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An algorithm is proposed for computing equilibrium averages of Markov chains which suffer from metastability -- the tendency to remain in one or more subsets of state space for long time intervals. The algorithm, called the parallel replica…

Large-scale atomistic simulations rely on interatomic potentials providing an efficient representation of atomic energies and forces. Modern machine-learning (ML) potentials provide the most precise representation compared to electronic…

We study dynamic algorithms robust to adaptive input generated from sources with bounded capabilities, such as sparsity or limited interaction. For example, we consider robust linear algebraic algorithms when the updates to the input are…

Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…

We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a…

Most atomistic machine learning (ML) models rely on a locality ansatz, and decompose the energy into a sum of short-ranged, atom-centered contributions. This leads to clear limitations when trying to describe problems that are dominated by…

We develop a class of interacting particle systems for implementing a maximum marginal likelihood estimation (MMLE) procedure to estimate the parameters of a latent variable model. We achieve this by formulating a continuous-time…

The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…

While machine learning approaches have been successfully used to represent interatomic potentials, their speed has typically lagged behind conventional formalisms. This is often due to the complexity of the structural fingerprints used to…

Simulating the long-timescale dynamics of biomolecules is a central challenge in computational science. While enhanced sampling methods can accelerate these simulations, they rely on pre-defined collective variables that are often difficult…

In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…

Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Machine learning potentials have revolutionised the field of atomistic simulations in recent years and are becoming a mainstay in the toolbox of computational scientists. This paper aims to provide an overview and introduction into machine…

Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in…

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is…

Simulating long-term mass diffusion kinetics with atomic precision is important to predict chemical and mechanical properties of alloys over time scales of engineering interest in applications, including (but not limited to) alloy heat…

A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of…