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...

In this work, the empirical-Gramian-based model reduction methods: Empirical poor man’s truncated balanced realization, empirical approximate balancing, dominant subspaces, truncation, and gains are compared in a non-parametric two parametric variants, via ten error measures: Approximate Lebesgue \(L_0\), \(L_1\), \(L_2\), \(L_\infty \), Hardy \(H_2\), \(H_\infty Hankel, Hilbert-Schmidt-Hankel,...

In this paper, we bring together the worlds of model order reduction for stochastic linear systems and H2-optimal deterministic systems. particular, supplement complete theory error bounds differential equations. With these bounds, establish a link between output (with additive multiplicative noise) modified versions H2-norm both bilinear When deriving respective optimality conditions minimizin...

Multiple expansion points are introduced to the multiport Cauer ladder network method realize an efficient model order reduction of eddy-current field. The proposed can set multiple target frequencies cover a wide frequency range with small number electric elements. A time-dependent response pulsewidth-modulation (PWM) excitation is accurately reconstructed by setting at both fundamental and ca...