Related papers: Solving time dependent Fokker-Planck equations via…

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable…

The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $\alpha$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications,…

We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in…

A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…

A common issue in simulating geometric evolution of surfaces is unexpected clustering of points that may cause numerical instability. We propose a novel artificial tangential velocity method for this matter. The artificial tangential…

Time series forecasting plays a central role in many real-world applications and has been extensively studied. Most existing approaches rely on deterministic models. However, real-world environments exhibit inherently uncertain and complex…

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…

In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces.…

Personalized federated learning algorithms have shown promising results in adapting models to various distribution shifts. However, most of these methods require labeled data on testing clients for personalization, which is usually…

Predictive models of the future are fundamental for an agent's ability to reason and plan. A common strategy learns a world model and unrolls it step-by-step at inference, where small errors can rapidly compound. Geometric Horizon Models…

We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…

We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…

Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement…

In this paper we develop a method to solve evolution equations on Gelfand triples with time-fractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasi-linear partial differential…

Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional…

Estimating time-resolved velocity and pressure fields from Particle Image Velocimetry (PIV) remains challenging due to its limited temporal resolution in many applications. Data-driven approaches that combine snapshot PIV with…

In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract…

In this work we present new exact similarity solutions with moving boundaries of the Fokker-Planck equation having both time-dependent drift and diffusion coefficients.

We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict…

We present a machine-learning approach, based on normalizing flows, for modelling atomic solids. Our model transforms an analytically tractable base distribution into the target solid without requiring ground-truth samples for training. We…