Related papers: Easy-to-Implement One-Step Schemes for Stochastic …
Supported by the recent contributions in multiple branches, the first-order splitting algorithms became central for structured nonsmooth optimization. In the large-scale or noisy contexts, when only stochastic information on the smooth part…
We develop and analyze numerical methods for a stochastic Keller-Segel system perturbed by Stratonovich noise, which models chemotactic behavior under randomly fluctuating environmental conditions. The proposed fully discrete scheme couples…
The class of stochastic Runge-Kutta methods for stochastic differential equations due to R\"o{\ss}ler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Kutta (DDISRK) methods of weak order one and two are…
We consider monotone inclusion problems where the operators may be expectation-valued, a class of problems that subsumes convex stochastic optimization problems as well as subclasses of stochastic variational inequality and equilibrium…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schr\"odinger equation with multiplicative noise. Based on the splitting…
Three schemes, whose expressions are not too complex, are selected for the numerical integration of a system of stochastic differential equations in the Stratonovich interpretation: the integration methods of Heun, Milstein, and…
Runge-Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order, DIRK (diagonally implicit Runge-Kutta) schemes are…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients,…
Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable accuracy and stability problems, they give rise to large and complicated systems of…
In this work modified Patankar-Runge-Kutta (MPRK) schemes up to order four are considered and equipped with a dense output formula of appropriate accuracy. Since these time integrators are conservative and positivity preserving for any time…
In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate time-integration with no…
This paper focuses on the strong convergence rate of both Runge--Kutta methods and simplified step-$N$ Euler schemes for stochastic differential equations driven by multi-dimensional fractional Brownian motions with $H\in(\frac12,1)$. Based…
In this paper a new Runge-Kutta type scheme is introduced for nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise. The proposed scheme converges with respect to the computational effort with a…
Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings.…
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient…
A mixed accuracy framework for Runge--Kutta methods presented in [Grant, JSC 2022] has been shown to speed up the computation in diagonally implicit Runge--Kutta (DIRK) methods by using less expensive low accuracy approaches for the…
In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…