Accelerating Neural ODEs Using Model Order Reduction

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are memory-efficient to train, process time series naturally, and incorporate knowledge of physical systems into deep learning (DL) models. However, the practical applications of Neural ODEs are limited due to long inference times because the outputs of the embedded ODE layers are computed numerically with differential equation solvers that can be computationally demanding. Here, we show that mathematical model order reduction (MOR) methods can be used for compressing and accelerating Neural ODEs by accurately simulating the continuous nonlinear dynamics in low-dimensional subspaces. We implement our novel compression method by developing Neural ODEs that integrate the necessary subspace-projection and interpolation operations as layers of the neural network. We validate our approach by comparing it to neuron pruning and singular value decomposition (SVD)-based weight truncation methods from the literature in image and time-series classification tasks. The methods are evaluated by acceleration versus accuracy when adjusting the level of compression. On this spectrum, we achieve a favorable balance over existing methods by using MOR when compressing a convolutional Neural ODE. In compressing a recurrent Neural ODE, SVD-based weight truncation yields good performance. Based on our results, our integration of MOR with Neural ODEs can facilitate efficient, dynamical system-driven DL in resource-constrained applications.publishedVersionPeer reviewe

On the Dynamics of a Recurrent Hopfield Network

In this research paper novel real/complex valued recurrent Hopfield Neural Network (RHNN) is proposed. The method of synthesizing the energy landscape of such a network and the experimental investigation of dynamics of Recurrent Hopfield Network is discussed. Parallel modes of operation (other than fully parallel mode) in layered RHNN is proposed. Also, certain potential applications are proposed.Comment: 6 pages, 6 figures, 1 table, submitted to IJCNN-201

Fleet Prognosis with Physics-informed Recurrent Neural Networks

Services and warranties of large fleets of engineering assets is a very profitable business. The success of companies in that area is often related to predictive maintenance driven by advanced analytics. Therefore, accurate modeling, as a way to understand how the complex interactions between operating conditions and component capability define useful life, is key for services profitability. Unfortunately, building prognosis models for large fleets is a daunting task as factors such as duty cycle variation, harsh environments, inadequate maintenance, and problems with mass production can lead to large discrepancies between designed and observed useful lives. This paper introduces a novel physics-informed neural network approach to prognosis by extending recurrent neural networks to cumulative damage models. We propose a new recurrent neural network cell designed to merge physics-informed and data-driven layers. With that, engineers and scientists have the chance to use physics-informed layers to model parts that are well understood (e.g., fatigue crack growth) and use data-driven layers to model parts that are poorly characterized (e.g., internal loads). A simple numerical experiment is used to present the main features of the proposed physics-informed recurrent neural network for damage accumulation. The test problem consist of predicting fatigue crack length for a synthetic fleet of airplanes subject to different mission mixes. The model is trained using full observation inputs (far-field loads) and very limited observation of outputs (crack length at inspection for only a portion of the fleet). The results demonstrate that our proposed hybrid physics-informed recurrent neural network is able to accurately model fatigue crack growth even when the observed distribution of crack length does not match with the (unobservable) fleet distribution.Comment: Data and codes (including our implementation for both the multi-layer perceptron, the stress intensity and Paris law layers, the cumulative damage cell, as well as python driver scripts) used in this manuscript are publicly available on GitHub at https://github.com/PML-UCF/pinn. The data and code are released under the MIT Licens