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Form a pure mathematical point of view, common functional forms representingdifferent physical phenomena can be defined. For example, rates of chemicalreactions, diffusion and heat transfer are all governed by exponential-typeexpressions. If machine learning is used for physical problems, inferred fromdomain knowledge, original features can be transformed in such a way that theend 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 byapproaching a problem from an agnostic position and propose a systematic anditerative methodology to discover theories underlying physical phenomena. Atfirst, commonly observed functional forms of theoretical expressions are usedto transform original features before conducting correlation analysis tooutput. Using random combinations of highly correlated expressions, training ofNeural Networks (NN) are performed. By comparing the rates of convergence ormean error in training, expressions describing the underlying physical problemscan be discovered, leading to extracting explicit analytic equations. Thisapproach was used in three blind demonstrations for different physicalphenomena.

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