相关论文: The Discrete Adjoint Method for Exponential Integr…

Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…

Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…

Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…

The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…

In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting…

The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…

In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…

Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…

We consider the adaptive-rank integration of {2D and 3D} time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled…

Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a…

This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…

This paper presents a detailed evaluation of the envelope-tracking adaptive integral method (ET-AIM), an FFT-accelerated algorithm for analyzing electromagnetic scattering. ET-AIM is used to solve progressively more complex benchmark…

Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…

We introduce a tamed exponential time integrator which exploits linear terms in both the drift and diffusion for Stochastic Differential Equations (SDEs) with a one sided globally Lipschitz drift term. Strong convergence of the proposed…

This manuscript presents an adaptive high order discretization technique for elliptic boundary value problems. The technique is applied to an updated version of the Hierarchical Poincar\'e-Steklov (HPS) method. Roughly speaking, the HPS…

We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…

A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and…

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…