Related papers: Probabilistic Exponential Integrators
Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilistic PDE solvers -- Bayesian statistical models mostly based on…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the…
In this work, we introduce a quadratically convergent and dynamically consistent integrator specifically designed for the replicator dynamics. The proposed scheme combines a two-stage rational approximation with a normalization step to…
In this paper we propose a novel way to integrate time-evolving partial differential equations that contain nonlinear advection and stiff linear operators, combining exponential integration techniques and semi-Lagrangian methods. The…
The paper deals with output feedback stabilization of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic PDE…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…
Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…
This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and…
We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential…
We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…
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…
A numerical integrator for $\dot{x}=f(x)$ is called \emph{stable} if, when applied to the 1D Dahlquist test equation $\dot{x}=\lambda x,\lambda\in\mathbb{C}$ with fixed timestep $h>0$, the numerical solution remains bounded as the number of…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…