Related papers: Analysis of Kinetic Models for Label Switching and…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
Optimal design for model training is a critical topic in machine learning. Active Learning aims at obtaining improved models by querying samples with maximum uncertainty according to the estimation model for artificially labeling; this has…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
As a fundamental problem in machine learning, dataset shift induces a paradigm to learn and transfer knowledge under changing environment. Previous methods assume the changes are induced by covariate, which is less practical for complex…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…
We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then…
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…
The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probable paths is a key issue to understand the mechanism of…
One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Stochastic gradient descent samples uniformly the training set to build an unbiased gradient estimate with a limited number of samples. However, at a given step of the training process, some data are more helpful than others to continue…