相关论文: Exact Model Reduction by a Slow-Fast Decomposition…
The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…
The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear…
We develop a framework for analyzing the training and learning rate dynamics on a variety of high- dimensional optimization problems trained using one-pass stochastic gradient descent (SGD) with data generated from multiple anisotropic…
The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the…
We study a slow-fast system with two slow and one fast variables. We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighbourhood of the fold. We derive a normal form for…
This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…
Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for…
Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the…
The Muon optimizer has recently demonstrated remarkable empirical success in training large language models. However, the theoretical understanding of its mechanisms remains limited. Current convergence guarantees for Muon rely heavily on…
Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics…
Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such a system, we propose a nonlinear modal decoupling (NMD) approach inversely constructing…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
Model-based manipulation of deformable objects has traditionally dealt with objects while neglecting their dynamics, thus mostly focusing on very lightweight objects at steady state. At the same time, soft robotic research has made…
A simple nonholonomic dynamics model is developed as a low-order model for generating undulatory swim-like motions, validated through computational fluid dynamics (CFD) simulations. The rigid-body-dynamics model generates swimming motion by…