MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

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Toward bridging classical optimal control and online learning, regret minimization has recently been proposed as a control design criterion. This competitive paradigm penalizes the loss relative to the optimal control actions chosen by a clairvoyant policy ...

The simulation of electromagnetic devices with complex geometries and large-scale discrete systems benefits from advanced computational methods like IsoGeometric Analysis and Domain Decomposition. In this paper, we employ both concepts in an Isogeometric T ...

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

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 ...

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

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Macroscopic fundamental diagrams (MFDs) have been widely adopted to model the traffic flow of large-scale urban networks. Coupling perimeter control and regional route guidance (PCRG) is a promising strategy to decrease congestion heterogeneity and reduce ...

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

Literature on linear induction motors (LIMs) has proposed several approaches to model the behavior of such devices for different applications. In terms of accuracy and fidelity, field analysis-based models are the most relevant. Closed-form or numerical so ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

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On the Guarantees of Minimizing Regret in Receding Horizon

Tree–cotree-based tearing and interconnecting for 3D magnetostatics: A dual–primal approach

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Reliable data-driven decision-making through optimal transport

From low-rank retractions to dynamical low-rank approximation and back

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Stability: a search for structure

Graph generative deep learning models with an application to circuit topologies

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

The time-domain Cartesian multipole expansion of electromagnetic fields

Identification of typical district configurations: A two-step global sensitivity analysis framework

An Iterative Adaptive Dynamic Programming Approach for Macroscopic Fundamental Diagram-Based Perimeter Control and Route Guidance

On the Generalization of Stochastic Gradient Descent with Momentum

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS