scholarly journals Impact of model inconsistencies on reconstructions of past mantle flow obtained using the adjoint method

2020 ◽  
Vol 221 (1) ◽  
pp. 617-639 ◽  
Author(s):  
L Colli ◽  
H-P Bunge ◽  
J Oeser
Keyword(s):  
Adjoint Method ◽  
Dynamic Models ◽  
Current Model ◽  
Synthetic Data ◽  
Model Parameters ◽  
Mantle Flow ◽  
Initial State ◽  
Final State ◽  
State Estimations ◽  
The Cost

SUMMARY The adjoint method is a powerful technique to compute sensitivities (Fréchet derivatives) with respect to model parameters, allowing one to solve inverse problems where analytical solutions are not available or the cost to determine many times the associated forward problem is prohibitive. In Geodynamics it has been applied to the restoration problem of mantle convection—that is, to reconstruct past mantle flow states with dynamic models by finding optimal flow histories relative to the current model state—so that poorly known mantle flow parameters can be tested against observations gleaned from the geological record. By enabling us to construct time dependent earth models the adjoint method has the potential to link observations from seismology, geology, mineral physics and palaeomagnetism in a dynamically consistent way, greatly enhancing our understanding of the solid Earth system. Synthetic experiments demonstrate for the ideal case of no model error and no data error that the adjoint method restores mantle flow over timescales on the order of a transit time (≈100 Myr). But in reality unavoidable limitations enter the inverse problem in the form of poorly known model parameters and uncertain state estimations, which may result in systematic errors of the reconstructed flow history. Here we use high-resolution, 3-D spherical mantle circulation models to perform a systematic study of synthetic adjoint inversions, where we insert on purpose a mismatch between the model used to generate synthetic data and the model used for carrying out the inversion. By considering a mismatch in rheology, final state and history of surface velocities we find that mismatched model parameters do not inhibit misfit reduction: the adjoint method still produces a flow history that fits the estimated final state. However, the recovered initial state can be a poor approximation of the true initial state, where reconstructed and true flow histories diverge exponentially back in time and where for the more divergent cases the reconstructed initial state includes physically implausible structures, especially in and near the thermal boundary layers. Consequently, a complete reduction of the cost function may not be desirable when the goal is a best fit to the initial condition. When the estimated final state is a noisy low-pass version of the true final state choosing an appropriate misfit function can reduce the generation of artefacts in the initial state. While none of the model mismatches considered in this study, taken singularly, results in a complete failure of the recovered flow history, additional work is needed to assess their combined effects.

The adjoint equations for thermochemical compressible mantle convection: derivation and verification by twin experiments

2020 ◽  
Author(s):  
Sia Ghelichkhan ◽  
Hans-Peter Bunge
Keyword(s):  
Mantle Convection ◽  
Compressible Flows ◽  
Adjoint Method ◽  
Reference Model ◽  
Adjoint Equations ◽  
Mantle Flow ◽  
Dynamic Topography ◽  
Final State ◽  
Flow Models ◽  
The Cost

<div> <div> <div> <p>The adjoint method is an efficient way to obtain gradient information in a mantle convection model relative to past flow structure, allowing one to retrodict mantle flow from observations of the present-day mantle state. While adjoint equations for isochemical mantle flow have been derived for both incompressible and compressible flows, here we extend the method to thermochemical mantle flow models, and present thermochemical adjoint equations in the elastic-liquid approximation. We verify the method with twin experiments, and retrodict the flow history of a thermochemical reference model (reference twin) assuming for the final state, either a consistent thermochemical interpretation, using the thermochemical adjoint equations, or an inconsistent purely thermal interpretation, using the isochemical adjoint equations. The consistent simulation correctly retrodicts the flow evolution of the reference twin. The inconsistent case, instead, restores a false flow history whereby internal buoyancy forces and convectively maintained topography are overestimated. Because the cost function is reduced in either case, our results suggest that the adjoint method can be used to link assumptions on the role of chemical mantle heterogeneity to geologic inferences of dynamic topography, thus providing additional means to test hypotheses on mantle composition and dynamics.</p> </div> </div> </div>

scholarly journals The adjoint equations for thermochemical compressible mantle convection: derivation and verification by twin experiments

