Inverse Optimization Research Articles

Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems

Traditional numerical discretization-based solvers of partial differential equations (PDEs) are fundamentally agnostic to domains, boundary conditions and coefficients. In contrast, machine learnt solvers have a limited generalizability across these elements of boundary value problems. This is strongly true in the case of surrogate models that are typically trained on direct numerical simulations of PDEs applied to one specific boundary value problem. In a departure from this direct approach, the label-free machine learning of solvers is centered on a loss function that does not use computed field solutions as labels. Instead, the PDE and boundary conditions are directly incorporated in residual form to express the loss function during training. However, their generalization across boundary conditions is limited and they remain strongly domain-dependent. Here, we present a framework that generalizes across domains, boundary conditions and coefficients while simultaneously learning the PDE in weak form. Our work explores the ability of convolutional neural network (CNN)-based encoder–decoder architectures to learn to solve a PDE in greater generality than its restriction to a particular boundary value problem. In this first Communication, we take the canonical path through elliptic PDEs and focus on steady-state diffusion, linear and nonlinear elasticity. Importantly, the learning happens independently of any labeled field data from either experiments or direct numerical solutions. We develop probabilistic CNNs in the Bayesian setting using variational inference. Extensive results for these problem classes demonstrate the framework’s ability to learn PDE solvers that generalize across hundreds of thousands of domains, boundary conditions and coefficients, including extrapolation beyond the learning regime. Once trained, the machine learning solvers are orders of magnitude faster than discretization-based solvers. They therefore have relevance to high-throughput solutions of PDEs on varied domains, boundary conditions and coefficients, such as for inverse modeling, optimization, design and decision-making. We place our work in the context of other recent machine learning solvers of PDEs including continuous operator learning frameworks, as well as make comparisons of performance where possible. Finally, we note extensions to transfer learning, active learning and reinforcement learning.

Inverse data envelopment analysis optimization approaches with flexible measures

PurposeThe purpose of this study is to estimate inputs (outputs) and flexible measures when outputs (inputs) are changed provided that the relative efficiency values remain without change.Design/methodology/approachA novel inverse data envelopment analysis (DEA) approach with flexible measures is proposed in this research to assess inputs (outputs) and flexible measures when outputs (inputs) are perturbed on condition that the relative efficiency scores remain unchanged. Furthermore, flexible inverse DEA approaches proposed in this study are used for a numerical example from the literature and an application of Iranian banking industry to clarify and validate them.FindingsThe findings show that including flexible measures into the investigation effects on the changes of performance measures estimated and leads to more reasonable achievements.Originality/valueThe traditional inverse DEA models usually investigate the changes of some determinate input-output factors for the changes of other given input-output indicators assuming that the efficiency values are preserved. However, there are situations that the changes of performance measures should be tackled while some measures, called flexible measures, can play either input or output roles. Accordingly, inverse DEA optimization models with flexible measures are rendered in this paper to address these issues.

Application of Particle Swarm Optimization (PSO) Algorithm in Determining Thermodynamics of Solid Combustibles

The thermodynamics of a solid are crucial in predicting thermal responses and fire behaviors, and they are commonly determined by inverse modeling and optimization algorithms at constant heat flux. However, in practical scenarios, the imposed heat flux frequently varies with time, and related thermodynamics determination methods are rarely reported. In this study, the particle swarm optimization (PSO) algorithm and a 1D numerical model were utilized to determine temperature-dependent thermal conductivity and specific heat of beech wood and polymethyl methacrylate (PMMA). Surface, 3 and 6 mm in-depth temperatures were measured in three sets of ignition tests where constant and time-dependent heat fluxes (HFs) were applied. In each set, PSO was implemented at individual HFs, and the average value was deemed as the final outcome. Reliability of the optimized thermodynamics was verified by comparing with the reported values in the literature and predicting the experimental measurements that were not employed during parameterization. The results showed that wood thermodynamics attained under constant and time-dependent HFs in agreement with previously reported ones. Similar optimization procedures were conducted for PMMA, and good agreement with literature values was found. Using the obtained thermodynamics of wood under constant HF, the numerical model successfully captured the surface temperature at time-dependent HFs. Meanwhile, comparisons using wood temperatures at constant HFs and PMMA temperatures at linear HFs also verified the feasibility of PSO.

Deep learning-based inverse design optimization of efficient multilayer thermal emitters in the near-infrared broad spectrum.

