Data Efficient Deep Learning Of Dynamical Systems
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Data-efficient Deep Learning of Dynamical Systems
The synergy between dynamical systems and deep learning (DL) has become an increasingly popular research topic because of the limitation of classic methods and the great potential of DL in addressing these challenges through the data-fitting and feature-extraction power of deep neural networks (DNNs). DNNs have demonstrated their ability to approximate highly complicated functions while enjoying good trainability, which can help dynamical system modeling with both the search of solution and the expressiveness of models. Furthermore, the feature extraction ability of DNNs have proven useful in identifying system states identification when the state cannot be defined from first-principles. Conversely, the study of dynamical systems has benefited DL. Viewing DNNs as discretization of ordinary differential equations (ODEs) inspires a novel family of models named neural differential equations which offer unique advantages in time series learning, especially the modeling of dynamical systems. From another perspective, viewing the optimization of deep learning models as a dynamical system on the loss landscape enables better analysis and enhancement of the optimization processes. This work focuses on this interplay. We develop novel deep learning methods to efficiently model dynamical systems, incorporating physical prior knowledge and meta-learning techniques. By analyzing the dynamics of the optimization process, we also design a novel variant of stochastic gradient descent to enhance the resilience of DNNs against weight perturbations, enabling their deployment on analog in-memory computing platforms where analog noise is inevitable. Through these investigations, we contribute to the growing body of research on the intersection of dynamical systems and deep learning, paving the way for innovative solutions to complex real-world problems.
Data-Driven Science and Engineering
Author: Steven L. Brunton
language: en
Publisher: Cambridge University Press
Release Date: 2022-05-05
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Dynamic Mode Decomposition
Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.