Related papers: High-Dimensional Enhanced Sampling via Regularized…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…
Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and…
We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…
Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations…
Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…
Approximate inference in Bayesian deep networks exhibits a dilemma of how to yield high fidelity posterior approximations while maintaining computational efficiency and scalability. We tackle this challenge by introducing a novel…
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Molecular dynamics (MD) simulations are useful in obtaining thermodynamic and kinetic properties of bio-molecules but are limited by the timescale barrier, i.e., we may be unable to efficiently obtain properties because we need to run…
Many biological processes occur on time scales longer than those accessible to molecular dynamics simulations. Identifying collective variables (CVs) and introducing an external potential to accelerate them is a popular approach to address…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples…
Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…
Threshold biasing of a Gaussian random field gives a linear amplification of the reduced two point correlation function at large distances. We show that for standard cosmological models this does not translate into a linear amplification of…
Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…
We investigate a dynamic inverse problem using a regularization which implements the so-called Wasserstein-$1$ distance. It naturally extends well-known static problems such as lasso or total variation regularized problems to a (temporally)…