Related papers: Stochastic diffusion using mean-field limits to ap…

In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as…

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…

Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…

This paper introduces a system of stochastic differential equations (SDE) of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at, and move along, walls, by means of sticky boundaries and boundary…

A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…

Diffusion models are currently the leading generative AI approach used for image generation in e.g. DALL-E and Stable Diffusion. In this talk we relate diffusion models to stochastic quantisation in field theory and employ it to generate…

The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…

Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…

Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…

The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…

In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…

Predicting future states in uncertain environments, such as wildfire spread, medical diagnosis, or autonomous driving, requires models that can consider multiple plausible outcomes. While diffusion models can effectively learn such…

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample…