Universal Differential Equations for Scientific Machine Learning

Significance statement:

"Incorporation of prior scientific knowledge into learnable structures could allow for a new form of machine learning that is data-efficient: thereby side stepping the issue of acquiring large expensive datasets by utilizing the condensed knowledge of the scientific literature. This manuscript develops a novel learning framework, the universal differential equation, which allows for machine-learning-augmented scientific models. We showcase the ability to incorporate prior scientific knowledge and train accurate neural architectures with small data. We demonstrate how the method is interpretable [sic] back to mechanistic equations and how it can accelerate climate simulations by 15,000x. The broad applications coupled with a software implementation demonstrates a viable path for small-data scientific machine learning."