Related papers: Extended dynamic mode decomposition with dictionar…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…
We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…
This paper presents a data-learned linear Koopman embedding of nonlinear networked dynamics and uses it to enable real-time model predictive emergency voltage control in a power network. The approach involves a novel data-driven…
Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…
This paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional…
Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…
Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network (DNN) behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability.…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work,…
Nonlinear ordinary differential equations can rarely be solved analytically. Koopman operator theory provides a way to solve nonlinear systems by mapping nonlinear dynamics to a linear space using eigenfunctions. Unfortunately, finding such…
Human emotional speech is, by its very nature, a variant signal. This results in dynamics intrinsic to automatic emotion classification based on speech. In this work, we explore a spectral decomposition method stemming from fluid-dynamics,…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be…
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…
In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed…