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Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…

Human motion prediction is a stochastic process: Given an observed sequence of poses, multiple future motions are plausible. Existing approaches to modeling this stochasticity typically combine a random noise vector with information about…

We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…

Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…

A fundamental feature of complex biological systems is the ability to form feedback interactions with their environment. A prominent model for studying such interactions is reservoir computing, where learning acts on low-dimensional…

A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…

Diffusion models have emerged as the de facto choice for generating high-quality visual signals across various domains. However, training a single model to predict noise across various levels poses significant challenges, necessitating…

Noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. While the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it…

Spectrum analysis systems in online water quality testing are designed to detect types and concentrations of pollutants and enable regulatory agencies to respond promptly to pollution incidents. However, spectral data-based testing devices…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Recently, video recognition is emerging with the help of multi-modal learning, which focuses on integrating distinct modalities to improve the performance or robustness of the model. Although various multi-modal learning methods have been…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

Often, the data used to train ranking models is subject to label noise. For example, in web-search, labels created from clickstream data are noisy due to issues such as insufficient information in item descriptions on the SERP, query…

Numerous empirical evidence has corroborated that the noise plays a crucial rule in effective and efficient training of neural networks. The theory behind, however, is still largely unknown. This paper studies this fundamental problem…

Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…

Reservoir computation is a recurrent framework for learning and predicting time series data, that benefits from extremely simple training and interpretability, often as the the dynamics of a physical system. In this paper, we will study the…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

We analyze order-disorder phase transitions driven by noise that occur in two kinds of network models closely related to the self-propelled model proposed by Vicsek et. al. to describe the collective motion of groups of organisms…

Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is…