Related papers: Exact Model Reduction and Fast Forced Response Cal…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…

Continuum robots exhibit high-dimensional, nonlinear dynamics which are often coupled with their actuation mechanism. Spectral submanifold (SSM) reduction has emerged as a leading method for reducing high-dimensional nonlinear dynamical…

In computational engineering, enhancing the simulation speed and efficiency is a perpetual goal. To fully take advantage of neural network techniques and hardware, we present the SLiding-window Initially-truncated Dynamic-response Estimator…

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…

Tools from random matrix theory have become central to deep learning theory, using spectral information to provide mechanisms for modeling generalization, robustness, scaling, and failure modes. While often capable of modeling empirical…

The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system.…

Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges…

We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The mean idea is to take advantage of the fact that such structures are dissipative and…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…

Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To…

Bolted joints can exhibit nonsmooth and significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric…

We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…

Given a stochastic differential equation (SDE) in $\mathbb{R}^n$ whose solution is constrained to lie in some manifold $M \subset \mathbb{R}^n$, we propose a class of numerical schemes for the SDE whose iterates remain close to $M$ to high…

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning…

We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also…