Data-based Discovery of Governing Equations

TL;DR

This paper introduces a Data-based Physics Discovery framework that automatically uncovers governing equations from observed data, integrating prior models and expert feedback, demonstrated on aerospace data.

Contribution

The paper presents a novel framework for automatic discovery of governing equations that combines data-driven methods with prior physical models and expert input.

Findings

Successfully discovered governing equations from real-world aerospace data.

Can incorporate prior models and refine them with correction terms.

Effective in both data-rich and data-scarce scenarios.

Abstract

Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly describing the underlying physical process that generated the data. We propose a Data-based Physics Discovery (DPD) framework for automatic discovery of governing equations from observed data. Without a prior definition of the model structure, first a free-form of the equation is discovered, and then calibrated and validated against the available data. In addition to the observed data, the DPD framework can utilize available prior physical models, and domain expert feedback. When prior models are available, the DPD framework can discover an additive or multiplicative correction term represented symbolically. The correction term can be a function of the existing input variable to the prior model, or a newly introduced variable. In case a prior model is not available, the DPD framework discovers a new data-based standalone model governing the observations. We demonstrate the performance of the proposed framework on a real-world application in the aerospace industry.