An Iterative Scientific Machine Learning Approach for Discovery of Theories Underlying Physical Phenomena
This work addresses the challenge of theory discovery in physics for researchers, offering a systematic method that could reduce training effort, though it appears incremental as it builds on existing ideas of feature transformation and correlation analysis.
The authors tackled the problem of discovering explicit analytic equations underlying physical phenomena by proposing an iterative scientific machine learning approach that transforms features based on common functional forms and uses neural networks to identify highly correlated expressions, resulting in successful demonstrations across three different physical phenomena.
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type expressions. If machine learning is used for physical problems, inferred from domain knowledge, original features can be transformed in such a way that the end expressions are highly aligned and correlated with the underlying physics. This should significantly reduce the training effort in terms of iterations, architecture and the number of required data points. We extend this by approaching a problem from an agnostic position and propose a systematic and iterative methodology to discover theories underlying physical phenomena. At first, commonly observed functional forms of theoretical expressions are used to transform original features before conducting correlation analysis to output. Using random combinations of highly correlated expressions, training of Neural Networks (NN) are performed. By comparing the rates of convergence or mean error in training, expressions describing the underlying physical problems can be discovered, leading to extracting explicit analytic equations. This approach was used in three blind demonstrations for different physical phenomena.