相关论文: Stable Optimization of a Tensor Product Variationa…

A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…

An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in the form of non-physical oscillations in the pressure field are observed in 3D problems…

Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state…

Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…

We propose a practical finite volume method on cut cells using state redistribution. Our algorithm is provably monotone, total variation diminishing, and GKS stable in many situations, and shuts off continuously as the cut cell size…

This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…

We propose a method to construct the ground state $\psi(\lambda)$ of local lattice hamiltonians with the generic form $H_0 + \lambda H_1$, where $\lambda$ is a coupling constant and $H_0$ is a hamiltonian with a non degenerate ground state…

Variational quantum algorithms provide feasible approaches for simulating quantum systems and are applied widely. For lattice gauge theory, however, variational quantum simulation faces a challenge as local gauge invariance enforces a…

A fast and reliable geometry optimization algorithm is presented that optimizes atomic positions and lattice vectors simultaneously. Using a series of benchmarks, it is shown that the method presented in this paper outperforms in most cases…

The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the…

We present a hybrid quantum-classical variational scheme to enhance precision in quantum metrology. In the scheme, both the initial state and the measurement basis in the quantum part are parameterized and optimized via the classical part.…

We study equilibrium properties of a system of particles in two dimensions, interacting with pair and three body potentials, which undergoes a structural transition from a square to a rhombic lattice and thus constitutes a simple model for…

In the setting of continuum elasticity, phase transformations involving martensitic variants are modeled by a free energy density function that is non-convex in strain space. Here, we adopt an existing mathematical model in which we…

We study prethermal time-crystalline order in periodically driven quantum Ising models on disorder-free decorated lattices. Using a tensor network ansatz for the state which reflects the geometry of a unit cell of the lattice, we show…

We introduce a variational ansatz based on Gaussian states for (1+1)-dimensional lattice gauge models. To this end we identify a set of unitary transformations which decouple the gauge degrees of freedom from the matter fields. Using our…

We consider variational principles related to V. I. Arnold's stability criteria for steady-state solutions of the two-dimensional incompressible Euler equation. Our goal is to investigate under which conditions the quadratic forms defined…

We establish differentiability properties of the value function of problems of Static Optimization in an abstract infinite dimensional setting and we apply that to problems of Calculus of Variations. We lighten the assumptions of existing…

This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a…