2018 ◽  
Vol 474 (2220) ◽  
pp. 20180329 ◽  
Author(s):  
S. Ghelichkhan ◽  
H-.P. Bunge
Keyword(s):  
Mantle Convection ◽  
Compressible Flows ◽  
Adjoint Method ◽  
Reference Model ◽  
Adjoint Equations ◽  
Mantle Flow ◽  
Dynamic Topography ◽  
Final State ◽  
Flow Models ◽  
The Cost

The adjoint method is an efficient way to obtain gradient information in a mantle convection model relative to past flow structure, allowing one to retrodict mantle flow from observations of the present-day mantle state. While adjoint equations for isochemical mantle flow have been derived for both incompressible and compressible flows, here we extend the method to thermochemical mantle flow models, and present thermochemical adjoint equations in the elastic-liquid approximation. We verify the method with twin experiments, and retrodict the flow history of a thermochemical reference model (reference twin) assuming for the final state, either a consistent thermochemical interpretation, using the thermochemical adjoint equations, or an inconsistent purely thermal interpretation, using the isochemical adjoint equations. The consistent simulation correctly retrodicts the flow evolution of the reference twin. The inconsistent case, instead, restores a false flow history whereby internal buoyancy forces and convectively maintained topography are overestimated. Because the cost function is reduced in either case, our results suggest that the adjoint method can be used to link assumptions on the role of chemical mantle heterogeneity to geologic inferences of dynamic topography, thus providing additional means to test hypotheses on mantle composition and dynamics.

scholarly journals The Application of an Evolutionary Algorithm to the Optimization of a Mesoscale Meteorological Model

2009 ◽  
Vol 48 (2) ◽  
pp. 317-329 ◽  
Author(s):  
Lance O’Steen ◽  
David Werth
Keyword(s):  
Cost Function ◽  
Evolutionary Algorithm ◽  
Synthetic Data ◽  
Atmospheric Model ◽  
Atmospheric Modeling ◽  
Model Parameters ◽  
Meteorological Model ◽  
Rms Error ◽  
Mesoscale Atmospheric Model ◽  
The Cost

Abstract It is shown that a simple evolutionary algorithm can optimize a set of mesoscale atmospheric model parameters with respect to agreement between the mesoscale simulation and a limited set of synthetic observations. This is illustrated using the Regional Atmospheric Modeling System (RAMS). A set of 23 RAMS parameters is optimized by minimizing a cost function based on the root-mean-square (rms) error between the RAMS simulation and synthetic data (observations derived from a separate RAMS simulation). It is found that the optimization can be done with relatively modest computer resources; therefore, operational implementation is possible. The overall number of simulations needed to obtain a specific reduction of the cost function is found to depend strongly on the procedure used to perturb the “child” parameters relative to their “parents” within the evolutionary algorithm. In addition, the choice of meteorological variables that are included in the rms error and their relative weighting are also found to be important factors in the optimization.

scholarly journals Accommodating Taste and Scale Heterogeneity for Front-Seat Passenger’ Choice of Seat Belt Usage

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 460 ◽  
Author(s):  
Mahdi Rezapour ◽  
Khaled Ksaibati
Keyword(s):  
Mixed Model ◽  
Seat Belt ◽  
Model Fit ◽  
Model Parameters ◽  
Extended Model ◽  
Random Parameters ◽  
Front Seat ◽  
Scale Heterogeneity ◽  
Error Terms ◽  
The Cost

