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At least 487 records · Page 27

Probabilistic neural networks for fluid flow surrogate modeling and data recovery

We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (i) the shallow-water equations, (ii) a two-dimensional cylinder flow, (iii) the wake of a NACA0012 airfoil with a Gurney flap, and (iv) the NOAA sea surface temperature data set. Furthermore, the present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow surrogate model but also systematically quantifies the uncertainty therein to assist with model interpretability.

42 ENGINEERING↗

Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been recently reported that successfully solve PDEs, with examples including deep feed forward networks, generative networks, and deep encoder-decoder networks. However, practical adoption of these approaches is limited by the difficulty in training these models, especially to make predictions at large output resolutions (≥1024×1024). Here we report on a software framework for data parallel distributed deep learning that resolves the twin challenges of training these large SciML models - training in reasonable time as well as distributing the storage requirements. Our framework provides several out of the box functionality including (a) loss integrity independent of number of processes, (b) synchronized batch normalization, and (c) distributed higher-order optimization methods. We show excellent scalability of this framework on both cloud as well as HPC clusters, and report on the interplay between bandwidth, network topology and bare metal vs cloud. We deploy this approach to train generative models of sizes hitherto not possible, showing that neural PDE solvers can be viably trained for practical applications. We also demonstrate that distributed higher-order optimization methods are 2-3× faster than stochastic gradient-based methods and provide minimal convergence drift with higher batch-size.

PDEs↗

AGGREGATE: dAta-driven modelinG preservinG contRollable dEr for outaGe mAnagemenT and rEsiliency (Report for Task 9: Viability of Data-Driven Approach for Outage Management (Deliverable D6))

This technical report is provided to US Department of Energy for progress made on the AGGERGATE project led by the Washington State University. This report is specifically related to the deliverable: ’D6: Technical report discussing the viability of the developed data-driven models and co-simulation architecture for models for operation in a real-world operational setting and the results of Tasks 1 to 8, summarizing the project findings and accomplishments to date’.

42 ENGINEERING↗

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient surrogate modeling methods for large-scale Earth system models based on machine-learning techniques

Abstract. Improving predictive understanding of Earth system variability and change requires data–model integration. Efficient data–model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a surrogate of a large-scale Earth system model (ESM) with many output variables is computationally intensive because it involves a large number of expensive ESM simulations. In this effort, we propose an efficient surrogate method capable of using a few ESM runs to build an accurate and fast-to-evaluate surrogate system of model outputs over large spatial and temporal domains. We first use singular value decomposition to reduce the output dimensions and then use Bayesian optimization techniques to generate an accurate neural network surrogate model based on limited ESM simulation samples. Our machine-learning-based surrogate methods can build and evaluate a large surrogate system of many variables quickly. Thus, whenever the quantities of interest change, such as a different objective function, a new site, and a longer simulation time, we can simply extract the information of interest from the surrogate system without rebuilding new surrogates, which significantly reduces computational efforts. We apply the proposed method to a regional ecosystem model to approximate the relationship between eight model parameters and 42 660 carbon flux outputs. Results indicate that using only 20 model simulations, we can build an accurate surrogate system of the 42 660 variables, wherein the consistency between the surrogate prediction and actual model simulation is 0.93 and the mean squared error is 0.02. This highly accurate and fast-to-evaluate surrogate system will greatly enhance the computational efficiency of data–model integration to improve predictions and advance our understanding of the Earth system.

58 GEOSCIENCES↗

Global Modeling and Data Assimilation: Documentation of the Tangent Linear and Adjoint Models of the Relaxed Arakawa-Schubert Moisture Parameterization of the NASA GEOS-1 GCM - Volume 11

A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in the NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail.

Suarez, Max J.↗

Constraining Bedrock Groundwater Residence Times in a Mountain System with Environmental Tracer Observations and Bayesian Uncertainty Quantification: Modeling and Data Package

Groundwater residence times provide fundamental descriptions of hydrologic dynamics and mixing processes in mountainous watersheds. Yet, few observational datasets that can constrain groundwater residence times over broad timescales are available in high elevation mountain systems. Here we present field observations from May 2021 of dissolved noble gases (He, Ne, Ar, Kr, and Xe), Chloroflourcarbons (CFCs), Sulfurhexaflouride (SF6), and tritium (3H) sampled from the Pumphouse Lower Montane study site (wells PLM1, PLM6, and PLM7) within the East River Watershed, Colorado. The presented noble gas (PLM_noblegas_2021.csv) and environmental tracer (PLM_tracers_2021.csv) observation datasets, along with the associated modeling scripts, aide in quantifying groundwater residence times and recharge conditions in a high elevation mountain system. Furthermore, the modeling scripts quantify groundwater residence time and noble gas recharge condition uncertainties using a novel Markov-chain Monte Carlo approach. All data modeling scripts are written in the Python code.

