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In this work we present two new families of multirate time step adaptivity controllers, that are designed to work with embedded multirate infinitesimal (MRI) time integration methods for adapting time steps when solving problems with…
Mitigating measurement errors in quantum systems without relying on quantum error correction is of critical importance for the practical development of quantum technology. Deep learning-based quantum measurement error mitigation has…
We present a family of distributed forward-backward methods with variable stepsizes to find a solution of structured monotone inclusion problems. The framework is constructed by means of relocated fixed-point iterations, extending the…
An 11-dimensional family of embedded (4, 5) pairs of explicit 9-stage Runge-Kutta methods with an interpolant of order 5 is derived. Two optimized for efficiency pairs are presented.
This topical review introduces the theoretical and experimental advances in continuous-variable (CV) --- i.e., qumode-based in lieu of qubit-based --- large-scale, fault-tolerant quantum computing and quantum simulation. An introduction to…
We study the effect of global error control in the numerical solution of Hamiltonian systems. In particular, we apply the RKQ algorithm in the numerical solution of a Hamiltonian system. This algorithm is designed to provide stepwise…
This paper introduces a new quantum computing framework integrated with a two-step compressed sensing technique, applied to a joint channel estimation and user identification problem. We propose a variational quantum circuit (VQC) design as…
This paper is devoted to examining the stability of Runge-Kutta methods for solving nonlinear Volterra delay-integro-differential-algebraic equations (DIDAEs) with constant delay. Hybrid numerical schemes combining Runge-Kutta methods and…
In order to solve continuous-time optimal control problems, direct methods transcribe the infinite-dimensional problem to a nonlinear program (NLP) using numerical integration methods. In cases where the integration error can be manipulated…
It is well known that symplectic Runge-Kutta and Partitioned Runge-Kutta methods exactly preserve {\em quadratic} first integrals (invariants of motion) of the system being integrated. While this property is often seen as a mere curiosity…
This paper presents a method to construct variational integrators for time-dependent lagrangian systems. The resulting algorithms are symplectic, preserve the momentum map associated with a Lie group of symmetries and also describe the…
This paper presents a method for controlling the voltage of inverter-based Microgrids by proposing a new scale-free distributed cooperative controller. The communication network is modeled by a general time-varying graph which enhances the…
SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This paper overviews several significant improvements and new features added over the last three years to support…
We review error estimation methods for co-simulation, in particular methods that are applicable when the subsystems provide minimal interfaces. By this, we mean that subsystems do not support rollback of time steps, do not output…
We study the problem of efficient integration of variational equations in multi-dimensional Hamiltonian systems. For this purpose, we consider a Runge-Kutta-type integrator, a Taylor series expansion method and the so-called `Tangent Map'…
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…
Runge-Kutta methods are affine equivariant: applying a method before or after an affine change of variables yields the same numerical trajectory. However, for some applications, one would like to perform numerical integration after a…
In this paper, we present error estimates of the integral deferred correction method constructed with stiffly accurate implicit Runge-Kutta methods with a nonsingular matrix $A$ in its Butcher table representation, when applied to stiff…
In this work, we use path integral techniques to predict the switching rate in a single-mode bistable open quantum system. While analytical expressions are well-known to be accessible for systems subject to Gaussian noise obeying classical…
Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is…