Related papers: A Variational Approach to Enhanced Sampling and Fr…
We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution to the energy, which is intrinsically non-local. Under…
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…
A simple, efficient, and accurate method is proposed to map multi-dimensional free energy landscapes. The method combines the temperature-accelerated molecular dynamics (TAMD) proposed in [Maragliano & Vanden-Eijnden, Chem. Phys. Lett. 426,…
Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently metadynamics was shown to be mathematically well…
The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested towards its solution. These methods are often grouped into two broad families. On the one hand…
A simple modification of the Monte-Carlo algortihm is proposed to explore the topography and the scaling of the energy landscape. We apply this idea to a simple hard-core fluid. The results for different packing fractions show a power law…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation…
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
In this PhD thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary…
We study Monte Carlo calculations of the effective potential for a scalar field theory using three techniques. One of these is a new method proposed and tested for the first time. In each case we extract the renormalised quantities of the…
Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the…
First principles calculations based on density functional theory are having an incerasing impact on our understanding of molecule-surface interactions. For example, calculations of the multi-dimensional potential energy surface have…
Studies aimed at understanding the global properties of the hyperpolarizabilities have focused on identifying universal properties when the hyperpolarizabilities are at the fundamental limit. These studies have taken two complimentary…
This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential $V$ to be computed using a Monte Carlo simulation for a…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…