Uncovering differential equations from data with hidden variables

02/06/2020
by   Agustín Somacal, et al.
19

Finding a set of differential equations to model dynamical systems is a difficult task present in many branches of science and engineering. We propose a method to learn systems of differential equations directly from data. Our method is based on solving a tailor-made ℓ_1-regularised least-squares problem and can deal with latent variables by adding higher-order derivatives to account for the lack of information. Extensive numerical studies show that our method can recover useful representations of the dynamical system that generated the data even when some variables are not observed. Moreover, being based on solving a convex optimisation problem, our method is much faster than competing approaches based on solving combinatorial problems. Finally, we apply our methodology to a real data-set of temperature time series.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset