Explicit stabilized integration of stiff determinisitic or stochastic problems

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In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

This work presents a new computational optimization framework for the robust control of parks of Wave Energy Converters (WEC) in irregular waves. The power of WEC parks is maximized with respect to the individual control damping and stiffness coefficients ...

Stabilized explicit methods are particularly efficient, for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they lose their efficiency when a severe stiffness is induced by very few "fast" de ...

Stabilized Runge???Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge???Kutta me ...

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

At the beginning of the 19th century, the Napoleonic administration introduced a new standardised description system to give an objective account of the form and functions of the city of Venice. The cadastre, deployed on a European scale, was offering for ...

Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...

Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system ...

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...

Governments choose to issue risky or riskless debt depending on the nature of the stochastic process of output. We use Brownian motion and Poisson shocks a modeling method in the literature on corporate default known as Levy processes to approximate a deco ...

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

In this paper, we propose a monolithic algorithm for the numerical solution of the electromechanics model of the left ventricle in the human heart. Our coupled model integrates the monodomain equation with the Bueno-Orovio minimal model for electrophysiolo ...

We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a ...

To reach optimal/better conceptual designs of energy systems, key design variables should be optimized/adapted with system layouts, which may contribute significantly to system improvement. Layout improvement can be proposed by combining system analysis wi ...

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

In this paper, we study the Besov regularity of Levy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for gene ...

Inertial sensors are increasingly being employed in different types of applications. The reduced cost and the extremely small size makes them the number-one-choice in miniature embedded devices like phones, watches, and small unmanned aerial vehicles. The ...

As the power industry considers moving from a deterministic paradigm to a stochastic one to clear the day-ahead market in systems with significant stochastic production, the following question arises: how should a stochastic clearing algorithm be formulate ...

Explicit stabilized integration of stiff determinisitic or stochastic problems

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Low-Rank Tensor Methods for High-Dimensional Problems

Tensor approximation of the self-diffusion matrix of tagged particle processes

Robust optimization of control parameters for WEC arrays using stochastic methods

Explicit Stabilized Multirate Method For Stiff Stochastic Differential Equations

Explicit Stabilized Multirate Method For Stiff Differential Equations

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Une approche computationnelle du cadastre napoléonien de Venise

Numerical methods for deterministic and stochastic differential equations with multiple scales and high contrasts

Novel corrector problems with exponential decay of the resonance error for numerical homogenization

Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation

The sources of sovereign risk: a calibration based on Levy stochastic processes

Path properties of the solution to the stochastic heat equation with Levy noise

A monolithic algorithm for the simulation of cardiac electromechanics in the human left ventricle

A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

A Review of Evaluation, Optimization and Synthesis of Energy Systems: Methodology and Application to Thermal Power Plants

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility

On the Besov regularity of periodic Levy noises

An overview of a new sensor calibration platform

Three- or Two-Stage Stochastic Market-Clearing Algorithm?