Related papers: Hyper-reduction-free reduced-order Newton solvers …
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
We propose to accelerate a high order discontinuous Galerkin solver using neural networks. We include a corrective forcing to a low polynomial order simulation to enhance its accuracy. The forcing is obtained by training a deep fully…
We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…
To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that…
This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly…
We show in this paper that third- and fourth-order low storage Runge-Kutta algorithms can be built specifically for quadratic nonlinear operators, at the expense of roughly doubling the time needed for evaluating the temporal derivatives.…
In this paper, we propose an efficient proper orthogonal decomposition based reduced-order model(POD-ROM) for nonstationary Stokes equations, which combines the classical projection method with POD technique. This new scheme mainly owns two…
This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of…
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…
Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…
In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds,…
This paper presents a numerical function optimization framework designed for constrained optimization problems in robotics. The tool is designed with real-time considerations and is suitable for online trajectory and control input…
In this work, we develop first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. For that, we employ finite difference…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…
Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the…
This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…
This paper is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary…
This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…