Abstract. Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally demanding. In this work, we explore the use of partitioning to distribute the contraction task across a distributed memory architecture, commonly found in high-performance computing environments. This approach offers a promising alternative to the widely used parallelization based on slicing, which often incurs significant computational overhead. We particularly investigate how a given partitioning can be optimized to enable efficient contraction, as both computational and memory costs are highly sensitive to the chosen strategy. To this end, we introduce a simulated annealing-based method that iteratively refines a partitioning to minimize the operation count along the critical path, thereby reducing time-to-solution. The algorithm is evaluated on MQT Bench circuits and achieves a lower computational cost in 47 of 71 circuits, with improvements up to [Formula: see text] orders of magnitude compared to contraction paths generated by Cotengra, a state-of-the-art contraction path finding library.
Abstract. Data access time is an essential part of the mathematical design of asynchronous iterative methods, which makes it necessary to strongly link theoretical analysis and practical implementation. In particular, coarse-space correction implies two independent communications stages, one for updating the right-hand side (RHS) of each local fine problem, and the other one for updating the RHS of the coarse problem. This results in two different sets of communication delays, creating a gap between the fine- and the coarse-projected RHSs. So far, asynchronous domain decomposition methods (DDMs) have applied additive coarse-space correction only on a subset of iterations, depending on the average gap between the RHSs. Here, we achieve asynchronous additive coarse-space correction at all iterations and hence propose the first totally two-level asynchronous DDMs of such kind. The approach is presented using a general Schwarz-type domain decomposition framework formulated as a multisplitting one. Several iterative models are considered with implied implementation aspects. Both weak and strong scaling experimental results for the standard Poisson’s equation in two and three dimensions show some remarkable performances of our approach.
Abstract. We propose a novel, rigorous, and conservative invariant-domain preserving (IDP) projection technique between solution spaces of differing discretizations. The projection preserves important physical invariants of the underlying hyperbolic system, for example, positivity of material density and internal energy for the compressible Euler equations. When coupled with suitable refinement indicators, the proposed scheme enables a provably IDP adaptive numerical method for hyperbolic systems where preservation of physical properties is essential. In addition to proofs of these characteristics, we supply a detailed construction of the method in the context of a high-performance finite element code. To illustrate our proposed scheme, we study a suite of computationally challenging benchmark problems, demonstrating enhanced accuracy and efficiency properties while entirely avoiding ad hoc corrections to preserve physical invariants. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/conservation-laws/ryujin and in the supplementary materials ( ryujin-development.zip [938KB]). [Formula: see text]
Abstract. We propose a novel approach to approximate the basic reproduction number [Formula: see text] as the spectral radius of the Next-Generation Operator in time-periodic population models by characterizing the latter via evolution semigroups. Once birth/infection and transition operators are identified, we discretize them via either Fourier or Chebyshev collocation methods. Then [Formula: see text] is obtained by solving a generalized matrix eigenvalue problem. The order of convergence of the approximating reproduction numbers to the true one is shown to depend on the regularity of the model coefficients, and spectral accuracy is proved. We validate the theoretical results by discussing applications to epidemiology, viz. a large-size multigroup epidemic model with periodic contact rates, and a vector-borne disease model with seasonal vector recruitment. We illustrate how the method facilitates implementation compared to existing approaches and how it can be easily adapted to also compute type-reproduction numbers. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://gitlab.com/SIMONE.DEREGGI/R0_periodicODEs and in the supplementary materials ( R0_periodicODEs-main.zip [14.9KB]). [Formula: see text]
Abstract. Differential equations (DEs) are widely used to model the evolution of natural or engineered systems. Traditionally, the parameters in DEs are adjusted to fit data obtained through system observations. However, in fields such as politics, economics, and biology, the observed data points are often collected independently (i.e., repeated cross-sectional (RCS) data). In this paper, we first demonstrate that conventional optimization techniques struggle to accurately estimate DE parameters when RCS data exhibit various heterogeneities, leading to a significant loss of information. To address this issue, we propose a new estimation method, the emulator-informed deep-generative model (EIDGM), designed to handle RCS data. Specifically, EIDGM integrates a physics-informed neural network–based emulator that immediately generates DE solutions and a Wasserstein-generative adversarial network–based parameter generator that can effectively mimic the RCS data. We then evaluated the effectiveness of EIDGM across various models, including exponential and logistic growth models, and the Lorenz system, demonstrating its superior ability to accurately capture parameter distributions. In addition, we applied EIDGM to real-world datasets, successfully capturing diverse shapes of parameter distributions. This result highlights that EIDGM can be applied to model a wide range of systems with limited data availability, and our approach can be significantly extended to uncover the operating principles of systems based on limited data. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/CHWmath/EIDGM/tree/main and in the supplementary materials ( EIDGM-main.zip [19.5MB]). [Formula: see text]
