Adaptive Grid Algorithm Research Articles

Modeling Pharmacokinetics in Individual Patients Using Therapeutic Drug Monitoring and Artificial Population Quasi-Models: A Study with Piperacillin.

Population pharmacokinetic (pop-PK) models constructed for model-informed precision dosing often have limited utility due to the low number of patients recruited. To augment such models, an approach is presented for generating fully artificial quasi-models which can be employed to make individual estimates of pharmacokinetic parameters. Based on 72 concentrations obtained in 12 patients, one- and two-compartment pop-PK models with or without creatinine clearance as a covariate were generated for piperacillin using the nonparametric adaptive grid algorithm. Thirty quasi-models were subsequently generated for each model type, and nonparametric maximum a posteriori probability Bayesian estimates were established for each patient. A significant difference in performance was found between one- and two-compartment models. Acceptable agreement was found between predicted and observed piperacillin concentrations, and between the estimates of the random-effect pharmacokinetic variables obtained using the so-called support points of the pop-PK models or the quasi-models as priors. The mean squared errors of the predictions made using the quasi-models were similar to, or even considerably lower than those obtained when employing the pop-PK models. Conclusion: fully artificial nonparametric quasi-models can efficiently augment pop-PK models containing few support points, to make individual pharmacokinetic estimates in the clinical setting.

Numerical study on the electromagnetic force control of the flow based on an advanced parallel adaptive technology

ABSTRACT Developing a technology that can reduce drag and oscillations on objects in a flowing fluid has been a long dream of researchers. Here, a parallel adaptive-grid algorithm for capturing the flow field is adopted to construct an electromagnetic force solver. Based on this solver, the impact of different Reynolds numbers (Re) and computational domain sizes on the vortex structure distribution is investigated in detail. Grid-adaptive criteria for capturing the flow details based on multiple physical quantities are studied to increase the numerical accuracy and improve the calculation efficiency. Numerical simulations of the flow around a bluff body are performed for different Re to establish the effect of the Lorentz force on the flow. By introducing this parallel adaptive-grid algorithm, the number of grids and computing resources is considerably reduced. In addition, parallel algorithms that can realize multi-threaded dynamic load balancing and further reduce the length of computational cycles.

An energy optimal schedule method for distribution network considering the access of distributed generation and energy storage

AbstractThe access of large‐scale distributed generation (DG) easily leads to energy imbalance in distribution network. To deal with this issue, this paper proposes an energy optimal schedule method for distribution network considering the participation of source‐load‐storage aggregation groups (SAGs). Firstly, the system model consisting of distribution network layer and SAGs layer is established, and the schedule objectives and constraints of each layer are also given. Secondly, considering the fluctuation on the load side, a forecasting method based on Adaboost integrated convolutional neural networks and bidirectional long‐short term memory is proposed. Then, the improved sparrow search algorithm (ISSA) is proposed by using the tent map and Levy flight on the original sparrow search algorithm. At the same time, by introducing Pareto dominance relation and adaptive grid algorithm, the multi‐objective sparrow search algorithm (MOSSA) is derived. After that, a two‐layer optimization framework (ISSA–MOSSA) is proposed to solve the studied system. The simulation results verify the accuracy of the proposed load forecasting model, the superiority of ISSA as well as MOSSA, and the effectiveness of ISSA–MOSSA in solving the energy optimal schedule problem of the distribution system with the access of DG.

Deep optimization of model predictive control performance for wind turbine yaw system based on intelligent fuzzy deduction