54 ENVIRONMENTAL SCIENCES↗

Modeling the Effects of Irrigation on Land Surface Fluxes and States over the Conterminous United States: Sensitivity to Input Data and Model Parameters

Previous studies on irrigation impacts on land surface fluxes/states were mainly conducted as sensitivity experiments, with limited analysis of uncertainties from the input data and model irrigation schemes used. In this study, we calibrated and evaluated the performance of irrigation water use simulated by the Community Land Model version 4 (CLM4) against observations from agriculture census. We investigated the impacts of irrigation on land surface fluxes and states over the conterminous United States (CONUS) and explored possible directions of improvement. Specifically, we found large uncertainty in the irrigation area data from two widely used sources and CLM4 tended to produce unrealistically large temporal variations of irrigation demand for applications at the water resources region scale over CONUS. At seasonal to interannual time scales, the effects of irrigation on surface energy partitioning appeared to be large and persistent, and more pronounced in dry than wet years. Even with model calibration to yield overall good agreement with the irrigation amounts from the National Agricultural Statistics Service (NASS), differences between the two irrigation area datasets still dominate the differences in the interannual variability of land surface response to irrigation. Our results suggest that irrigation amount simulated by CLM4 can be improved by (1) calibrating model parameter values to account for regional differences in irrigation demand and (2) accurate representation of the spatial distribution and intensity of irrigated areas.

CLM4↗

Integrating Wind Profiling Radars and Radiosonde Observations with Model Point Data to Develop a Decision Support Tool to Assess Upper-Level Winds for Space Launch

On the day-of-launch, the 45th Weather Squadron (45 WS) Launch Weather Officers (LWOs) monitor the upper-level winds for their launch customers to include NASA's Launch Services Program and NASA's Ground Systems Development and Operations Program. They currently do not have the capability to display and overlay profiles of upper-level observations and numerical weather prediction model forecasts. The LWOs requested the Applied Meteorology Unit (AMU) develop a tool in the form of a graphical user interface (GUI) that will allow them to plot upper-level wind speed and direction observations from the Kennedy Space Center (KSC) 50 MHz tropospheric wind profiling radar, KSC Shuttle Landing Facility 915 MHz boundary layer wind profiling radar and Cape Canaveral Air Force Station (CCAFS) Automated Meteorological Processing System (AMPS) radiosondes, and then overlay forecast wind profiles from the model point data including the North American Mesoscale (NAM) model, Rapid Refresh (RAP) model and Global Forecast System (GFS) model to assess the performance of these models. The AMU developed an Excel-based tool that provides an objective method for the LWOs to compare the model-forecast upper-level winds to the KSC wind profiling radars and CCAFS AMPS observations to assess the model potential to accurately forecast changes in the upperlevel profile through the launch count. The AMU wrote Excel Visual Basic for Applications (VBA) scripts to automatically retrieve model point data for CCAFS (XMR) from the Iowa State University Archive Data Server (http://mtarchive.qeol.iastate.edu) and the 50 MHz, 915 MHz and AMPS observations from the NASA/KSC Spaceport Weather Data Archive web site (http://trmm.ksc.nasa.gov). The AMU then developed code in Excel VBA to automatically ingest and format the observations and model point data in Excel to ready the data for generating Excel charts for the LWO's. The resulting charts allow the LWOs to independently initialize the three models 0-hour forecasts against the observations to determine which is the best performing model and then overlay the model forecasts on time-matched observations during the launch countdown to further assess the model performance and forecasts. This paper will demonstrate integration of observed and predicted atmospheric conditions into a decision support tool and demonstrate how the GUI is implemented in operations.

