This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.2 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.
This paper describes an efficient reverse-mode differentiation algorithm for contraction operations for arbitrary and unconventional tensor network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have a single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve eficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.
The TChem open-source software is a toolkit for computing thermodynamic properties, source term, and source term’s Jacobian matrix for chemical kinetic models that involve gas and surface reactions.
CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE/DAE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems.
We present a simple, near-real-time Bayesian method to infer and forecast a multiwave outbreak, and demonstrate it on the COVID-19 pandemic. The approach uses timely epidemiological data that has been widely available for COVID-19. It provides short-term forecasts of the outbreak’s evolution, which can then be used for medical resource planning. The method postulates one- and multiwave infection models, which are convolved with the incubation-period distribution to yield competing disease models. The disease models’ parameters are estimated via Markov chain Monte Carlo sampling and information-theoretic criteria are used to select between them for use in forecasting. The method is demonstrated on two- and three-wave COVID-19 outbreaks in California, New Mexico and Florida, as observed during Summer-Winter 2020. We find that the method is robust to noise, provides useful forecasts (along with uncertainty bounds) and that it reliably detected when the initial single-wave COVID-19 outbreaks transformed into successive surges as containment efforts in these states failed by the end of Spring 2020.
This report investigates the use of unsupervised probabilistic learning techniques for the analysis of hypersonic trajectories. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. Using the diffusion coordinates on the graph of training samples, the probabilistic framework augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path-planing algorithm. In this framework the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time. A 3DOF model was employed to generate optimal hypersonic trajectories that comprise the training datasets. The diffusion map algorithm identfied that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. In addition to the path-planing worflow we also propose an algorithm that utilizes the diffusion map coordinates along the manifold to label and possibly remove outlier samples from the training data. This algorithm can be used to both identify edge cases for further analysis as well as to remove them from the training set to create a more robust set of samples to be used for the path-planing process.
In this paper we investigate the utility of one-dimensional convolutional neural network (CNN) models in epidemiological forecasting. Deep learning models, in particular variants of recurrent neural networks (RNNs) have been studied for ILI (Influenza-Like Illness) forecasting, and have achieved a higher forecasting skill compared to conventional models such as ARIMA. In this study, we adapt two neural networks that employ one-dimensional temporal convolutional layers as a primary building block—temporal convolutional networks and simple neural attentive meta-learners—for epidemiological forecasting. We then test them with influenza data from the US collected over 2010-2019. We find that epidemiological forecasting with CNNs is feasible, and their forecasting skill is comparable to, and at times, superior to, plain RNNs. Thus CNNs and RNNs bring the power of nonlinear transformations to purely data-driven epidemiological models, a capability that heretofore has been limited to more elaborate mechanistic/compartmental disease models.
Bayesian inference is used to calibrate a bottom-up home PLC network model with unknown loads and wires at frequencies up to 30 MHz. A network topology with over 50 parameters is calibrated using global sensitivity analysis and transitional Markov Chain Monte Carlo (TMCMC). The sensitivity-informed Bayesian inference computes Sobol indices for each network parameter and applies TMCMC to calibrate the most sensitive parameters for a given network topology. A greedy random search with TMCMC is used to refine the discrete random variables of the network. This results in a model that can accurately compute the transfer function despite noisy training data and a high dimensional parameter space. The model is able to infer some parameters of the network used to produce the training data, and accurately computes the transfer function under extrapolative scenarios.
We have extended the computational singular perturbation (CSP) method to differential algebraic equation (DAE) systems and demonstrated its application in a heterogeneous-catalysis problem. The extended method obtains the CSP basis vectors for DAEs from a reduced Jacobian matrix that takes the algebraic constraints into account. We use a canonical problem in heterogeneous catalysis, the transient continuous stirred tank reactor (T-CSTR), for illustration. The T-CSTR problem is modelled fundamentally as an ordinary differential equation (ODE) system, but it can be transformed to a DAE system if one approximates typically fast surface processes using algebraic constraints for the surface species. We demonstrate the application of CSP analysis for both ODE and DAE constructions of a T-CSTR problem, illustrating the dynamical response of the system in each case. We also highlight the utility of the analysis in commenting on the quality of any particular DAE approximation built using the quasi-steady state approximation (QSSA), relative to the ODE reference case.