Because wind direction has the trait of time varying, yaw is a common state of wind turbine (WT). To improve the energy capture and reduce the yaw actuator usage time, a Model Predictive Control (MPC) method based on the Fuzzy Deduction Weight Coefficient Evaluator (FDWE) is proposed. Specifically, in view of the two contradictory control objectives of energy capture loss ratio and yaw actuator usage ratio in MPC, FDWE is designed to dynamically adjusts the weight coefficient connecting the two objectives according to the predicted wind direction. On this basis, to fully exert the advantage of FDWE, the fuzzy rule and membership function (MF) are tried to be simultaneously optimized. For this complex optimization problem involving different types of multiple design variables, three different solving strategies are proposed: fuzzy rule-MF ordered optimization, mixed integer optimization, and association optimization. Finally, an improved Adaptive Grid Algorithm Multi-Objective Particle Swarm Optimization is presented to solve the formulated optimization problems. The results indicate that the optimized FDWE-MPC using the three strategies not only improves the energy capture of the WT, but also reduces the use of yaw actuator compared to the baseline MPC. Consequently, the proposed method is promising in reducing the production cost for the WTs.

Fitting Multiplet Simulations to L-Edge XAS Spectra of Transition-Metal Complexes Using an Adaptive Grid Algorithm.

A new methodology based on an adaptive grid algorithm followed by an analysis of the ground state from the fit parameters is presented to analyze and interpret experimental XAS L2,3-edge data. The fitting method is tested first in a series of multiplet calculations for d0-d7 systems and for which the solution is known. In most cases, the algorithm is able to find the solution, except for a mixed-spin Co2+ Oh complex, where it instead revealed a correlation between the crystal field and the electron repulsion parameters near spin-crossover transition points. Furthermore, the results for the fitting of previously published experimental data sets on CaO, CaF2, MnO, LiMnO2, and Mn2O3 are presented and their solution discussed. The presented methodology has allowed the evaluation of the Jahn-Teller distortion in LiMnO2, which is consistent with the observed implications in the development of batteries, which use this material. Moreover, a follow-up analysis of the ground state in Mn2O3 has demonstrated an unusual ground state for the highly distorted site which would be impossible to optimize in a perfect octahedral environment. Ultimately, the presented methodology can be used in the analysis of X-ray absorption spectroscopy data measured at the L2,3-edge for a large number of materials and molecular complexes of first-row transition metals and can be expanded to the analysis of other X-ray spectroscopic data in future studies.

An Optimal Adaptive Grid Method Based on L1 Scheme for a Nonlinear Caputo Fractional Differential Equation

A nonlinear fractional differential equation with a Caputo derivative of order α is studied. This problem is discretized by using the L1 scheme on an arbitrary nonuniform mesh. By utilizing the Taylor expansion with integral remainder term, an optimal local truncation error estimation of L1 scheme is proved. Based on this truncation error estimation and the mesh equidistribution principle, a new monitor function is constructed to construct an adaptive grid generation algorithm. Numerical experiments are performed to confirm the accuracy of our new adaptive grid algorithm.

Model-Informed Rationale for Early Therapeutic Drug Monitoring of Colistin in Critically Ill Patients.

Adequate colistin exposure is important for microbiological clearance. This study was performed in critically ill patients >18 years old to develop a simplified nonparametric pharmacokinetic (PK) model of colistin for routine clinical use and to determine the role of dose optimization. The Non-Parametric Adaptive Grid algorithm within the Pmetrics software package for R was used to develop a PK model from 47 patients, and external validation of the final model was performed in 13 patients. A 1-compartment multiplicative gamma error model with 0-order input and first-order elimination of colistin was developed with creatinine clearance and serum albumin as covariates on elimination rate constant. An R2 for observed vs individual predicted colistin concentrations of 0.92 was obtained in the validation cohort. High interindividual variability in colistin steady-state area under the plasma concentration-time curve (AUC) from from 120 hours to 144 hours (coefficient of variation=80.1%) and a high interoccasion variability (median coefficient of variation of AUC from time 0 to hours predicted every 8hours for initial 96hours after starting colistin=23.8) was predicted in patients who received this antibiotic for a period of over 152hours (n=22). With the model-suggested dose regimen, only 20% of simulated profiles achieved AUC from time 0 to 24 hours in the range of 50 to 60mg• h/L due to high variability in population PK. In this group of patients, steady-state colistin concentrations were predicted to be achieved >96hours after initiation of colistimethate sodium. This study advocates the need for early and repeated therapeutic drug monitoring and dose optimization in critically ill patients to achieve adequate therapeutic concentration of colistin.

