Temporal Learning in Video Data Using Deep Learning and Gaussian Processes

This paper presents an approach for data-driven modeling of hidden, stationary temporal dynamics in sequential images or videos using deep learning and Bayesian non-parametric techniques. In particular, a deep Convolutional Neural Network (CNN) is used to extract spatial features in an unsupervised fashion from individual images and then, a Gaussian process is used to model the temporal dynamics of the spatial features extracted by the deep CNN. By decomposing the spatial and temporal components and utilizing the strengths of deep learning and Gaussian processes for the respective sub-problems, we are able to construct a model that is able to capture complex spatio-temporal phenomena while using relatively small number of free parameters. The proposed approach is tested on high-speed grey-scale video data obtained of combustion flames in a swirl-stabilized combustor, where certain protocols are used to induce instability in combustion process. The proposed approach is then used to detect and predict the transition of the combustion process from stable to unstable regime. It is demonstrated that the proposed approach is able to detect unstable flame conditions using very few frames from high-speed video. This is useful as early detection of unstable combustion can lead to better control strategies to mitigate instability. Results from the proposed approach are compared and contrasted with several baselines and recent work in this area. The performance of the proposed approach is found to be significantly better in terms of detection accuracy, model complexity and lead-time to detection

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

Stochastic dynamical system identification applied to combustor stability margin assessment

A new approach was developed to determine the operational stability margin of a laboratory scale combustor. Applying modern and robust techniques and tools from Dynamical System Theory, the approach was based on three basic steps. In the first step, a gray-box thermoacoustical model for the combustor was derived. The second step consisted in applying System Identification techniques to experimental data in order to validate the model and estimate its parameters. The application of these techniques to experimental data under different operating conditions allowed us to determine the functional dependence of the model parameters upon changes in an experimental control parameter. Finally, the third step consisted in using that functional dependence to predict the response of the system at different operating conditions and, ultimately, estimate its operational stability margin. The results indicated that a low-order stochastic non-linear model, including two excited modes, has been identified and the combustor operational stability margin could be estimated by applying a continuation method.Ph.D.Committee Chair: Zinn, Ben; Committee Member: Ferri, Aldo; Committee Member: Lieuwen, Timothy; Committee Member: Prasad, J. V. R.; Committee Member: Ruzzene, Massim

Studies on Dynamics of Financial Markets and Reacting Flows

One of the central problems in financial markets analysis is to understand the nature of the underlying stochastic dynamics. Several intraday behaviors are analyzed to study trading day ensemble averages of both high frequency foreign exchange and stock markets data. These empirical results indicate that the underlying stochastic processes have nonstationary increments. The three most liquid foreign exchange markets and five most actively traded stocks each contains several time intervals during the day where the mean square fluctuation and variance of increments can be fit by power law scaling in time. The fluctuations in return within these intervals follow asymptotic bi-exponential distributions. Based on these empirical results, an intraday stochastic model with linear variable diffusion coefficient is proposed to approximate the real dynamics of financial markets to the lowest order, and to test the effects of time averaging techniques typically used for financial time series analysis. The proposed model replicates major statistical characteristics of empirical financial time series and only ensemble averaging techniques deduce the underlying dynamics correctly. The proposed model also provides new insight into the modeling of financial markets' dynamics in microscopic time scales. Also discussed are analytical and computational studies of reacting flows. Many dynamical features of the flows can be inferred from modal decompositions and coupling between modes. Both proper orthogonal (POD) and dynamic mode (DMD) decompositions are conducted on high-frequency, high-resolution empirical data and their results and strengths are compared and contrasted. In POD the contribution of each mode to the flow is quantified using the latency only, whereas each DMD mode can be associated a latency as well as a unique complex growth rate. By comparing DMD spectra from multiple nominally identical experiments, it is possible to identify "reproducible" modes in a flow. A similar differentiation cannot be made using POD. Time-dependent coefficients of DMD modes are complex. Even in noisy experimental data, it is found that the phase of these coefficients (but not their magnitude) exhibits repeatable dynamics. Hence it is suggested that dynamical characterizations of complex flows are best analyzed through the phase dynamics of reproducible DMD modes.Physics, Department o

Semiannual report

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period 1 Oct. 1994 - 31 Mar. 1995