相关论文: Removing External Degrees of Freedom from Transiti…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

Using the standard finite element method (FEM) to solve general partial differential equations, the round-off error is found to be proportional to $N^{\beta_{\rm R}}$, with $N$ the number of degrees of freedom (DoFs) and $\beta_{\rm R}$ a…

Euler angles determining rotations of a system as a whole are conveniently separated in three-particle basis functions. Analytic integration of matrix elements over Euler angles is done in a general form. Results for the Euler angle…

This paper proposes and analyzes an iterative minimization formulation for search- ing index-1 saddle points of an energy function. This formulation differs from other eigenvector-following methods by constructing a new objective function…

We present the incorporation of a surrogate Gaussian Process Regression (GPR) atomistic model to greatly accelerate the rate of convergence of classical Nudged Elastic Band (NEB) calculations. In our surrogate model approach, the cost of…

The use of ensemble Monte Carlo (EMC) methods for the simulation of transport in semiconductor devices has become extensive over the past few decades. This method allows for simulation utilizing particles while addressing the full physics…

This paper presents a class of efficient manifold optimization algorithms for computing the ground state solutions of a semilinear elliptic system, which are unstable saddle points of the variational functional. Variational arguments show…

We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…

We compute the minimal energy cost for extracting entanglement from the ground state of a bosonic or fermionic quadratic system. Specifically, we find the minimal energy increase $\Delta E_{\mathrm{min}}$ in the system resulting from…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…

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.…

Convex optimization over the spectrahedron, i.e., the set of all real $n\times n$ positive semidefinite matrices with unit trace, has important applications in machine learning, signal processing and statistics, mainly as a convex…

We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

Recently a non-empirical stochastic walker algorithm has been developed to search for the minimum-energy escape paths (MEP) from the minima of the potential surface [J. Phys. Soc. Jpn. 87, 063801 (2018); Physica A, 528, 121481 (2019)]. This…

The spectral function of the closed-shell Neon atom is computed by expanding the electron self-energy through a set of Faddeev equations. This method describes the coupling of single-particle degrees of freedom with correlated two-electron,…

Within the MNPBEM toolbox, we show how to simulate electron energy loss spectroscopy (EELS) of plasmonic nanoparticles using a boundary element method approach. The methodology underlying our approach closely follows the concepts developed…

Data sparsity is a common issue to train machine learning tools such as neural networks for engineering and scientific applications, where experiments and simulations are expensive. Recently physics-constrained neural networks (PCNNs) were…

A well known procedure to get quantum hydrodynamical models for charge transport is to resort to the Wigner equations and deduce the hierarchy of the moment equations as in the semiclassical approach. If one truncates the moment hierarchy…

Model degrees of freedom ($\df$) is a fundamental concept in statistics because it quantifies the flexibility of a fitting procedure and is indispensable in model selection. To investigate the gap between $\df$ and the number of independent…