Imipenem/cilastatin/relebactam pharmacokinetics in critically ill patients with augmented renal clearance.

Imipenem and relebactam are predominantly excreted via glomerular filtration. Augmented renal clearance (ARC) is a common syndrome in critically-ill patients with sepsis, and sub-therapeutic antibiotic concentrations are of concern. Herein, we describe the pharmacokinetics of imipenem/relebactam in critically-ill patients with ARC. Infected patients in the ICU with ARC (CLCR ≥ 130 mL/min) received a single dose of imipenem/cilastatin/relebactam 1.25 g as a 30 min infusion. Blood samples were collected over 6 h for concentration determination. Protein binding was assessed by ultrafiltration. An 8 h urine creatinine collection confirmed ARC. Population pharmacokinetic models with and without covariates were fit using the non-parametric adaptive grid algorithm in Pmetrics. A 5000 patient Monte Carlo simulation assessed joint PTA using relebactam fAUC/MIC ≥8 and imipenem ≥40% fT>MIC. Eight patients with ARC completed the study. A base population pharmacokinetic model with two-compartments fitted the data best. The mean ± SD parameters were: CL, 17.31 ± 5.76 L/h; Vc, 16.15 ± 7.75 L; k12, 1.62 ± 0.99 h-1; and k21, 3.53 ± 3.31 h-1 for imipenem, and 11.51 ± 4.79 L/h, 16.54 ± 7.43 L, 1.59 ± 1.12 h-1, and 2.83 ± 2.91 h-1 for relebactam. Imipenem/cilastatin/relebactam 1.25 g as a 30 min infusion every 6 h achieved 100% and 93% PTA at MICs of 1 and 2 mg/L, respectively. Despite enhanced clearance of both imipenem and relebactam, the currently approved dosing regimen for normal renal function was predicted to achieve optimal exposure in critically-ill patients with ARC sufficient to treat most susceptible pathogens.

Differential Privacy-Based Location Protection in Spatial Crowdsourcing

Spatial crowdsourcing (SC) is a location-based outsourcing service whereby SC-server allocates tasks to workers with mobile devices according to the locations outsourced by requesters and workers. Since location information contains individual privacy, the locations should be protected before being submitted to untrusted SC-server. However, the encryption schemes limit data availability, and existing differential privacy (DP) methods do not protect the tasks’ location privacy. In this paper, we propose a differential privacy-based location protection (DPLP) scheme, which protects the location privacy of both workers and tasks, and achieves task allocation with high data utility. Specifically, DPLP splits the exact locations of both workers and tasks into noisy multi-level grids by using adaptive three-level grid decomposition (ATGD) algorithm and DP-based adaptive complete pyramid grid (DPACPG) algorithm, respectively, thereby considering the grid granularity and location privacy. Furthermore, DPLP adopts an optimal greedy algorithm to calculate a geocast region around the task grid, which achieves the trade-off between acceptance rate and system overhead. Detailed privacy analysis demonstrates that our DPLP scheme satisfies <inline-formula><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -differential privacy. The extensive analysis and experiments over two real-world datasets confirm high efficiency and data utility of our scheme.

A Novel Second-Order Adaptive Grid Method for Singularly Perturbed Convection–Diffusion Equations

In this paper, a singularly perturbed convection–diffusion equation is studied. At first, the original problem is transformed into a parameterized singularly perturbed Volterra integro-differential equation by using an integral transform. Then, a second-order finite difference method on an arbitrary mesh is given. The stability and local truncation error estimates of the discrete schemes are analyzed. Based on the mesh equidistribution principle and local truncation error estimation, an adaptive grid algorithm is given. In addition, in order to calculate the parameters of the transformation equation, a nonlinear unconstrained optimization problem is constructed. Numerical experiments are given to illustrate the effectiveness of our presented adaptive grid algorithm.

