
Universal Differential Equations for Scientific Machine Learning - formalsystem
https://arxiv.org/abs/2001.04385
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ipnon
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."

