discover governing ODEs from observational data. ## Metadata - **Source**: arXiv:2605.07323 - **Authors**: Sum Kyun Song, Bong Gyun Shin, Jae Yong Lee - **Published**: 2026-05-08 - **Venue**: ICML 2026 ## Core Methodology ### Key Innovation Existing symbolic regression relies primarily on quantitative metrics (fit quality, complexity). Real-world ODE modeling also requires **domain knowledge** for physical plausibility. DoLQ bridges this gap with a multi-agent architecture that evaluates candidates on **both** qualitative and quantitative criteria. ### Multi-Agent Architecture **1. Sampler Agent** - Proposes dynamic system candidates (symbolic ODE forms) - Explores the space of possible equation structures **2. Parameter Optimizer** - Refines proposed equations for numerical accuracy - Optimizes coefficients to minimize prediction error **3. Scientist Agent (LLM-based)** - Conducts **qualitative evaluation**: domain knowledge, physical plausibility, known constraints - Conducts **quantitative evaluation**: fit metrics, error measures, complexity - **Synthesizes** both evaluations to iteratively guide the search ### Search Loop 1. Sampler proposes candidate ODEs 2. Parameter Optimizer fits coefficients 3. Scientist Agent evaluates (qualitative + quantitative) 4. Synthesized feedback guides next iteration of proposals ## Implementation Guide ### Prerequisites - LLM with scientific reasoning capability - Numerical ODE solver (e.g., scipy.integrate) - Symbolic expression representation ### Key Design Patterns - Multi-agent decomposition: separate proposal, optimization, and evaluation - LLM as domain expert: qualitative assessment beyond numerical metrics - Iterative refinement: feedback loop guides search direction - Dual evaluation: both physical plausibility and numerical accuracy ### Evaluation Metrics - Success rate on multi-dimensional ODE benchmarks - Accuracy of recovered symbolic terms vs. ground truth - Comparison with existing symbolic regression methods ## Applications - Scientific discovery of governing equations from data - Physics-informed ML with domain knowledge integration - Automated scientific hypothesis generation - Engineering system identification - Computational biology model discovery ## Pitfalls - LLM qualitative evaluation depends on prompt quality and domain specificity - Requires ground truth for validation — may be unavailable for novel domains - Multi-agent overhead vs. single-agent approaches - Symbolic term recovery accuracy depends on search space definition - Physical plausibility assessment requires well-designed evaluation criteria ## Related Skills - dolq-ode-discovery-llm - pem-ude-neural-governing-equations