Adaptive Multilevel Nonuniform Grid Algorithm for the Accelerated Analysis of Composite Metallic–Dielectric Radomes

An adaptive multilevel nonuniform grid (MLNG) algorithm is developed for the accelerated computation of fields radiated through composite metallic–dielectric radomes as well as antenna-radome interactions. The MLNG approach is applied to the mixed potential formulation of the coupled surface and volume electric field integral equations. The radome is decomposed into a hierarchy of subdomains (SDs) by an adaptive algorithm that closely follows the radome geometry, allowing significant savings in memory and CPU time. In the MLNG algorithm, only local generalized impedance matrices of the finest level SDs are evaluated. Far-zone potentials and fields are indirectly evaluated through a multilevel aggregation involving phase-and amplitude-compensated interpolation on nonuniform grids (NGs), requiring considerably fewer calculations as compared with the classical method of moments (MoM). The MLNG algorithm is incorporated in a preconditioned iterative solver. Accuracy as well as memory consumption and computation times of the algorithm are studied on realistic examples. The radome effect on the antenna input impedance and electric current density distribution is demonstrated. The method is validated by comparison with a commercial MoM software and shown to exhibit a computational complexity (CC) of O(NlogN), N being the number of unknowns.

Numerical analysis of a system of semilinear singularly perturbed first‐order differential equations on an adaptive grid

An adaptive grid method based on the backward Euler formula for a system of semilinear singularly perturbed initial value problems is studied. Based on the a priori error analysis and mesh equidistribution principle, we prove that the convergence rate of our semidiscrete adaptive grid method is first order, which is robust with respect to the perturbation parameters. Then, in order to construct a fully discrete adaptive grid method, a standard residual‐type a posterior error estimation is constructed by using the linear polynomial interpolation technique. A partly heuristic argument based on this a posteriori error estimator leads to an optimal monitor function, which is used to design an adaptive grid algorithm. Furthermore, we also extend our presented adaptive grid method to a nonlinear system of singularly perturbed problem arising in the modeling of enzyme kinetics and a system of singularly perturbed delay differential equations, respectively. Finally, numerical results are provided to illustrate the effectiveness of our presented adaptive grid method.

A posteriori error estimation and adaptive strategy for a nonlinear fractional differential equation

A nonlinear fractional differential equation with Caputo fractional derivative is considered. The problem is discretized by an upwind finite difference scheme for which a posteriori error analysis in the maximum norm is derived. A partly heuristic argument based on this a posteriori error estimation leads to several suitable monitor functions, and a new monitor function is constructed to design an adaptive grid algorithm. Numerical results are presented to illustrate the performance of the presented adaptive method. Compared with the other monitor functions, the presented adaptive grid method based on the new monitor function is more suitable to solve this type of nonlinearfractional differential equation.

Optimization of Fluconazole Dosing for the Prevention and Treatment of Invasive Candidiasis Based on the Pharmacokinetics of Fluconazole in Critically Ill Patients.

The efficacy of fluconazole is related to the area under the plasma concentration-time curve (AUC) over the MIC of the microorganism. Physiological changes in critically ill patients may affect the exposure of fluconazole, and therefore dosing adjustments might be needed. The aim of this study was to evaluate variability in fluconazole drug concentration in intensive care unit (ICU) patients and to develop a pharmacokinetic model to support personalized fluconazole dosing. A prospective observational pharmacokinetic study was performed in critically ill patients receiving fluconazole either as prophylaxis or as treatment. The association between fluconazole exposure and patient variables was studied. Pharmacokinetic modeling was performed with a nonparametric adaptive grid (NPAG) algorithm using R package Pmetrics. Data from 33 patients were available for pharmacokinetic analysis. Patients on dialysis and solid organ transplant patients had a significantly lower exposure to fluconazole. The population was best described with a one-compartment model, where the mean volume of distribution was 51.52 liters (standard deviation [SD], 19.81) and the mean clearance was 0.767 liters/h (SD, 0.46). Creatinine clearance was tested as a potential covariate in the model, but was not included in the final population model. A significant positive correlation was found between the fluconazole exposure (AUC) and the trough concentration (Cmin). Substantial variability in fluconazole plasma concentrations in critically ill adults was observed, where the majority of patients were underexposed. Fluconazole Cmin therapeutic drug monitoring (TDM)-guided dosing can be used to optimize therapy in critically ill patients. (This study has been registered at ClinicalTrials.gov under identifier NCT02491151.).

