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computer model calibration with Time Series Data Using Deep Learning and Quantile Regression

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION 2022年第1期10卷 1-26页

作者： Bhatnagar, Saumya Chang, Won Kim, Seonjin Wang, Jiali Univ Cincinnati Cincinnati OH 45221 USA Miami Univ Oxford OH 45056 USA Argonne Natl Lab Lemont IL 60439 USA

computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiments is input parameter uncertainty. computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data, such as large time series, due to the difficulty in building an emulator and the nonidentifiability between effects from input parameters and data-model discrepancy. To overcome these challenges, we propose a new calibration framework based on a deep neural network (DNN) with long shortterm memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the "learning with noise" idea, we train our DNN model to filter out the effects from data-model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with the Weather Research and Forecasting model Hydrological modeling system (WRF-Hydro), we show our approach can yield accurate point estimates and well-calibrated interval estimates for input parameters.

关键词： computer model calibration deep learning long short-term memory network data-model discrepancy

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A sequential approach for stochastic computer model calibration and prediction

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2013年 111卷 273-286页

作者： Yuan, Jun Ng, Szu Hui Natl Univ Singapore Dept Ind & Syst Engn Singapore 117576 Singapore

computer models are widely used to simulate complex and costly real processes and systems. When the computer model is used to assess and certify the real system for decision making, it is often important to calibrate the computer model so as to improve the model's predictive accuracy. A sequential approach is proposed in this paper for stochastic computer model calibration and prediction. More precisely, we propose a surrogate based Bayesian approach for stochastic computer model calibration which accounts for various uncertainties including the calibration parameter uncertainty in the follow up prediction and computer model analysis. We derive the posterior distribution of the calibration parameter and the predictive distributions for both the real process and the computer model which quantify the calibration and prediction uncertainty and provide the analytical calibration and prediction results. We also derive the predictive distribution of the discrepancy term between the real process and the computer model that can be used to validate the computer model. Furthermore, in order to efficiently use limited data resources to obtain a better calibration and prediction performance, we propose a two-stage sequential approach which can effectively allocate the limited resources. The accuracy and efficiency of the proposed approach are illustrated by the numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： computer model calibration Stochastic computer simulation Guassian process model Bayesian analysis Parameter uncertainty Uncertainty quantification

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calibration of Stochastic computer models Using Stochastic Approximation Methods

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2013年第1期10卷 171-186页

作者： Yuan, Jun Szu Hui Ng Tsui, Kwok Leung Natl Univ Singapore Dept Ind & Syst Engn Singapore 119077 Singapore Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

computer models are widely used to simulate real processes. Within the computer model, there always exist some parameters which are unobservable in the real process but need to be specified in the model. The procedure to adjust these unknown parameters in order to fit the model to observed data and improve predictive capability is known as calibration. Practically, calibration is typically done manually. In this paper, we propose an effective and efficient algorithm based on the stochastic approximation (SA) approach that can be easily automated. We first demonstrate the feasibility of applying stochastic approximation to stochastic computer model calibration and apply it to three stochastic simulation models. We compare our proposed SA approach with another direct calibration search method, the genetic algorithm. The results indicate that our proposed SA approach performs equally as well in terms of accuracy and significantly better in terms of computational search time. We further consider the calibration parameter uncertainty in the subsequent application of the calibrated model and propose an approach to quantify it using asymptotic approximations.

关键词： computer model calibration parameter uncertainty stochastic approximation stochastic computer simulation

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IMPROVING ICE SHEET model calibration USING PALEOCLIMATE AND MODERN DATA

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ANNALS OF APPLIED STATISTICS 2016年第4期10卷 2274-2302页

作者： Chang, Won Haran, Murali Applegate, Patrick Pollard, David Univ Cincinnati Dept Math Sci Cincinnati OH 45221 USA Penn State Univ Dept Stat University Pk PA 16802 USA Penn State Univ Earth & Environm Syst Inst University Pk PA 16802 USA

Human-induced climate change may cause significant ice volume loss from the West Antarctic Ice Sheet (WAIS). Projections of ice volume change from ice sheet models and corresponding future sea-level rise have large uncertainties due to poorly constrained input parameters. In most future applications to date, model calibration has utilized only modern or recent (decadal) observations, leaving input parameters that control the long-term behavior of WAIS largely unconstrained. Many paleo-observations are in the form of localized time series, while modern observations are non-Gaussian spatial data;combining information across these types poses nontrivial statistical challenges. Here we introduce a computationally efficient calibration approach that utilizes both modern and paleo-observations to generate better constrained ice volume projections. Using fast emulators built upon principal component analysis and a reduced dimension calibration model, we can efficiently handle high-dimensional and non-Gaussian data. We apply our calibration approach to the PSU3D-ICE model which can realistically simulate long-term behavior of WAIS. Our results show that using paleo-observations in calibration significantly reduces parametric uncertainty, resulting in sharper projections about the future state of WAIS. One benefit of using paleo-observations is found to be that unrealistic simulations with overshoots in past ice retreat and projected future regrowth are eliminated.