There is growing interest in implementation of the mixed model to account for heterogeneity across population observations. However, it has been argued that the assumption of independent and identically distributed (i.i.d) error terms might not be realistic, and for some observations the scale of the error is greater than others. Consequently, that might result in the error terms’ scale to be varied across those observations. As the standard mixed model could not account for the aforementioned attribute of the observations, extended model, allowing for scale heterogeneity, has been proposed to relax the equal error terms across observations. Thus, in this study we extended the mixed model to the model with heterogeneity in scale, or generalized multinomial logit model (GMNL), to see if accounting for the scale heterogeneity, by adding more flexibility to the distribution, would result in an improvement in the model fit. The study used the choice data related to wearing seat belt across front-seat passengers in Wyoming, with all attributes being individual-specific. The results highlighted that although the effect of the scale parameter was significant, the scale effect was trivial, and accounting for the effect at the cost of added parameters would result in a loss of model fit compared with the standard mixed model. Besides considering the standard mixed and the GMNL, the models with correlated random parameters were considered. The results highlighted that despite having significant correlation across the majority of the random parameters, the goodness of fits favors more parsimonious models with no correlation. The results of this study are specific to the dataset used in this study, and due to the possible fact that the heterogeneity in observations related to the front-seat passengers seat belt use might not be extreme, and do not require extra layer to account for the scale heterogeneity, or accounting for the scale heterogeneity at the cost of added parameters might not be required. Extensive discussion has been made in the content of this paper about the model parameters’ estimations and the mathematical formulation of the methods.

scholarly journals Dual subtractions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Renato Maria Prisco ◽  
Francesco Tramontano
Keyword(s):  
Field Theory ◽  
Quantum Field ◽  
Matrix Elements ◽  
Leading Order ◽  
Initial State ◽  
Final State ◽  
Dual Representation ◽  
Subtraction Scheme ◽  
Theoretical Predictions ◽  
Perturbative Quantum

Abstract We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.

scholarly journals Cost-effectiveness of TAS-102 plus bevacizumab versus TAS-102 monotherapy in patients with metastatic colorectal cancer

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Kiyoaki Sugiura ◽  
Yuki Seo ◽  
Takayuki Takahashi ◽  
Hideyuki Tokura ◽  
Yasuhiro Ito ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Health Care ◽  
Sensitivity Analysis ◽  
Cost Effectiveness ◽  
Combination Therapy ◽  
Metastatic Colorectal Cancer ◽  
Cost Effective ◽  
Model Parameters ◽  
Combination Regimen ◽  
The Cost

Abstract Background TAS-102 plus bevacizumab is an anticipated combination regimen for patients who have metastatic colorectal cancer. However, evidence supporting its use for this indication is limited. We compared the cost-effectiveness of TAS-102 plus bevacizumab combination therapy with TAS-102 monotherapy for patients with chemorefractory metastatic colorectal cancer. Method Markov decision modeling using treatment costs, disease-free survival, and overall survival was performed to examine the cost-effectiveness of TAS-102 plus bevacizumab combination therapy and TAS-102 monotherapy. The Japanese health care payer’s perspective was adopted. The outcomes were modeled on the basis of published literature. The incremental cost-effectiveness ratio (ICER) between the two treatment regimens was the primary outcome. Sensitivity analysis was performed and the effect of uncertainty on the model parameters were investigated. Results TAS-102 plus bevacizumab had an ICER of $21,534 per quality-adjusted life-year (QALY) gained compared with TAS-102 monotherapy. Sensitivity analysis demonstrated that TAS-102 monotherapy was more cost-effective than TAS-102 and bevacizumab combination therapy at a willingness-to-pay of under $50,000 per QALY gained. Conclusions TAS-102 and bevacizumab combination therapy is a cost-effective option for patients who have metastatic colorectal cancer in the Japanese health care system.

scholarly journals A flexible framework for sequential estimation of model parameters in computational hemodynamics

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Christopher J. Arthurs ◽  
Nan Xiao ◽  
Philippe Moireau ◽  
Tobias Schaeffter ◽  
C. Alberto Figueroa
Keyword(s):  
Unscented Kalman Filter ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Sequential Estimation ◽  
Wall Material ◽  
Patient Specific ◽  
Model Parameters ◽  
Computational Framework ◽  
Lumped Parameter ◽  
Estimation Of Model Parameters

