相关论文: Hyper-reduction over nonlinear manifolds for large…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay…

We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…

This paper presents a generalized weak Galerkin (gWG) finite element method for linear elasticity problems on general polygonal and polyhedral meshes. The proposed framework is flexible and efficient, allowing for the use of nonpolynomial…

This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear parametrizations such as deep networks. The proposed…

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…

We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…

In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…

In this paper one first shows that the slow flow of a mechanical system with one unstable mode coupled to a Nonlinear Energy Sink (NES) can be reduced, in the neighborhood of a fold point of its critical manifold, to a normal form of the…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

One of strengths in the finite element (FE) and Galerkin methods is their capability to apply weak formulations via integration by parts, which leads to elements matching at lower degree of continuity and relaxes requirements of choosing…

A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…

Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…

Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…

This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our…

Semi-implicit time-stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…

In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…

Motivated by recent developments in serverless systems for large-scale computation as well as improvements in scalable randomized matrix algorithms, we develop OverSketched Newton, a randomized Hessian-based optimization algorithm to solve…