Related papers: A Geometric Framework for Stochastic Shape Analysi…

This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…

The Fokker-Plank-Kolmogorov (FPK) equation is an idealized model representing many stochastic systems commonly encountered in the analysis of stochastic structures as well as many other applications. Its solution thus provides an invaluable…

Capturing the shape and spatially-varying appearance (SVBRDF) of an object from images is a challenging task that has applications in both computer vision and graphics. Traditional optimization-based approaches often need a large number of…

The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of…

For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means…

In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…

This paper proposes a probabilistic motion prediction method for long motions. The motion is predicted so that it accomplishes a task from the initial state observed in the given image. While our method evaluates the task achievability by…

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary…

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…

This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages a recent model for probabilities \cite{rudi2021psd} (the…

Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic…

In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…

Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct…

We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective…

Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated…

We introduce in this paper a learning paradigm in which the training data is transformed by a diffeomorphic transformation before prediction. The learning algorithm minimizes a cost function evaluating the prediction error on the training…