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Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

In multistable dynamical systems driven by weak Gaussian noise, transitions between competing states are often assumed to pass via a saddle on the separating basin boundary. By contrast, we show that timescale separation can cause saddle…

An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their…

Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have…

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian…

Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…

Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of…

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…

A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…