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A fundamental challenge in developing data-driven approaches to ecological systems for tasks such as state estimation and prediction is the paucity of the observational or measurement data. For example, modern machine-learning techniques…
We consider a linearized dynamical system modelling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model…
We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…
Earth and soils are indispensable elements of river environment. Dam-downstream environment and ecosystems have been severely affected by reduced or even stopped sediment supply from the upstream. Replenishing earth and soils from outside…
One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are…
Understanding the interaction between turbulence and zonal flows is critical for modeling turbulence transport in fusion plasmas, often described through predator-prey dynamics. However, traditional deterministic models like the…
We introduce and test a general machine-learning-based technique for the inference of short term causal dependence between state variables of an unknown dynamical system from time series measurements of its state variables. Our technique…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…
Analyzing when noisy trajectories, in the two dimensional plane, of a stochastic dynamical system exit the basin of attraction of a fixed point is specifically challenging when a periodic orbit forms the boundary of the basin of attraction.…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…
The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
Generative Flow Networks (or GFlowNets for short) are a family of probabilistic agents that learn to sample complex combinatorial structures through the lens of "inference as control". They have shown great potential in generating…
We present a numerical framework for learning unknown stochastic dynamical systems using measurement data. Termed stochastic flow map learning (sFML), the new framework is an extension of flow map learning (FML) that was developed for…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…