Data-based Discovery of Governing Equations

by   Waad Subber, et al.

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.



There are no comments yet.


page 1

page 2

page 3

page 4


Probabilistic Grammars for Equation Discovery

Equation discovery, also known as symbolic regression, is a type of auto...

Data-driven Identification of 2D Partial Differential Equations using extracted physical features

Many scientific phenomena are modeled by Partial Differential Equations ...

Dominant motion identification of multi-particle system using deep learning from video

Identifying underlying governing equations and physical relevant informa...

An Iterative Scientific Machine Learning Approach for Discovery of Theories Underlying Physical Phenomena

Form a pure mathematical point of view, common functional forms represen...

Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data

Although deep-learning has been successfully applied in a variety of sci...

The synthesis of data from instrumented structures and physics-based models via Gaussian processes

A recent development which is poised to disrupt current structural engin...

Automated Mathematical Equation Structure Discovery for Visual Analysis

Finding the best mathematical equation to deal with the different challe...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.