DoLQ method uses LLMs to discover differential equations from data
Multi-agent system outperforms symbolic regression by adding qualitative checks
A team of researchers (Sum Kyun Song, Bong Gyun Shin, Jae Yong Lee) has introduced DoLQ, a novel method for discovering governing differential equations from observational data. Published on arXiv and accepted at ICML 2026, DoLQ addresses a key limitation of traditional symbolic regression: reliance solely on numerical accuracy without considering physical plausibility. The method employs a multi-agent LLM architecture where a Sampler Agent generates candidate dynamic systems, a Parameter Optimizer fits the equations to data, and a Scientist Agent uses an LLM to evaluate both quantitative fit and qualitative physical soundness, then synthesizes results to guide iterative search.
On multi-dimensional ODE benchmarks, DoLQ significantly outperforms existing symbolic regression methods, achieving higher success rates and more accurate recovery of correct symbolic terms. This hybrid approach combines the pattern-matching power of LLMs with rigorous numerical optimization, enabling the discovery of equations that are not only mathematically accurate but also physically meaningful. The code is publicly available. The work highlights a promising direction for integrating LLMs into scientific discovery workflows.
- DoLQ uses a multi-agent system: Sampler Agent, Parameter Optimizer, and Scientist Agent (LLM) for iterative equation discovery
- Achieves higher success rates and more accurate symbolic term recovery on multi-dimensional ODE benchmarks than existing methods
- Accepted at ICML 2026; code open-sourced for reproducibility
Why It Matters
Brings LLM reasoning into scientific model discovery, improving both accuracy and physical plausibility of discovered equations.