A flexible and adaptive grid algorithm for global optimization utilizing basin hopping Monte Carlo.

Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore the potential energy surface of the system of interest. These simulations can be very demanding due to the high-dimensional configurational search space. The effective search space can be reduced by utilizing grids for the atomic positions, but at the cost of possibly biasing the results if fixed grids are employed. In this paper, we present a flexible grid algorithm for global optimization that allows us to exploit the efficiency of grids without biasing the simulation outcome. The method is general and applicable to very heterogeneous systems, such as interfaces between two materials of different crystal structures or large clusters supported at surfaces. As a benchmark case, we demonstrate its performance for the well-known global optimization problem of Lennard-Jones clusters containing up to 100 particles. Despite the simplicity of this model potential, Lennard-Jones clusters represent a challenging test case since the global minima for some "magic" numbers of particles exhibit geometries that are very different from those of clusters with only a slightly different size.

Multilevel Adaptive Sparse Leja Approximations for Bayesian Inverse Problems

Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations, deterministic quadrature is usually unable to efficiently investigate an informative and thus concentrated likelihood. This leads to a large number of required expensive evaluations of the mathematical model. To overcome these challenges, we formulate and test a multilevel adaptive sparse Leja algorithm. At each level, adaptive sparse grid interpolation and quadrature are used to approximate the posterior and perform all quadrature operations, respectively. Specifically, our algorithm uses coarse discretizations of the underlying mathematical model to investigate the parameter space and to identify areas of high posterior probability. Adaptive sparse grid algorithms are then used to place points in these areas, and ignore other areas of small posterior probability. The points are weighted Leja points. As the model discretization is coarse, the construction of the sparse grid is computationally efficient. On this sparse grid, the posterior measure can be approximated accurately with few expensive, fine model discretizations. The efficiency of the algorithm can be enhanced further by exploiting more than two discretization levels. We apply the proposed multilevel adaptive sparse Leja algorithm in numerical experiments involving elliptic inverse problems in 2D and 3D space, in which we compare it with Markov chain Monte Carlo sampling and a standard multilevel approximation.

1573. Population Pharmacokinetic Analyses for Cefepime in Adult and Pediatric Patients

BackgroundCefepime (CEF) is commonly used for adult and pediatric infections. Several studies have examined CEF’s pharmacokinetics (PK) in various populations; however, a unifying PK model for adult and pediatric subjects does not yet exist. We developed a combined population model for adult and pediatric patients and validated the model.MethodsThe initial model includes adult and pediatric patients with a rich cefepime sampling design. All adults received 2 g CEF while pediatric subjects received a mean of 49 (SD 5) mg/kg. One- and two-compartment models were considered as base models and were fit using a non-parametric adaptive grid algorithm within the Pmetrics package 1.5.2 (Los Angeles, CA) for R 3.5.1. Compartmental model selection was based on Akaike information criteria (AIC). Covariate relationships with PK parameters were visually inspected and mathematically assessed. Predictive performance was evaluated using bias and imprecision of the population and individual prediction models. External validation was conducted using a separate adult cohort.ResultsA total of 45 subjects (n = 9 adults; n = 36 pediatrics) were included in the initial PK model build and 12 subjects in the external validation cohort. Overall, the data were best described using a two-compartment model with volume of distribution (V) normalized to total body weight (TBW/70 kg) and an allometric scaled elimination rate constant (Ke) for pediatric subjects (AIC = 4,138.36). Final model observed vs. predicted plots demonstrated good fit (population R2 = 0.87, individual R2 = 0.97, Figure 1a and b). For the final model, the population median parameter values (95% credibility interval) were V0 (total volume of distribution), 11.7 L (10.2–14.6); Ke for adult, 0.66 hour−1 (0.38–0.78), Ke for pediatrics, 0.82 hour−1 (0.64–0.85), KCP (rate constant from central to peripheral compartment), 1.4 hour−1 (1.3–1.8), KPC (rate constant from peripheral to central compartment), 1.6 hour−1 (1.2–1.8). The validation cohort has 12 subjects, and the final model fit the data well (individual R2 = 0.75).ConclusionIn this diverse group of adult and pediatrics, a two-compartment model described CEF PK well and was externally validated with a unique cohort. This model can serve as a population prior for real-time PK software algorithms. Disclosures All authors: No reported disclosures.

