Related papers: Learning Stochastic Behaviour from Aggregate Data
Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…
One of the significant problems of streaming data classification is the occurrence of concept drift, consisting of the change of probabilistic characteristics of the classification task. This phenomenon destabilizes the performance of the…
This letter presents a high-dimensional analysis of the training dynamics for a single-layer nonlinear contrastive learning model. The empirical distribution of the model weights converges to a deterministic measure governed by a…
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…
Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the Fokker-Planck equation as a system of…
We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…
We describe the application of tools from statistical mechanics to analyse the dynamics of various classes of supervised learning rules in perceptrons. The character of this paper is mostly that of a cross between a biased non-encyclopedic…
New technologies for recording the activity of large neural populations during complex behavior provide exciting opportunities for investigating the neural computations that underlie perception, cognition, and decision-making. Nonlinear…
Sampling invariant distributions from an It\^o diffusion process presents a significant challenge in stochastic simulation. Traditional numerical solvers for stochastic differential equations require both a fine step size and a lengthy…
The realistic modeling intended to quantify precisely some biological mechanisms is a task requiering a lot of a priori knowledge and generally leading to heavy mathematical models. On the other hand, the structure of the classical Machine…
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…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
Deep learning-based trajectory prediction models for autonomous driving often struggle with generalization to out-of-distribution (OOD) scenarios, sometimes performing worse than simple rule-based models. To address this limitation, we…
This paper aims to investigate the non-Markovian dynamics. The governing equations are derived for the probability density functions (PDFs) of non-Markovian stochastic responses to Langevin equation excited by combined fractional Gaussian…
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…
In this paper we suggest a consistent approach to derivation of generalized Fokker-Planck equation (GFPE) for Gaussian non-Markovian processes with stationary increments. This approach allows us to construct the probability density function…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…