Related papers: High-Dimensional Enhanced Sampling via Regularized…
We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington-Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature $\beta < 1/2$. Prior work obtained TVD error guarantees…
Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is…
We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy…
The energy-conserving sampling and weighting (ECSW) method is a hyperreduction method originally developed for accelerating the performance of Galerkin projection-based reduced-order models (PROMs) associated with large-scale finite element…
This article develops a general-purpose adaptive sampler that approximates the target density by a mixture of multivariate t densities. The adaptive sampler is based on reversible proposal distributions each of which has the mixture of…
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…
Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research,…
Performing k-space variable density sampling is a popular way of reducing scanning time in Magnetic Resonance Imaging (MRI). Unfortunately, given a sampling trajectory, it is not clear how to traverse it using gradient waveforms. In this…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
The bottleneck in enhanced sampling lies in finding collective variables (CVs) that can effectively accelerate protein conformational changes. True reaction coordinates (tRCs) that can predict the committor are considered the optimal CVs,…
Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational…
Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…
Variational inference with normalizing flows (NFs) is an increasingly popular alternative to MCMC methods. In particular, NFs based on coupling layers (Real NVPs) are frequently used due to their good empirical performance. In theory,…
A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods…
Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…
A deterministic-stochastic coupling scheme is developed for simulating rarefied gas flows, where the key process is the alternative solving of the macroscopic synthetic equations [Su et al., J. Comput. Phys., 407 (2020) 109245] and the…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
We propose a mathematical framework to explain implicit regularization from early stopping during the training of overparametrized neural networks. In the mean-field limit, the parameter distribution evolves according to a gradient flow on…
The use of accelerated sampling methods such as metadynamics has shown significant advantage in calculations that involve infrequent events, which would otherwise require sampling a prohibitive number of configurations to determine, e.g.,…
We present a new method for sampling the Levy area for a two-dimensional Wiener process conditioned on its endpoints. An efficient sampler for the Levy area is required to implement a strong Milstein numerical scheme to approximate the…