关键词： Paleoclimate West Antarctic Ice Sheet computer model calibration Gaussian process dimension reduction

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Inferring likelihoods and climate system characteristics from climate models and multiple tracers

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ENVIRONMETRICS 2012年第4期23卷 345-362页

作者： Bhat, K. Sham Haran, Murali Olson, Roman Keller, Klaus Los Alamos Natl Lab Stat Sci Div Los Alamos NM 87545 USA Penn State Univ Dept Stat University Pk PA 16802 USA Penn State Univ Dept Geosci University Pk PA 16802 USA Penn State Univ Earth & Environm Syst Inst University Pk PA 16802 USA

Characterizing the risks of anthropogenic climate change poses considerable statistical challenges. A key problem is how to combine the information contained in large-scale observational data sets with simulations of Earth system models in a statistically sound and computationally tractable manner. Here, we describe a statistical approach for improving projections of the North Atlantic meridional overturning circulation (AMOC). The AMOC is part of the global ocean conveyor belt circulation and transfers heat between low and high latitudes in the Atlantic basin. The AMOC might collapse in a tipping point response to anthropogenic climate forcings. Assessing the risk of an AMOC collapse is of considerable interest because it may result in major impacts on natural and human systems. AMOC projections rely on simulations from complex climate models. One key source of uncertainty in AMOC projections is uncertainty about background ocean vertical diffusivity (Kv), an important model parameter. Kv cannot be directly observed but can be inferred by combining climate model output with observations on the oceans (so-called tracers). Here, we combine information from multiple tracers, each observed on a spatial grid. Our two-stage approach emulates the computationally expensive climate model using a flexible hierarchical model to connect the tracers. We then infer Kv using our emulator and the observations via a Bayesian approach, accounting for observation error and model discrepancy. We utilize kernel mixing and matrix identities in our Gaussian process model to considerably reduce the computational burdens imposed by the large data sets. We find that our approach is flexible, reduces identifiability issues, and enables inference about Kv based on large data sets. We use the resulting inference about Kv to improve probabilistic projections of the AMOC. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： computer model calibration Bayesian hierarchical modeling Gaussian process computer experiments multivariate spatial data climate change

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Upscaling Uncertainty with Dynamic Discrepancy for a Multi-Scale Carbon Capture System

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2017年第520期112卷 1453-1467页

作者： Bhat, K. Sham Mebane, David S. Mahapatra, Priyadarshi Storlie, Curtis B. Los Alamos Natl Lab Los Alamos NM 87545 USA West Virginia Univ Dept Mech & Aerosp Engn Morgantown WV 26506 USA Natl Energy Technol Lab Morgantown WV USA Mayo Clin Rochester MN USA

Uncertainties from model parameters and model discrepancy from small-scale models impact the accuracy and reliability of predictions of large-scale systems. Inadequate representation of these uncertainties may result in inaccurate and overconfident predictions during scale-up to larger systems. Hence, multiscale modeling efforts must accurately quantify the effect of the propagation of uncertainties during upscaling. Using a Bayesian approach, we calibrate a small-scale solid sorbent model to thermogravimetric (TGA) data on a functional profile using chemistry-based priors. Crucial to this effort is the representation of model discrepancy, which uses a Bayesian smoothing splines (BSS-ANOVA) framework. Our uncertainty quantification (UQ) approach could be considered intrusive as it includes the discrepancy function within the chemical rate expressions;resulting in a set of stochastic differential equations. Such an approach allows for easily propagating uncertainty by propagating the joint model parameter and discrepancy posterior into the larger scale system of rate expressions. The broad UQ framework presented here could be applicable to virtually all areas of science where multiscale modeling is used. Supplementary materials for this article are available online.

关键词： Bayesian hierarchical modeling BSS-ANOVA computer model calibration Extrapolation Functional data Propagation of uncertainty

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A FAST PARTICLE-BASED APPROACH FOR CALIBRATING A 3-D model OF THE ANTARCTIC ICE SHEET

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ANNALS OF APPLIED STATISTICS 2020年第2期14卷 605-634页

作者： Lee, Ben Seiyon Haran, Murali Fuller, Robert W. Pollard, David Keller, Klaus Penn State Univ Dept Stat University Pk PA 16802 USA Penn State Univ Dept Geosci University Pk PA 16802 USA Penn State Univ Earth & Environm Syst Inst University Pk PA 16802 USA

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we in

关键词： Antarctic ice sheet model computer model calibration paleoclimate sequential Monte Carlo uncertainty quantification

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PVactVal: A Validation Approach for Agent-based modeling of Residential Photovoltaic Adoption 18

PVactVal: A Validation Approach for Agent-based Modeling of ...

