Related papers: Dynamically Optimized Wang-Landau Sampling with Ad…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion. We study recovery of an order-$k$ low-rank tensor of dimension $n \times \cdots \times n$ from a subset of its entries. Unlike the standard…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
We introduce adaptive, tuning-free step size schedules for gradient-based sampling algorithms obtained as time-discretizations of Wasserstein gradient flows. The result is a suite of tuning-free sampling algorithms, including tuning-free…
We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating…
We present a new Monte Carlo algorithm based on the Stochastic Approximation Monte Carlo (SAMC) algorithm for directly calculating the density of states. The proposed method is Stochastic Approximation with a Dynamic update factor (SAD)…
In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…
We consider the activated random walk (ARW) model on $\mathbb{Z}^d$, which undergoes a transition from an absorbing regime to a regime of sustained activity. In any dimension we prove that the system is in the active regime when the…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions, and the interaction between wakes. Physics-based models that capture the wake flow-field with high-fidelity are…
A macroscopically constrained Wang-Landau Monte Carlo method was recently proposed to calculate the joint density of states (DOS) for systems with multiple order parameters. Here we demonstrate results for a nearest-neighbor Ising…
In this work we propose a criterion to finish the simulations of the Wang-Landau sampling. Instead of determining a final modification factor for all simulations and every sample sizes, we investigate the behavior of the temperature of the…
We consider a one-dimensional totally asymmetric exclusion process on a ring with extended inhomogeneities, consisting of several segments with different hopping rates. Depending upon the underlying inhomogeneity configurations and for…
Diffusion-based samplers learn to sample complex, high-dimensional distributions using energies or log densities alone, without training data. Yet, they remain impractical for molecular sampling because they are often slower than molecular…
We derive a novel efficient scheme to measure the rate constant of transitions between stable states separated by high free energy barriers in a complex environment within the framework of transition path sampling. The method is based on…
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…
Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…