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In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range…
In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for…
Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…
Learning interpretable disentangled representations is a crucial yet challenging task. In this paper, we propose a weakly semi-supervised method, termed as Dual Swap Disentangling (DSD), for disentangling using both labeled and unlabeled…
The discrete dipole approximation (DDA) is a widely used and versatile numerical method for solving electromagnetic scattering by arbitrarily shaped objects. Despite its popularity, quantitative comparisons between independent…
This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO). We generalize the usual consecutive dual dynamic programming (DDP) algorithm to DR-MCO and propose…
To address the communication bottleneck challenge in distributed learning, our work introduces a novel two-stage quantization strategy designed to enhance the communication efficiency of distributed Stochastic Gradient Descent (SGD). The…
In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from…
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…
Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices.…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to their efficiency and their reduced memory requirements. We…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…