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18th International Conference on the European Energy Market (EEM)

作者： Johanning, Simon Abitz, Daniel Schulte, Emily Scheller, Fabian Bruckner, Thomas Univ Leipzig Inst Infrastruct & Resources Management IIRM Leipzig Germany Univ Leipzig Univ Comp Ctr Res & Dev Leipzig Germany Tech Univ Denmark Dept Technol Management & Econ Lyngby Denmark

ISBN: (数字)9781665408967

ISBN: (纸本)9781665408967

Agent-based simulation models are an important tool to study the effectiveness of policy interventions on the uptake of residential photovoltaic systems by households, a cornerstone of sustainable energy system transition. In order for these models to be trustworthy, they require rigorous validation. However, the canonical approach of validating emulation models through calibration with parameters that minimize the difference of model results and reference data fails when the model is subject to many stochastic influences. The residential photovoltaic diffusion model PVact features numerous stochastic influences that prevent straightforward optimization-driven calibration. From the analysis of the results of a case-study on the cities Dresden and Leipzig (Germany) based on three error metrics (mean average error, root mean square error and cumulative average error), this research identifies a parameter range where stochastic fluctuations exceed differences between results of different parameterization and a minimization-based calibration approach fails. Based on this observation, an approach is developed that aggregates model behavior across multiple simulation runs and parameter combinations to compare results between scenarios representing different future developments or policy interventions of interest.

关键词： Agent-based modeling computer model Validation computer model calibration Innovation Diffusion Rooftop Photovoltaic Diffusion

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Quantifying cognitive bias in educational researchers

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INTERNATIONAL JOURNAL OF RESEARCH & METHOD IN EDUCATION 2021年第4期44卷 395-413页

作者： Bierema, Andrea Hoskinson, Anne-Marie Moscarella, Rosa Lyford, Alex Haudek, Kevin Merrill, John Urban-Lurain, Mark Michigan State Univ Ctr Integrat Studies Gen Sci E Lansing MI 48824 USA Michigan State Univ Dept Integrat Biol E Lansing MI 48824 USA South Dakota State Univ Dept Biol & Microbiol Brookings SD 57007 USA Univ Massachusetts Dept Biol Amherst MA 01003 USA Middlebury Coll Dept Math Middlebury VT 05753 USA Michigan State Univ Dept Biochem & Mol Biol E Lansing MI 48824 USA Michigan State Univ Dept Microbiol & Mol Genet E Lansing MI 48824 USA Michigan State Univ CREATE STEM E Lansing MI 48824 USA

As we take advantage of new technologies that allow us to streamline the coding process of large qualitative datasets, we must consider whether human cognitive bias may introduce statistical bias in the process. Our research group analyzes large sets of student responses by developing computer models that are trained using human-coded responses and a suite of machine-learning techniques. Once a model is initially trained, it may be insufficiently accurate. Increasing the number of human-coded responses typically enhances these models to an acceptable level of accuracy. Alternatively, instead of human coding responses, we can rapidly increase the number of coded responses by verifying computer-predicted codes for each response. However, having access to this information may bias human coders. We designed the present study to test for differences in level of agreement with computer-predicted codes in terms of magnitude and direction during computer model calibration if information about computer-predicted codes is available. Our results indicate human coding bias despite being disciplinary experts who were aware of the possibility of cognitive bias creating statistical bias and that magnitude and direction of that bias varies across experts.

关键词： Coding computer model calibration cognitive bias confirmation bias experimenter bias logistic regression machine learning

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Spatiotemporal modeling and optimization for personalized cardiac simulation

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IISE TRANSACTIONS ON HEALTHCARE SYSTEMS ENGINEERING 2021年第2期11卷 145-160页

作者： Yao, Bing Oklahoma State Univ Sch Ind Engn & Management Stillwater OK 74078 USA

Computational modeling of the heart has contributed tremendously in quantitatively understanding the cardiac functions, showing great potential to assist medical doctors in heart-disease diagnosis. However, cardiac simulation is generally subject to uncertainties and variabilities among different individuals. Traditional "one-size-fits-all" simulation is limited in providing individualized optimal diagnosis and treatment for patients with heart disease. Realizing the full potential of cardiac computational modeling in clinical practice requires effective and efficient model personalization. In this paper, we develop a spatiotemporal modeling and optimization framework for cardiac model calibration. The proposed calibration framework not only effectively quantifies the spatiotemporal discrepancy between the simulation model and the physical cardiac system, but also increases the computational efficiency in personalized modeling of cardiac electrophysiology. The model performance is validated and evaluated in the 3D cardiac simulation. Numerical experiments demonstrate that the proposed framework significantly outperforms traditional approaches in calibrating the cardiac simulation.

关键词： Dynamic spatiotemporal warping hierarchical Gaussian process cardiac electrophysiology modeling computer model calibration

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