Related papers: Efficient Long-Time Simulations of Multiscale Syst…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
This paper considers the problem of real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of hybrid control algorithms is often prohibitive for real-time applications…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
Optimization-based falsification employs stochastic optimization algorithms to search for error input of hybrid systems. In this paper we introduce a simple idea to enhance falsification, namely time staging, that allows the time-causal…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp.…
Systems across different industries consist of interrelated processes and decisions in different time scales including long-time decisions and short-term decisions. To optimize such systems, the most effective approach is to formulate and…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
An efficient numerical algorithm for the laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…