Cardiocirculatory mathematical models are valuable tools for investigating both physiological and pathological conditions of the circulatory system. To assess an individual's clinical condition, these models must be tailored through parameter calibration. ...
We study the composite convex optimization problems with a quasi-self-concordant smooth component. This problem class naturally interpolates between classic self-concordant functions and functions with Lipschitz continuous Hessian. Previously, the best com ...
We investigate reduced order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the construction of a reduc ...
Reservoir Computing (RC) has become popular in recent years thanks to its fast and efficient computational capabilities. Standard RC has been shown to be equivalent in the asymptotic limit to Recurrent Kernels, which helps in analyzing its expressive power ...
We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, E-chains are finite collections of points with distance at most E between consecutive points. They play the role of discre ...
In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...
Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...
Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly w ...
Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...
This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...
We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...
The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...
In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems wi ...
Data-driven approaches have been applied to reduce the cost of accurate computational studies on materials, by using only a small number of expensive reference electronic structure calculations for a representative subset of the materials space, and using ...
The European Union's Green Deal aims for a 55% reduction in greenhouse gas emissions by 2030. To reach this goal, a massive integration of Renewable Energy Sources (RES) into the power grid is necessary. As RES become a large part of the electricity genera ...
Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...
Herein, machine learning (ML) models using multiple linear regression (MLR), support vector regression (SVR), random forest (RF) and artificial neural network (ANN) are developed and compared to predict the output features viz. specific capacitance (Csp), ...
In this paper, we present a new parameterization and optimization procedure for minimizing the weight of ribbed plates. The primary goal is to reduce embodied CO2 in concrete floors as part of the effort to diminish the carbon footprint of the construction ...
In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...
Electronic devices play an irreplaceable role in our lives. With the tightening time to market, exploding demand for computing power, and continuous desire for smaller, faster, less energy-consuming, and lower-cost chips, computer-aided design for electron ...
