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Evolutionary algorithms provide gradient-free optimisation which is beneficial for models that have difficulty in obtaining gradients; for instance, geoscientific landscape evolution models. However, such models are at times computationally…

In this work, we consider two kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery i.e. in an artery that is located far away from the heart.…

We propose a way to transform synchronous distributed algorithms solving locally greedy and mendable problems into self-stabilizing algorithms in anonymous networks. Mendable problems are a generalization of greedy problems where any…

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. In this paper, we develop,…

In this effort we introduce and analyze a novel reduced basis approach, used to construct an approximating subspace for a given set of data. Our technique, which we call the Natural Greedy Algorithm (NGA), is based on a recursive approach…

Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…

Reinforcement learning is a promising paradigm for solving sequential decision-making problems, but low data efficiency and weak generalization across tasks are bottlenecks in real-world applications. Model-based meta reinforcement learning…

Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…

The data-centric construction of inexpensive surrogates for fine-grained, physical models has been at the forefront of computational physics due to its significant utility in many-query tasks such as uncertainty quantification. Recent…

Simulating complex physical processes across a domain of input parameters can be very computationally expensive. Multi-fidelity surrogate modeling can resolve this issue by integrating cheaper simulations with the expensive ones in order to…

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of non-linear system identification…

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…

Simulation-based optimization is a useful method for practical design problems. However, it is difficult for complicated problems due to expensive-computational costs. A popular way to overcome this issue is to use a surrogate model to save…

Stochastic First-Order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where…

We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control…

In this paper we present the greedy step averaging(GSA) method, a parameter-free stochastic optimization algorithm for a variety of machine learning problems. As a gradient-based optimization method, GSA makes use of the information from…

It is a survey on recent results in constructive sparse approximation. Three directions are discussed here: (1) Lebesgue-type inequalities for greedy algorithms with respect to a special class of dictionaries, (2) constructive sparse…

This paper introduces a modular and scalable design optimization framework for the glider wing design process that enables faster early-phase design while ensuring aerodynamic stability. The pipeline starts with the generation of initial…

We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is…

Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable…