LLM-PDESR framework uses LLMs to improve PDE discovery from noisy data

Researchers have developed LLM-PDESR, a new framework designed to improve the discovery of partial differential equations (PDEs) from noisy data. This method combines the symbolic hypothesis generation capabilities of Large Language Models (LLMs) with a robust evaluation environment. LLM-PDESR utilizes C^4-continuous quintic splines for accurate differentiation and subdomain weighted residuals to filter out noise, thereby creating a more stable fitness landscape for optimization. The framework was tested on 23 canonical PDEs and five novel equations, demonstrating superior performance in structural recovery and noise resilience compared to existing methods. It was also successfully applied to extract a dynamical surrogate from noisy ERA5 reanalysis data. AI

IMPACT This framework could accelerate scientific discovery by improving the accuracy and efficiency of extracting governing equations from complex datasets.

RANK_REASON This is a research paper detailing a new computational framework for scientific machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

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• 1D-CACE
• ERA5
• Large Language Models
• LLM-PDESR
• partial differential equations

• paper
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