Using nonlinear projections and preserving structure in model order reduction (MOR) are
currently active research fields. In this paper, we provide a novel differential geometric …

In this work, we present a hybrid numerical method for solving evolution partial differential
equations (PDEs) by merging the time finite element method with deep neural networks. In …

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-
temporal scales is a fundamental challenge in many scientific and engineering domains …

Abstract This survey discusses Neural Galerkin schemes that leverage nonlinear
parametrizations such as deep networks to numerically solve time-dependent partial …

Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov
barrier that affects transport-dominated problems. In this work, we build on the reduced …

Shape-morphing solutions (also known as evolutional deep neural networks, reduced-order
nonlinear solutions, and neural Galerkin schemes) are a new class of methods for …

A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data
is introduced. The framework utilizes neural networks' universal approximation capacity to …

Evolutionary deep neural networks have emerged as a rapidly growing field of research.
This paper studies numerical integrators for such and other classes of nonlinear …

In this paper, a spring cantilever beam type piezoelectric electromagnetic energy harvester
is proposed and the prototype increases the vibration frequency by adopting a spring, which …