08:30
- CANCELED - Real-time Stochastic Volatility Tracking via Filtering for a Partially-Observed Heston Model
Yong Zeng | University of Missouri - Kansas City and National Science Foundation (NSF) | United States
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Authors:
Yong Zeng | University of Missouri - Kansas City and National Science Foundation (NSF) | United States
Brent Bundick | Federal Reserve Bank of Kansas City | United States
Junqi Yin | Oak Ridge National Laboratory | United States
For a partially-observed Heston stochastic volatility model at random times with contaminated additive, clustering and rounding noise, we demonstrate how online tracking of Heston stochastic volatility is made possible by GPU computing. The evolving distribution of stochastic volatility and other parameters as new trade occurs is governed by a filtering equation (FE), which is a stochastic partial differential equation (SPDE). Numerically solving such a FE provides the tracking of stochastic volatility, which is the Bayesian estimation as new data flowing in. We present simulation and empirical results obtained from both supercomputers and GPUs to demonstrate that real-time volatility tracking is possible.
09:10
A micro-macro Markov chain Monte Carlo method for molecular dynamics using reaction coordinate proposals
Hannes Vandecasteele | KU Leuven | Germany
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Hannes Vandecasteele | KU Leuven | Germany
Giovanni Samaey | KU Leuven | Belgium
In this talk we present a new micro-macro Markov chain Monte Carlo method (mM-MCMC) to sample invariant distributions in molecular dynamics systems for which the associated Langevin dynamics exhibits a time-scale separation between the microscopic (fast) dynamics, and the (slow) dynamics of some low-dimensional (macroscopic) set of reaction coordinates. The algorithm enhances exploration of the state space in the presence of metastability by allowing larger proposal moves at the macroscopic level, on which a conditional accept-reject procedure is applied. Only when the macroscopic proposal is accepted, the full microscopic state is reconstructed from the newly sampled reaction coordinate value. We also present an algorithm in which this reconstruction yields a microscopic state that only approximately corresponds to the prescribed reaction coordinate. The computational gain stems from the fact that most proposals are rejected at the macroscopic level, at low computational cost, while microscopic states, once reconstructed, are almost always accepted. We numerically illustrate their efficiency two standard molecular test cases.
09:30
System Norms for Sensitivity Analysis of Random Differential-Algebraic Equations
Roland Pulch | Universität Greifswald | Germany
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Authors:
Roland Pulch | Universität Greifswald | Germany
Akil Narayan | University of Utah/SCI Institute | United States
We consider linear dynamical systems consisting of differential-algebraic equations (DAEs), which include physical parameters. A single output is defined as a quantity of interest (QoI). We change the parameters into random variables to perform an uncertainty quantification. The QoI becomes a random process. Our aim is a sensitivity analysis of the random QoI with respect to the individual random variables. Sobol’s concept uses partial variances and implies time-dependent total effect sensitivity indices. Alternatively, we derive sensitivity measures independent of both time and transient inputs of the system. The random QoI is expanded into a series of the polynomial chaos. The stochastic Galerkin method yields a larger system of DAEs with multiple outputs, which represent approximations of unknown coefficients. We arrange different overlapping groups of outputs associated to the partial variances. Consequently, system norms of the stochastic Galerkin DAEs produce sensitivity measures. We apply the H-infinity norm of the transfer function in the frequency domain. However, evaluations of this norm are costly in the case of high-dimensional systems. Hence we investigate methods of model order reduction to decrease this computational effort. The balanced truncation technique provides a priori error bounds for the H-infinity norms. We demonstrate results of numerical computations for a test example.
09:50
- CANCELED - Sequential Optimal Design for Complex Systems with Time Delay Under Uncertainty
Changqing Cheng | Binghamton University | United States
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Authors:
Changqing Cheng | Binghamton University | United States
Yiming Che | Binghamton University | United States
Dynamic evolution of time-delay systems can be represented by a delay differential equation (DDE). Numerous high-fidelity simulations, such as temporal finite element method (TFEM), have been attempted to evaluate system stability under time delay. However, it is cumbersome to explore a large parameter design space with expensive-to-evaluate high-fidelity simulations, particularly considering the complex contour of stability boundary. Moreover, the uncertainty associated with process variables that cannot be controlled could further compound the design effort. Alternatively, low-fidelity surrogate models efficiently emulate a high-fidelity simulation, albeit at the expense of accuracy, not ideal to inspect the system behavior near the boundary.
