Related papers: Variance Reduction Result for a Projected Adaptive…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
External biasing forces are often applied to enhance sampling in regions of phase space which would otherwise be rarely observed. While the typical goal of these experiments is to calculate the potential of mean force (PMF) along the…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
We present a generalisation of Rosenblatt's traditional perceptron learning algorithm to the class of proximal activation functions and demonstrate how this generalisation can be interpreted as an incremental gradient method applied to a…
We propose an experimental approach for determining thermodynamic properties of ultracold atomic gases with short-range interactions. As a test case, we focus on the one-dimensional (1D) Bose gas described by the integrable Lieb-Liniger…
In [Meurant, Pape\v{z}, Tich\'y; Numerical Algorithms 88, 2021], we presented an adaptive estimate for the energy norm of the error in the conjugate gradient (CG) method. In this paper, we extend the estimate to algorithms for solving…
Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…
A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…
We introduce in this paper a new approach to the problem of the convergence to equilibrium for kinetic equations. The idea of the approach is to prove a 'weak' coercive estimate, which implies exponential or polynomial convergence rate. Our…
We propose an Expected Free Energy-based acquisition function for Bayesian optimization to solve the joint learning and optimization problem, i.e., optimize and learn the underlying function simultaneously. We show that, under specific…
We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
Inspired by the recent development on calculating the free energy change via a relaxation process [Nat. Phys. 14, 842 (2018)], we investigate the role of heat released in an irreversible relaxation following a large perturbation. Utilizing…
We describe a method for calculating action-angle variables in axisymmetric galactic potentials using Birkhoff normalization, a technique from Hamiltonian perturbation theory. An advantageous feature of this method is that it yields…
Machine learning is a powerful method of extracting meaning from data; unfortunately, current digital hardware is extremely energy-intensive. There is interest in an alternative analog computing implementation that could match the…
In our work, we propose a novel yet simple approach to obtain an adaptive learning rate for gradient-based descent methods on classification tasks. Instead of the traditional approach of selecting adaptive learning rates via the decayed…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
Exploring the free-energy landscape along reaction coordinates or system parameters $\lambda$ is central to many studies of high-dimensional model systems in physics, e.g. large molecules or spin glasses. In simulations this usually…
Training machine learning interatomic potentials often requires optimizing a loss function composed of three variables: potential energies, forces, and stress. The contribution of each variable to the total loss is typically weighted using…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…