Publications related to Homogeneous differential equation

Explicit Stabilized Multirate Method For Stiff Differential Equations

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 ...

AMER MATHEMATICAL SOC2022

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

CO2-Driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

Mrudhula Baskaran

We investigate experimentally and theoretically diffusiophoretic separation of negatively charged particles in a rectangular channel flow, driven by CO2 dissolution from one side-wall. Since the negatively charged particles create an exclusion zone near th ...

ROYAL SOC CHEMISTRY2021

Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed

Florent Gérard Krzakala, Lenka Zdeborová, Maria Refinetti

A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance of neural netwo ...

PMLR2021

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Xavier Fernandez-Real Girona

We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...

MATHEMATICAL SCIENCE PUBL2021

A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation

Alfio Quarteroni, Andrea Manzoni

In the context of cardiac electrophysiology, we propose a novel computational approach to highlight and explain the long-debated mechanisms behind atrial fibrillation (AF) and to reliably numerically predict its induction and sustainment. A key role is pla ...

FRONTIERS MEDIA SA2021

On the stability of blowup solutions for the critical corotational wave-map problem

Joachim Krieger, Shuang Miao

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter

λ(t)=t−1−ν

is sufficiently close to ...

2020

Normalized Gaussian path integrals

Giulio Corazza

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...

AMER PHYSICAL SOC2020

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Jan Sickmann Hesthaven

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...

SPRINGER/PLENUM PUBLISHERS2020

Homogeneous differential equation

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Explicit Stabilized Multirate Method For Stiff Differential Equations

A Continuized View on Nesterov Acceleration

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

CO2-Driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation

On the stability of blowup solutions for the critical corotational wave-map problem

Normalized Gaussian path integrals

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Explicit Stabilized Multirate Method For Stiff Differential Equations

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

A Continuized View on Nesterov Acceleration

CO2-Driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation

On the stability of blowup solutions for the critical corotational wave-map problem

Normalized Gaussian path integrals