Enforcing sparse structure within learning has led to significant advances in the field of data-
driven discovery of dynamical systems. However, such methods require access not only to …

Complex dynamical systems are notoriously difficult to model because some degrees of
freedom (eg, small scales) may be computationally unresolvable or are incompletely …

Although the governing equations of many systems, when derived from first principles, may
be viewed as known, it is often too expensive to numerically simulate all the interactions they …

We introduce a novel approach for decomposing and learning every scale of a given
multiscale objective function in R d, where d⩾ 1. This approach leverages a recently …

In many physical, technological, social, and economic applications, one is commonly faced
with the task of estimating statistical properties, such as mean first passage times of a …

We study the problem of drift estimation for two-scale continuous time series. We set
ourselves in the framework of overdamped Langevin equations, for which a single-scale …

We consider the problem of estimating unknown parameters in stochastic differential
equations driven by colored noise, which we model as a sequence of Gaussian stationary …

Motivated by the challenge of incorporating data into misspecified and multiscale dynamical
models, we study a McKean–Vlasov equation that contains the data stream as a common …

In many applications it is desirable to infer coarse-grained models from observational data.
The observed process often corresponds only to a few selected degrees of freedom of a …

We consider the setting of multiscale overdamped Langevin stochastic differential
equations, and study the problem of learning the drift function of the homogenized dynamics …