Related papers: Recovering Hidden Degrees of Freedom Using Gaussia…

Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…

Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…

State-space graphical models and the variational autoencoder framework provide a principled apparatus for learning dynamical systems from data. State-of-the-art probabilistic approaches are often able to scale to large problems at the cost…

Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach…

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

We present a unified view of likelihood based Gaussian progress regression for simulation experiments exhibiting input-dependent noise. Replication plays an important role in that context, however previous methods leveraging replicates have…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…

Alzheimer's disease is a major cause of dementia. Its diagnosis requires accurate biomarkers that are sensitive to disease stages. In this respect, we regard probabilistic classification as a method of designing a probabilistic biomarker…

The Gaussian Process (GP) assumption is often used in functional data analysis. We propose a method to assess departures from the GP assumption, both in terms of the shape of the distribution and its potential dependence on covariates,…

We present a way to dramatically accelerate Gaussian process models for interatomic force fields based on many-body kernels by mapping both forces and uncertainties onto functions of low-dimensional features. This allows for automated…

We develop a robust data fusion algorithm for field reconstruction of multiple physical phenomena. The contribution of this paper is twofold: First, we demonstrate how multi-spatial fields which can have any marginal distributions and…