Bauman, William H., III↗

Data Driven Model Development for the Supersonic Semispan Transport (S(sup 4)T)

We investigate two common approaches to model development for robust control synthesis in the aerospace community; namely, reduced order aeroservoelastic modelling based on structural finite-element and computational fluid dynamics based aerodynamic models and a data-driven system identification procedure. It is shown via analysis of experimental Super- Sonic SemiSpan Transport (S4T) wind-tunnel data using a system identification approach it is possible to estimate a model at a fixed Mach, which is parsimonious and robust across varying dynamic pressures.

Kukreja, Sunil L.↗

NAME Modeling and Data Assimilation: A Strategic Overview

In this presentation a strategic overview of modeling and related data analysis and assimilation components of the North American Monsoon Experiment (NAME) are given. Building on the NAME science plan, a strategy is outlined for accelerating progress on the fundamental modeling issues pertaining to NAME science goals. The strategy takes advantage of NAME enhanced observations, and should simultaneously provide model-based guidance to the evolving multi-tiered NAME observing program. The NAME modeling strategy recognizes three distinct, but related, roles that observations play in model development and assessment. These are: (1) to guide model development by providing constraints on model simulations at the process level (e.g. convection, land/atmosphere and ocean/atmosphere interactions); (2) to help assess the veracity of model simulations of the various key NAMS phenomena (e.g. low level jets, land sea breezes, tropical storms), and the linkages to regional and larger-scale climate variability; and (3) to provide initial and boundary conditions, and verification data for model predictions.

Schubert, Siegfried↗

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

97 MATHEMATICS AND COMPUTING↗

Compilation of Test Data on 111 Free-Spinning Airplane Models Tested in the Langley 15-Foot and 20-Foot Free-Spinning Tunnels

A compilation of free-spinning-airplane model data on the spin and recovery characteristics of 111 airplanes is presented. These data were previously published in separate memorandum reports and were obtained from free-spinning tests in the Langley 15-foot and the Langley 20-foot free-spinning tunnels. The model test data presented include the steady-spin and recovery characteristics of each model for various combinations of aileron and elevator deflections and for various loadings and dimensional configurations. Dimensional data, mass data, and a three-view drawing of the corresponding free-spinning tunnel model are also presented for each airplane. The data presented should be of value to designers and should facilitate the design of airplanes incorporating satisfactory spin-recovery characteristics.

Malvestuto, Frank S.↗

Data-driven modeling to enhance municipal water demand estimates in response to dynamic climate conditions

Altered precipitation and temperature patterns from a changing climate will affect supply, demand, and overall municipal water system operations throughout the arid western U.S. While supply forecasts leverage hydrological models to connect climate influences with surface water availability, demand forecasts typically estimate water use independent of climate and other externalities. Stemming from an increased focus on seasonal water demand management, we use the Salt Lake City, Utah municipal water system as a test bed to assess model accuracy versus complexity trade-offs between simple climate-independent econometric-based models and complex climate-sensitive data-driven models to average to extreme wet and dry climate conditions—representative of a new climate normal. Here, the climate-independent model displayed low performance during extreme dry conditions with predictions exceeding 90% and 40% of the observed monthly and seasonal volumetric demands, respectively, which we attribute to insufficient model complexity. The climate-sensitive models displayed greater accuracy in all conditions, with an ordinary least squares model demonstrating a measurable reduction in prediction bias (3.4% vs. -27.3%) and RMSE (74.0 lpcd vs. 294 lpcd) compared to the climate-independent model. The climate-sensitive workflow increased model accuracy and characterized climate-demand interactions, demonstrating a novel tool to enhance water system management.

54 ENVIRONMENTAL SCIENCES↗

USACM Thematic Workshop On Uncertainty Quantification And Data-Driven Modeling.

The USACM Thematic Workshop on Uncertainty Quantification and Data-Driven Modeling was held on March 23-24, 2017, in Austin, TX. The organizers of the technical program were James R. Stewart of Sandia National Laboratories and Krishna Garikipati of University of Michigan. The administrative organizer was Ruth Hengst, who serves as Program Coordinator for the USACM. The organization of this workshop was coordinated through the USACM Technical Thrust Area on Uncertainty Quantification and Probabilistic Analysis. The workshop website (http://uqpm2017.usacm.org) includes the presentation agenda as well as links to several of the presentation slides (permission to access the presentations was granted by each of those speakers, respectively). Herein, this final report contains the complete workshop program that includes the presentation agenda, the presentation abstracts, and the list of posters.

97 MATHEMATICS AND COMPUTING↗