相关论文: Entropy dissipation of moving mesh adaptation

In this paper, we introduce a hyperbolic model for entropy dissipative system of viscous conservation laws via a flux relaxation approach. We develop numerical schemes for the resulting hyperbolic relaxation system by employing the…

This work presents a novel interpolation-free mesh adaptation technique for the Euler equations within the arbitrary Lagrangian Eulerian framework. For the spatial discretization, we consider a residual distribution scheme, which provides a…

In this paper, the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors [18,16,17] for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids is extended to…

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free…

The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…

We describe a generic infrastructure for time evolution simulations in numerical relativity using multiple grid patches. After a motivation of this approach, we discuss the relative advantages of global and patch-local tensor bases. We…

Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…

In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…

We study the time evolution of the R\'enyi entanglement entropies following a quantum quench in a two-dimensional (2D) free-fermion system. By employing dimensional reduction, we effectively transform the 2D problem into decoupled chains, a…

Machine learning models must continuously self-adjust themselves for novel data distribution in the open world. As the predominant principle, entropy minimization (EM) has been proven to be a simple yet effective cornerstone in existing…

In this paper we study structure-preserving numerical methods for low Mach number barotropic Euler equations. Besides their asymptotic preserving properties that are crucial in order to obtain uniformly consistent and stable approximations…

We compare two different codes for simulations of cosmological structure formation to investigate the sensitivity of hydrodynamical instabilities to numerics, in particular, the hydro solver and the application of adaptive mesh refinement…

We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…

We analyse convergence of a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with time-scale separation between the (fast) evolution of individual trajectories and the (slow) evolution of…

We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…

The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer…

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…