Abstract
In the context of science, the well-known adage ä picture is worth a
thousand words" might well be ä model is worth a thousand datasets."
Scientific models, such as Newtonian physics or biological gene regulatory
networks, are human-driven simplifications of complex phenomena that serve as
surrogates for the countless experiments that validated the models. Recently,
machine learning has been able to overcome the inaccuracies of approximate
modeling by directly learning the entire set of nonlinear interactions from
data. However, without any predetermined structure from the scientific basis
behind the problem, machine learning approaches are flexible but
data-expensive, requiring large databases of homogeneous labeled training data.
A central challenge is reconciling data that is at odds with simplified models
without requiring "big data".
In this work we develop a new methodology, universal differential equations
(UDEs), which augments scientific models with machine-learnable structures for
scientifically-based learning. We show how UDEs can be utilized to discover
previously unknown governing equations, accurately extrapolate beyond the
original data, and accelerate model simulation, all in a time and
data-efficient manner. This advance is coupled with open-source software that
allows for training UDEs which incorporate physical constraints, delayed
interactions, implicitly-defined events, and intrinsic stochasticity in the
model. Our examples show how a diverse set of computationally-difficult
modeling issues across scientific disciplines, from automatically discovering
biological mechanisms to accelerating the training of physics-informed neural
networks and large-eddy simulations, can all be transformed into UDE training
problems that are efficiently solved by a single software methodology.
Users
Please
log in to take part in the discussion (add own reviews or comments).