Related papers: On Multilevel Energy-Based Fragmentation Methods
We present a consensus-based framework that unifies phase space exploration with posterior-residual-based adaptive sampling for surrogate construction in high-dimensional energy landscapes. Unlike standard approximation tasks where sampling…
We introduce multi-scale energy models to learn the prior distribution of images, which can be used in inverse problems to derive the Maximum A Posteriori (MAP) estimate and to sample from the posterior distribution. Compared to the…
The ensemble average of physical properties of molecules is closely related to the distribution of molecular conformations, and sampling such distributions is a fundamental challenge in physics and chemistry. Traditional methods like…
When considering the future generation wireless networks, non-orthogonal multiple access (NOMA) represents a viable multiple access technique for improving the spectral efficiency. The basic performance of NOMA is often enhanced using…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media. We will present the…
We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…
In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
A parameterization strategy for molecular models on the basis of force fields is proposed, which allows a rapid development of models for small molecules by using results from quantum mechanical (QM) ab initio calculations and thermodynamic…
Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The full-order solutions are…
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…
Most methods for estimating configurational entropy from molecular simulation data yield upper limits except for harmonic systems where they are exact. Problems arise at diffusive systems and the presence of conformational transitions.…
The relative energies of different phases or polymorphs of molecular solids can be small, less than a kiloJoule/mol. Reliable description of such energy differences requires high quality treatment of electron correlations, typically beyond…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
Treating electron correlation more accurately and efficiently is at the heart of the development of electronic structure methods. In the present work, we explore the use of stochastic approaches to evaluate high-order electron correlation…
We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…
The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…
We consider a class of adaptive multilevel domain decomposition-like algorithms, built from a combination of adaptive multilevel finite element, domain decomposition, and partition of unity methods. These algorithms have several interesting…
Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy,…