AbstractA major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A “Netlist” implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

scholarly journals Protocol for the health economic evaluation of increasing the weekend specialist to patient ratio in hospitals in England

BMJ Open ◽  
2018 ◽  
Vol 8 (2) ◽  
pp. e015561 ◽  
Author(s):  
Samuel I Watson ◽  
Yen-Fu Chen ◽  
Julian F Bion ◽  
Cassie P Aldridge ◽  
Alan Girling ◽  
...  
Keyword(s):  
Health Economic Evaluation ◽  
Care Quality ◽  
Expert Elicitation ◽  
Weekend Effect ◽  
Model Parameters ◽  
Risk Of Death ◽  
Causal Processes ◽  
Key Policy ◽  
The Uk ◽  
The Cost

IntroductionThis protocol concerns the evaluation of increased specialist staffing at weekends in hospitals in England. Seven-day health services are a key policy for the UK government and other health systems trying to improve use of infrastructure and resources. A particular motivation for the 7-day policy has been the observed increase in the risk of death associated with weekend admission, which has been attributed to fewer hospital specialists being available at weekends. However, the causes of the weekend effect have not been adequately characterised; many of the excess deaths associated with the ‘weekend effect’ may not be preventable, and the presumed benefits of improved specialist cover might be offset by the cost of implementation.Methods/designThe Bayesian-founded method we propose will consist of four major steps. First, the development of a qualitative causal model. Specialist presence can affect multiple, interacting causal processes. One or more models will be developed from the results of an expert elicitation workshop and probabilities elicited for each model and relevant model parameters. Second, systematic review of the literature. The model from the first step will provide search limits for a review to identify relevant studies. Third, a statistical model for the effects of specialist presence on care quality and patient outcomes. Fourth, valuation of outcomes. The expected net benefits of different levels of specialist intensity will then be evaluated with respect to the posterior distributions of the parameters.Ethics and disseminationThe study was approved by the Review Subcommittee of the South West Wales REC on 11 November 2013. Informed consent was not required for accessing anonymised patient case records from which patient identifiers had been removed. The findings of this study will be published in peer-reviewed journals; the outputs from this research will also form part of the project report to the HS&DR Programme Board.

scholarly journals Development and testing of a community flood resilience measurement tool

2016 ◽  
Author(s):  
Adriana Keating ◽  
Karen Campbell ◽  
Michael Szoenyi ◽  
Colin McQuistan ◽  
David Nash ◽  
...  
Keyword(s):  
Sustainable Livelihoods ◽  
Development Work ◽  
Measurement Tool ◽  
Disaster Resilience ◽  
Initial State ◽  
Final State ◽  
Sustainable Livelihoods Framework ◽  
Flood Characteristics ◽  
Over Time ◽  
Livelihoods Framework

Abstract. Given the increased attention on resilience-strengthening in international humanitarian and development work, there is a growing need to invest in its measurement and the overall accountability of "resilience strengthening" initiatives. We present a framework and tool for measuring community level resilience to flooding, built around the five capitals (5Cs) of the Sustainable Livelihoods Framework. At the time of writing the tool is being tested in 75 communities across 10 countries. Currently 88 potential sources of resilience are measured at the baseline (initial state) and endline (final state) approximately two years later. If a flood occurs in the community during the study period, resilience outcome measures are recorded. By comparing pre-flood characteristics to post flood outcomes, we aim to empirically verify sources of resilience, something which has never been done in this field. There is an urgent need for the continued development of theoretically anchored, empirically verified and practically applicable disaster resilience measurement frameworks and tools so that the field may: a) deepen understanding of the key components of "disaster resilience" in order to better target resilience enhancing initiatives, and b) enhance our ability to benchmark and measure disaster resilience over time, and compare how resilience changes as a result of different capacities, actions and hazards.

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