Jivani, Aniket; Huan, Xun; Safta, Cosmin S.; Zhou, Beckett Y.; Gauger, Nicolas R.
Understanding the behavior of turbulent jets under variable environment and uncertain conditions is critical for predicting and mitigating aircraft jet noise. However, uncertainty quantification (UQ) for jet noise, which requires repeated expensive eddy-resolving simulations, is often computationally prohibitive. We thus build surrogate models, in particular Karhunen-Loève expansions (KLEs) for field quantities of interest in three-dimensional turbulent round jets. We build them in a multifidelity manner by combining simulation data from high-fidelity enhanced delayed detached-eddy simulation (EDDES) and low-fidelity Reynolds-averaged Navier-Stokes (RANS), generated under uncertain nozzle exit stagnation pressure and inlet eddy viscosity ratio. Furthermore, we form the KLEs in conjunction with polynomial chaos expansions in order to explicitly associate their randomness to each physical source of uncertainty, and so justifying the combining procedure in the multifidelity construct. We illustrate advantages of the new multifidelity KLE against single-fidelity KLEs, with the former achieving more accurate predictions at locations away from existing high-fidelity training data. With the KLE surrogate, we conduct UQ inexpensively.
CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems. The software provides support for: General ODE models (gODE model class) for computing source terms and Jacobians for a generic ODE system; TChem model (ChemElemODETChem model class) for computing source term, Jacobian, other necessary chemical reaction data, as well as the rates of progress for a homogenous batch reactor using an elementary step detailed chemical kinetic reaction mechanism. This class relies on the TChem [2] library; A set of functions to compute essential elements of CSP analysis (Kernel class). This includes computations of the eigensolution of the Jacobian matrix, CSP basis vectors and co-vectors, time scales (reciprocals of the magnitudes of the Jacobian eigenvalues), mode amplitudes, CSP pointers, and the number of exhausted modes. This class relies on the Tines library; A set of functions to compute the eigensolution of the Jacobian matrix using Tines library GPU eigensolver; A set of functions to compute CSP indices (Index Class). This includes participation indices and both slow and fast importance indices.
We demonstrate a Bayesian method for the “real-time” characterization and forecasting of partially observed COVID-19 epidemic. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. The estimation problem is posed as one of Bayesian inference and solved using a Markov chain Monte Carlo technique. The data used in this study was sourced before the arrival of the second wave of infection in July 2020. The proposed modeling approach, when applied at the country level, generally provides accurate forecasts at the regional, state and country level. The epidemiological model detected the flattening of the curve in California, after public health measures were instituted. The method also detected different disease dynamics when applied to specific regions of New Mexico.
Chemical kinetics simulations are used to explore whether detailed measurements of relevant chemical species during the oxidation of very dilute fuels (less than 1 Torr partial pressure) in a high-pressure plug flow reactor (PFR) can predict autoignition propensity. We find that for many fuels the timescale for the onset of spontaneous oxidation in dilute fuel/air mixtures in a simple PFR is similar to the 1st-stage ignition delay time (IDT) at stoichiometric engine-relevant conditions. For those fuels that deviate from this simple trend, the deviation is closely related to the peak rate of production of OH, HO2, CH2O, and CO2 formed during oxidation. We use these insights to show that an accurate correlation between simulated profiles of these species in a PFR and 1st-stage IDT can be developed using convolutional neural networks. Our simulations suggest that the accuracy of such a correlation is 10–50%, which is appropriate for rapid fuel screening and may be sufficient for predictive fuel performance modeling.
In this report we describe an enhanced methodology for performing stochastic Bayesian inversions of atmospheric trace gas inversions that allows the time variation of model parameters to be inferred. We use measurements of methane atmospheric mixing ratio made in Livermore, California along with atmospheric transport modeling and published prior estmates of emissions to estimate the regional emissions of methane and the temporal variations in inferred bias parameters. We compute Bayesian model evidence and continuous rank probability score to optimize the model with respect to temporal resolution. Using two different emissions inventories, we perform inversions for a series of models with increasing temporal resolution in the model bias representation. We show that temporal variation in the model bias can improve the model fit and can also increase the likelihood that the parameterization is appropriate, as measured by the Baysian model evidence. .