Related papers: An Adaptive Parareal Algorithm
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
Discovering causal relationships from observational data is a crucial problem and it has applications in many research areas. The PC algorithm is the state-of-the-art constraint based method for causal discovery. However, runtime of the PC…
The paper presents a general strategy to solve ordinary differential equations (ODE), where some coefficient depend on the spatial variable and on additional random variables. The approach is based on the application of a recently developed…
We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the…
In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…
Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…
This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…
We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of…
We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…