Related papers: Spline-oriented inter/extrapolation-based multirat…
Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the…
Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges, since these enable ever…
We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…
This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods (Sandu and Guenther, 2013). Multirate schemes use different step sizes for different components and for…
We study scalar $d$-variate subdivision schemes, with dilation matrix 2I, satisfying the sum rules of order $k$. Using the results of M\"oller and Sauer, stated for general expanding dilation matrices, we characterize the structure of the…
We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the restarted trajectories. The proposed routine is implemented…
For linear and fully non-linear diffusion equations of Bellman-Isaacs type, we introduce a class of approximation schemes based on differencing and interpolation. As opposed to classical numerical methods, these schemes work for general…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
We propose a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility…
This paper extends the matrix based approach to the setting of multiple subdivision schemes studied in [Sauer 2012]. Multiple subdivision schemes, in contrast to stationary and non-stationary schemes, allow for level dependent subdivision…
We present a fast phase gate scheme that is experimentally achievable and has an operation time more than two orders of magnitude faster than current experimental schemes for low numbers of pulses. The gate time improves with the number of…
We propose and numerically validate an all-optical scheme to generate optical pulse trains with varying temporal pulse-to-pulse delay and pulse duration. Applying a temporal sinusoidal phase modulation followed by a shaping of the spectral…
In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…
The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…
We propose a new class of multi-layer iterative schemes for solving sparse linear systems in saddle point structure. The new scheme consist of an iterative preconditioner that is based on the (approximate) nullspace method, combined with an…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…