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Constructing robust and efficient experimental designs in groundwater modeling using a Galerkin method, proper orthogonal decomposition, and metaheuristic algorithms.

ABSTRACT: Estimating parameters accurately in groundwater models for aquifers is challenging because the models are non-explicit solutions of complex partial differential equations. Modern research methods, such as Monte Carlo methods and metaheuristic algorithms, for searching an efficient design to estimate model parameters require hundreds, if not thousands of model calls, making the computational cost prohibitive. One method to circumvent the problem and gain valuable insight on the behavior of groundwater is to first apply a Galerkin method and convert the system of partial differential equations governing the flow to a discrete problem and then use a Proper Orthogonal Decomposition to project the high-dimensional model space of the original groundwater model to create a reduced groundwater model with much lower dimensions. The reduced model can be solved several orders of magnitude faster than the full model and able to provide an accurate estimate of the full model. The task is still challenging because the optimization problem is non-convex, non-differentiable and there are continuous variables and integer-valued variables to optimize. Following convention, heuristic algorithms and a combination is used search to find efficient designs for the reduced groundwater model using various optimality criteria. The main goals are to introduce new design criteria and the concept of design efficiency for experimental design research in hydrology. The two criteria have good utility but interestingly, do not seem to have been implemented in hydrology. In addition, design efficiency is introduced. Design efficiency is a method to assess how robust a design is under a change of criteria. The latter is an important issue because the design criterion may be subjectively selected and it is well known that an optimal design can perform poorly under another criterion. It is thus desirable that the implemented design has relatively high efficiencies under a few criteria. As applications, two heuristic algorithms are used to find optimal designs for a small synthetic aquifer design problem and a design problem for a large-scale groundwater model and assess their robustness properties to other optimality criteria. The results show the proof of concept is workable for finding a more informed and efficient model-based design for a water resource study.

SUBMITTER: Ushijima TT

PROVIDER: S-EPMC8341624 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:To detect localized glaucomatous structural changes using proper orthogonal decomposition (POD) framework with false-positive control that minimizes confirmatory follow-ups, and to compare the results to topographic change analysis (TCA).We included 167 participants (246 eyes) with ?4 Heidelberg Retina Tomograph (HRT)-II exams from the Diagnostic Innovations in Glaucoma Study; 36 eyes progressed by stereo-photographs or visual fields. All other patient eyes (n = 210) were non-progressing. Specificities were evaluated using 21 normal eyes. Significance of change at each HRT superpixel between each follow-up and its nearest baseline (obtained using POD) was estimated using mixed-effects ANOVA. Locations with significant reduction in retinal height (red pixels) were determined using Bonferroni, Lehmann-Romano k-family-wise error rate (k-FWER), and Benjamini-Hochberg false discovery rate (FDR) type I error control procedures. Observed positive rate (OPR) in each follow-up was calculated as a ratio of number of red pixels within disk to disk size. Progression by POD was defined as one or more follow-ups with OPR greater than the anticipated false-positive rate. TCA was evaluated using the recently proposed liberal, moderate, and conservative progression criteria.Sensitivity in progressors, specificity in normals, and specificity in non-progressors, respectively, were POD-Bonferroni = 100%, 0%, and 0%; POD k-FWER = 78%, 86%, and 43%; POD-FDR = 78%, 86%, and 43%; POD k-FWER with retinal height change ?50 ?m = 61%, 95%, and 60%; TCA-liberal = 86%, 62%, and 21%; TCA-moderate = 53%, 100%, and 70%; and TCA-conservative = 17%, 100%, and 84%.With a stronger control of type I errors, k-FWER in POD framework minimized confirmatory follow-ups while providing diagnostic accuracy comparable to TCA. Thus, POD with k-FWER shows promise to reduce the number of confirmatory follow-ups required for clinical care and studies evaluating new glaucoma treatments. (ClinicalTrials.gov number, NCT00221897.).

Project description:PurposeIntraventricular blood flow dynamics are associated with cardiac function. Accurate, noninvasive, and easy assessments of hemodynamic quantities (such as velocity, vortex, and pressure) could be an important addition to the clinical diagnosis and treatment of heart diseases. However, the complex time-varying flow brings many challenges to the existing noninvasive image-based hemodynamic assessments. The development of reliable techniques and analysis tools is essential for the application of hemodynamic biomarkers in clinical practice.MethodsIn this study, a time-resolved particle tracking method, Shake-the-Box, was applied to reconstruct the flow in a realistic left ventricle (LV) silicone model with biological valves. Based on the obtained velocity, 4D pressure field was calculated using a Poisson equation-based pressure solver. Furthermore, flow analysis by proper orthogonal decomposition (POD) of the 4D velocity field has been performed.ResultsAs a result of the Shake-the-Box algorithm, we have extracted: (i) particle positions, (ii) particle tracks, and finally, (iii) 4D velocity fields. From the latter, the temporal evolution of the 3D pressure field during the full cardiac cycle was obtained. The obtained maximal pressure difference extracted along the base-to-apex was about 2.7 mmHg, which is in good agreement with those reported in vivo. The POD analysis results showed a clear picture of different scale of vortices in the pulsatile LV flow, together with their time-varying information and corresponding kinetic energy content. To reconstruct 95% of the kinetic energy of the LV flow, only the first six POD modes would be required, leading to significant data reduction.ConclusionsThis work demonstrated Shake-the-Box is a promising technique to accurately reconstruct the left ventricle flow field in vitro. The good spatial and temporal resolutions of the velocity measurements enabled a 4D reconstruction of the pressure field in the left ventricle. The application of POD analysis showed its potential in reducing the complexity of the high-resolution left ventricle flow measurements. For future work, image analysis, multi-modality flow assessments, and the development of new flow-derived biomarkers can benefit from fast and data-reducing POD analysis.

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Constructing robust and efficient experimental designs in groundwater modeling using a Galerkin method, proper orthogonal decomposition, and metaheuristic algorithms.

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