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We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…
An extension of the CCS-method [Chem. Phys. 2004, 304, p. 103-120] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schr\"{o}dinger equation for the motion of the nuclei is solved…
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer science, and learning theory. In this paper, we consider centered…
The Replica Exchange Wang-Landau Method is used to estimate the energy landscape of a polymer composed of a simple hydrophobic and polar sequence using the HP protein model. Calculations of state transitions between the energy levels of the…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an…
In many systems, the time scales of the microscopic dynamics and macroscopic dynamics of interest are separated by many orders of magnitude. Examples abound, for instance nucleation, protein folding, and chemical reactions. For these…
Microstructure reconstruction and compression techniques are designed to find a microstructure with desired properties. While the microstructure reconstruction searches for a microstructure with prescribed statistical properties, the…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
The cross-slip process of a screw $<$a$>$ dislocation from the basal to the prismatic plane in magnesium was studied using the density functional theory and the molecular dynamics calculations. An atomistic method for calculating the total…
This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…
Barrier functions are crucial for maintaining an intersection and inversion free simulation trajectory but existing methods which directly use distance can restrict implementation design and performance. We present an approach to rewriting…
In this paper we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white…
A first-principles coupled electron-nuclear dynamics simulation based on real-time, time-dependent density functional theory and Ehrenfest dynamics quantitatively repro-duces bimodal translational energy loss and angular distributions…
We use our recently proposed accelerated dynamics algorithm (Tiwary & van de Walle, 2011) to calculate temperature and stress dependence of activation free energy for surface nucleation of dislocations in pristine Gold nanopillars under…
Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
In recent times, the utilization of 3D models has gained traction, owing to the capacity for end-to-end training initially offered by Neural Radiance Fields and more recently by 3D Gaussian Splatting (3DGS) models. The latter holds a…
We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type…
Hierarchical computational methods for multiscale mechanics such as the FE$^2$ and FE-FFT methods are generally accompanied by high computational costs. Data-driven approaches are able to speed the process up significantly by enabling to…