Related papers: Efficient algorithm for computing large scale syst…

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…

Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective,…

Automated anomaly detection is essential for managing information and communications technology (ICT) systems to maintain reliable services with minimum burden on operators. For detecting varying and continually emerging anomalies as…

Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…

Black-box discrete optimization (BB-DO) problems arise in many real-world applications, such as neural architecture search and mathematical model estimation. A key challenge in BB-DO is epistasis among parameters where multiple variables…

There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…

We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…

The developments of quantum computing algorithms and experiments for atomic scale simulations have largely focused on quantum chemistry for molecules, while their application in condensed matter systems is scarcely explored. Here we present…

For nonlinear differential-algebraic equations (DAEs), we define two kinds of equivalences, namely, the external and internal equivalence. Roughly speaking, the word "external" means that we consider a DAE (locally) everywhere and…

In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to…

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…

This paper addresses the classic problem of parameter estimation (PE) in multimachine power system models. Such models are typically described by a set of nonlinear differential-algebraic equations (DAE), where generator physics and network…

Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments such as Modelica and MapleSim. Before a simulation starts and a numerical solution method is applied, some kind of structural…

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…

This work presents an unfitted boundary algebraic equation (BAE) method for solving three-dimensional elliptic partial differential equations on complex geometries using finite difference on structured meshes. We demonstrate that replacing…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…