We develop a multi-fidelity approach to delineate the stability boundary in a sequential fashion: (1) generalized polynomial chaos (GPC) is used to propagate uncertainty from process variables to the stability index. Compared to Monte Carlo method, GPC eliminates the cumbersome evaluation of TFEM at each possible realization of process variables, and obtains the mean and variance (intrinsic uncertainty) of stability index. (2) Stochastic kriging is then used to evaluate stability index at new sampling points, the predicted mean and variance (extrinsic uncertainty) are included to find the trade-off between local exploitation and global exploration. The application in the machining process corroborates our proposed approach.
10:10
Robust Identification of Frequency Response Function via a Multi-Fidelity Approach
Shuai Guo | Technical University of Munich | Germany
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Authors:
Shuai Guo | Technical University of Munich | Germany
Camilo F. Silva | Technical University of Munich | Germany
Wolfgang Polifke | Technical University of Munich | Germany
Frequency response function (FFR) of a linear time-invariant system is crucial for analyzing system dynamics. It is possible to derive FFR numerically by exciting the simulation of the dynamical system. To achieve a globally more accurate and less uncertain FFR identification, in this study, we propose a novel statistical approach to aggregate results with two different fidelities: one by harmonic excitations (high-fidelity), which provide accurate FFR estimations at several discrete frequencies; One by a short-time broadband excitation (low-fidelity), which provides FFR estimations over the entire frequency range of interest, but estimations are uncertain due to the limited length of the simulated time series and the associated low signal-to-noise ratio when a strong noise level is present. This approach is based on Hierarchical Gaussian Process, which takes the low-fidelity results as the global trend in the Gaussian Process model of the high-fidelity function. In addition, a bootstrapping strategy is proposed in our approach to propagate the uncertainties associated with the low-fidelity results to the multi-fidelity ones. We apply this approach to identify the FFR of a flame dynamical system in a gas turbine combustor, which describes the linear response of the flame heat release rate to upstream flow perturbations, and encapsulates multi-scale multi-physics features of the turbulent combustion process.
10:30
- CANCELED - Uncertainty Quantification and Propagation of Partially Unknown Dynamical Systems using Monitoring Data
Daniz Teymouri | Hong Kong University of Science and Technology | Hong Kong
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Authors:
Daniz Teymouri | Hong Kong University of Science and Technology | Hong Kong
Omid Sedehi | Hong Kong University of Science and Technology | Hong Kong
Lambros S. Katafygiotis | Hong Kong University of Science and Technology | Hong Kong
Costas Papadimitriou | University of Thessaly | Greece
The lack of knowledge about dynamical parameters, applied loadings, dynamical responses as well as measurement errors imposes significant uncertainties in data-driven structural identification problems. In this study, the problem of uncertainty quantification and propagation in partially unknown dynamical systems is addressed by developing a new sequential Bayesian method. The proposed method can estimate and update the state, the input, the parameters, and the noise characteristics in real-time while using the discrete-time state-space process and observation models. Thus, the first step is defining rational prior distributions for the state, parameters, inputs, and noise covariance matrices. Following a conjugate prior strategy, the noise characteristics are described as slow-varying processes using Inverse-Wishart distributions, whilst the joint probability distribution of the state, input, and parameters is characterized using a multivariate Gaussian distribution. This particular choice of priors enhances the computational efficiency of the method since it requires computing only the first and second statistical moments whereby the posterior distributions can be expressed explicitly. The efficacy of the proposed method is demonstrated and verified using two numerical examples, comparing the results in terms of both the estimations and the uncertainty bounds associated with the unobserved response quantities of interest.