Enterprise AI Analysis
LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models
This paper introduces LLM-SRBench, a novel and comprehensive benchmark for evaluating Large Language Models (LLMs) in scientific equation discovery. It features 239 challenging problems across four scientific domains, designed to prevent trivial memorization. The benchmark comprises two categories: LSR-Transform, which re-expresses known equations in less common forms, and LSR-Synth, which generates novel, discovery-driven problems with synthetic terms. Through extensive evaluations, the best-performing LLM-based system achieved only 31.5% symbolic accuracy, highlighting the significant challenges and ample room for future research in this field. LLM-SRBench provides a robust framework to assess LLMs' scientific reasoning, data-driven discovery, and generalization capabilities beyond simple recitation.
Key Impact Metrics
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Total Problems
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Max Symbolic Accuracy (LSR-Transform)
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Max Symbolic Accuracy (LSR-Synth)
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LLMs Evaluated
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Overview
LSR-Transform
LSR-Synth
Key Findings
Case Study: Population Growth
The Challenge of Genuine Scientific Discovery with LLMs
Traditional benchmarks for scientific equation discovery often rely on well-known equations, making LLMs vulnerable to memorization rather than true discovery. This leads to inflated performance metrics that do not reflect genuine scientific reasoning. LLM-SRBench addresses this by introducing novel problem categories designed to test reasoning beyond memorized forms and to require data-driven discovery. It aims to foster the development of LLM-based methods that can truly leverage embedded scientific knowledge for hypothesis generation and refinement.
LLM-based Scientific Equation Discovery Workflow
Goal / Instruction
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Scientific Context
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Prompt Input/Feedback Generation
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Hypothesis Generation
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Parameter Optimization
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Evaluation
31.5%
Highest Symbolic Accuracy Achieved So Far
This metric highlights the significant challenge LLMs face in achieving true symbolic accuracy on novel and transformed scientific problems, underscoring the early stage of this research area.
Beyond Memorization: The LSR-Transform Dataset
LSR-Transform challenges LLMs to discover equations in less common mathematical forms by transforming common physical models into alternative representations. This prevents reliance on memorization and tests the LLM's ability to reason through unfamiliar instantiations of otherwise familiar problems. It comprises 111 transformed equations from the Feynman benchmark, each sharing the same scientific context but presenting a less common mathematical form to be discovered.
| Method | Symbolic Accuracy (%) | Numeric Precision (Acc0.1 %) |
|---|---|---|
| LLM-SR (GPT-40-mini) | 31.53 | 39.64 |
| LaSR (GPT-3.5-turbo) | 12.61 | 47.74 |
| SGA (GPT-40-mini) | 9.91 | 8.11 |
| Direct Prompting (GPT-40-mini) | 7.21 | 6.306 |
Uncovering Novelty: The LSR-Synth Dataset
LSR-Synth assesses LLMs' capacity to discover equations that incorporate new synthetic terms alongside known scientific terms. This demands genuine data-driven reasoning and scientific knowledge beyond memorization, as the problems introduce novel and plausible variations. It features 128 problems spanning chemistry, biology, physics, and material science, all carefully designed for solvability, meaningful physical behavior, and uniqueness.
| Method | Symbolic Accuracy (%) | Numeric Precision (Acc0.1 %) |
|---|---|---|
| LLM-SR (GPT-40-mini) | 11.11 (Chemistry) | 52.77 (Chemistry) |
| LaSR (Llama-3.1-8B-Instruct) | 28.12 (Material Science) | 72.04 (Material Science) |
| SGA (GPT-40-mini) | 4.16 (Physics) | 12.51 (Physics) |
| Direct Prompting (GPT-40-mini) | 4.54 (Physics) | 9.09 (Physics) |
LLM-SRBench: Highlighting the Path Forward
The overall low performance across all methods (peak 31.5% symbolic accuracy) underscores the inherent difficulty of genuine scientific equation discovery for LLMs. This benchmark reveals that current approaches may be fundamentally limited in their ability to perform genuine scientific discovery, requiring a more complex interplay of domain knowledge, search capabilities with data-driven feedback, and mathematical manipulation skills. It provides a robust framework for future research to develop more advanced LLM-based discovery systems.
| Method | SA (%) | Acc0.1 (%) |
|---|---|---|
| LLM-SR (best) | 31.53 | 39.64 |
| LaSR (best) | 28.12 | 72.04 |
| SGA (best) | 9.91 | 36.11 |
| PySR | 8.11 | 56.76 |
Case Study: LLMs Tackling Population Dynamics (BPG0)
Challenge: The BPG0 problem from LSR-Synth Biology dataset requires discovering a population growth equation with both known ecological terms and synthetic, novel interactions. This tests the LLM's ability to combine prior knowledge with data-driven insights to model complex, unobserved phenomena.
Approach: Different LLM-based methods employ varied strategies. Direct Prompting might generate basic logistic growth models, while LLM-SR and LaSR leverage iterative refinement and concept learning to integrate more complex synthetic terms and periodicity, as shown in Figure 14 (d).
Result: The ground truth for BPG0 is dP/dt = 0.9540 * (1 - P/96.9069) * P + 0.9540 * P. LLM-SR (Llama-3.1-8b) produced an equation that included parameters for logistic growth and additional power law and interaction terms (P* (1-P) + P*P**params[3]), demonstrating an attempt to capture both known and synthetic dynamics. This shows an LLM's capacity to build upon foundational models while exploring novel mathematical structures.
Takeaway: This case study underscores the LLMs' potential to combine fundamental scientific principles with data-driven adaptations for novel scenarios, which is crucial for genuine scientific discovery. However, achieving precise symbolic matches for complex synthetic terms remains a challenge.
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