Abstract We consider a second‐order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields larger deterministic ODEs. apply model order reduction (MOR) this high‐dimensional dynamical system, where its internal energy represents quadratic quantity interest. investigate the properties MOR with respect to stability, passivity and di...

In this work, we investigate a model-order reduction scheme for polynomial systems. We begin with defining the generalized multivariate transfer functions system. Based on this, aim at constructing reduced-order system, interpolating defined given set of interpolation points. Furthermore, provide method, inspired by Loewner approach linear and (quadratic-)bilinear systems, to determine good-qua...

This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with autoencoder accelerate elastic simulation of deformable solids. Due inertia effect, dynamic equilibrium cannot be established without evaluating second-order derivatives network. is beyond capability off-the-shelf automatic di...