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We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite…

We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…

Incorporating novelties into deep learning systems remains a challenging problem. Introducing new information to a machine learning system can interfere with previously stored data and potentially alter the global model paradigm, especially…

In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…

The analysis of the damage on plasma facing materials (PFM), due to its direct interaction with the plasma environment, is needed to build the next generation of nuclear machines, where tungsten has been proposed as a candidate. In this…

Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…

In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…

This paper introduces an active learning approach to the fitting of machine learning interatomic potentials. Our approach is based on the D-optimality criterion for selecting atomic configurations on which the potential is fitted. It is…

All-atom dynamics simulations are an indispensable quantitative tool in physics, chemistry, and materials science, but large systems and long simulation times remain challenging due to the trade-off between computational efficiency and…

Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the…

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…

Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we…

Training state-of-the-art vision models has become prohibitively expensive for researchers and practitioners. For the sake of accessibility and resource reuse, it is important to focus on adapting these models to a variety of downstream…

Theoretically exploring the advantages of neural networks might be one of the most challenging problems in the AI era. An adaptive feature program has recently been proposed to analyze feature learning, the characteristic property of neural…

Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst…

Pervasive AI increasingly depends on on-device learning systems that deliver low-latency and energy-efficient computation under strict resource constraints. Liquid State Machines (LSMs) offer a promising approach for low-power temporal…

This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference in latent variable models. We propose a diffusion process…

We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to…

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

In this paper, a self-adaptive contractive (SAC) algorithm is proposed for enhanced dynamic phasor estimation in the diverse operating conditions of modern power systems. At a high-level, the method is composed of three stages: parameter…