相关论文: Forced extension of GNI techniques to dissipative …

An extension of the H-theorem for dissipative particle dynamics (DPD) to the case of a multi-component fluid is made. Detailed balance and an additional H-theorem are proved for an energy-conserving version of the DPD algorithm. The…

The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…

We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear meshes, with arbitrary accuracy. We derive an entropy…

We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…

We present a Graph Neural Network (GNN) that accurately simulates a multidisperse suspension of interacting spherical particles. Our machine learning framework is built upon the recent work of Sanchez-Gonzalez et al. ICML, PMLR, 119,…

We consider a non-isothermal compositional gas liquid model for the simulation of well operations in geothermal processes. The model accounts for phase transitions assumed to be at thermodynamical equilibrium and is based on an…

We consider a finite dimensional damped second order system and obtain spectral inclusion theorems for the related quadratic eigenvalue problem. The inclusion sets are the 'quasi Cassini ovals' which may greatly outperform standard…

A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…

A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is…

For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…

We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…

In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the…

We analyze the Ericksen--Leslie system equipped with the Oseen--Frank energy in three space dimensions. Recently, the author introduced the concept of dissipative solutions. These solutions show several advantages in comparison to the…

We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of…

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…

Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are…

Achieving chemical accuracy in quantum simulations is often constrained by the measurement bottleneck: estimating operators requires a large number of shots, which remains costly even on fault-tolerant devices and is further exacerbated on…

A new symplectic variational approach is developed for modeling dissipation in kinetic equations. This approach yields a double bracket structure in phase space which generates kinetic equations representing coadjoint motion under canonical…