Wavelet-based grid-adaptation for nonlinear scheduling subject to time-variable electricity prices

Using nonlinear process models in discrete-time scheduling typically prohibits long planning horizons with fine temporal discretizations. Therefore, we propose an adaptive grid algorithm tailored for scheduling subject to time-variable electricity prices. The scheduling problem is formulated in a reduced space. In the algorithm, the number of degrees of freedom is reduced by linearly mapping one degree of freedom to multiple intervals with similar electricity prices. The mapping is iteratively refined using a wavelet-based analysis of the previous solution. We apply the algorithm to the scheduling of a compressed air energy storage. We model the efficiency characteristics of the turbo machinery using artificial neural networks. Using our in-house global solver MAiNGO, the algorithm identifies a feasible near-optimal solution with < 1% deviation in the objective value within < 5% of the computational time compared to a solution considering the full dimensionality.

BOUSSINESQ MODELING OF SHIP-WAKES AND THEIR CONTRIBUTION TO COASTAL EROSION IN AN ADAPTIVE MESH REFINEMENT SYSTEM

Heavy ship traffic causes a growing concern with respect to public safety, potential damage of coastal structures, and corresponding environmental impacts. High-speed ship-generated wakes such as solitons, undular bores, and breaking bores behave differently compared to wind waves and have a great potential for damage in vulnerable areas such as low-energy coasts and wetlands. In this study, we are developing a multi-grid model framework for the Fully Nonlinear Boussinesq Wave Model, FUNWAVE-TVD (Shi et al., 2012), for simulating ship-wakes in both the operational scale and refined process scales using full two-way coupling. Physical processes in areas of interest requiring higher model resolution, such as the ship-wake generation region, wave breaking in the near-field, and wave evolution with wave-structure interaction in the nearshore field, will be modeled in refined grids embedded in the operational-scale domain. A dynamically adaptive grid algorithm is implemented in order to track a vessel and calculate the physical processes precisely in the wave generation and breaking region in the vicinity of the vessel. Both pressure source and panel source methods for ship wave generation will be tested in the model framework. A concept of nesting layers based on the hierarchical basis, and an efficient parallelization method in the context of the full domain partition are utilized to allow the model to deal with a large-scale computation efficiently in a High Performance Computing (HPC) system.

Adaptive Cartesian meshes for atmospheric single-column models: a study using Basilisk 18-02-16

Abstract. It is well known that the representation of certain atmospheric conditions in climate and weather models can still suffer from the limited grid resolution that is facilitated by modern-day computer systems. Herein we study a simple one-dimensional analogy to those models by using a single-column model description of the atmosphere. The model employs an adaptive Cartesian mesh that applies a high-resolution mesh only when and where it is required. The so-called adaptive-grid model is described, and we report our findings obtained for tests to evaluate the representation of the atmospheric boundary layer, based on the first two GEWEX ABL Study (GABLS) inter-comparison cases. The analysis shows that the adaptive-grid algorithm is indeed able to dynamically coarsen and refine the numerical grid whilst maintaining an accurate solution. This is an interesting result as in reality, transitional dynamics (e.g. due to the diurnal cycle or due to changing synoptic conditions) are the rule rather than the exception.