This study proposes a deep learning architecture for automatic modeling and optimization of multilayer thin film structures to address the need for specific spectral emitters and achieve rapid design of geometric parameters for an ideal spectral response. Multilayer film structures are ideal thermal emitter structures for thermophotovoltaic application systems because they combine the advantages of large area preparation and controllable costs. However, achieving good spectral response performance requires stacking more layers, which makes it more difficult to achieve fine spectral inverse design using forward calculation of the dimensional parameters of each layer of the structure. Deep learning is the main method for solving complex data-driven problems in artificial intelligence and provides an efficient solution for the inverse design of structural parameters for a target waveband. In this study, an eight-layer thin film structure composed of SiO2/Ti and SiO2/W is rapidly reverse engineered using a deep learning method to achieve a structural design with an emissivity better than 0.8 in the near-infrared band. Additionally, an eight-layer thin film structure composed of 3 × 3 cm SiO2/Ti is experimentally measured using magnetron sputtering, and the emissivity in the 1-4 µm band was better than 0.68. This research provides implications for the design and application of micro-nano structures, can be widely used in the fields of thermal imaging and thermal regulation, and will contribute to developing a new paradigm for optical nanophotonic structures with a fast target-oriented inverse design of structural parameters, such as required spectral emissivity, phase, and polarization.

Network revenue management game in the railway industry: Stackelberg equilibrium, global optimality, and mechanism design

Many countries have adopted the vertical separation governance structure in the railway freight industry over the past decades. Under this governance structure, an Infrastructure Manager (IM), which might be an independent company or a government agency, sells train itineraries to Freight Operating Companies (FOCs). After purchasing the itineraries, a FOC will have the rights to run trains on the designated paths at the designated times and thus can provide transport service to shippers. In the process, an IM needs to determine a list of prices for their train itineraries; and a FOC needs to determine which train itineraries to purchase to serve uncertain customer demands based on the IM's price list. This study considers the interaction between an IM and a FOC as a network-based Stackelberg game. Our study first formulates a bi-level optimisation model to determine the equilibrium prices that the IM would charge to maximise its own profits unilaterally without collaboration. A method involving gradient and local search has been developed to solve the bi-level model. Secondly, an inverse optimisation model is proposed to determine the prices leading to global optimality. A Fenchel cutting plane-based algorithm is developed to solve the inverse optimisation model. Thirdly, a subsidy contract is designed for the game to coordinate the players’ decisions. A two-layer gradient search method is developed to determine the optimal subsidy rate. Numerical cases based on the UK rail freight industry data are provided to validate the models and algorithms.

Inverse optimal extremum seeking under delays

We establish the inverse optimality in the average sense of our earlier Gradient- and Newton-based extremum seeking algorithms for maximizing unknown locally quadratic maps in the presence of constant delays. To compensate the delay, these algorithms employ a predictor feedback with a perturbation-based estimate for the unknown Hessian (or its inverse). The algorithm’s inverse optimality is the result of running the predictor through a simple first-order filter with a fast enough pole.

Inverse Evaluation of Monopile Pile–Soil Interaction Parameters Using Random Search

To deal with the uncertainties in modeling offshore wind turbines, we propose a parameter inversion method for the pile–soil interaction model based on structural health monitoring results and the numerical model. The proposed parameter inversion method has a numerical model, an objective function selected using both the numerical and identified results, and an inverse optimization using a random search algorithm in the assumed parameter space. The parameter results in the minimum optimization objective function are identified as the in situ parameter. The proposed method is confirmed to converge after some number of iterations, depending on what the initial parameter values are. However, different initial parameter cases may converge to slightly different optimal parameters, implying that the pile results are sensitive to geological parameters. Moreover, a comparison with the original design results shows design redundancy or risks. Though the proposed method has several flaws, it can shed light on the influence of parameter uncertainties on offshore wind turbines.

Genetic-Algorithm-Based Inverse Optimization Identification Method for Hot-Temperature Constitutive Model Parameters of Ti6Al4V Alloy.

A precise constitutive model is the foundation and key to finite element simulation in material volume forming and the optimization of the hot working process. Hence, to build a precise constitutive model, a method based on a genetic algorithm (GA) for the inverse optimization identification of parameters is presented in this paper. The idea of this method is to continuously adjust the model parameters through GA until the objective function reaches the minimum value. In this study, hot compression experiments were performed on the Gleeble-1500D thermal simulator at temperatures ranging from 800 °C to 1000 °C and strain rates of 0.01 s-1 to 1 s-1. The Arrhenius-type (A-T) model considering strain compensation and the Johnson-Cook (JC) model considering the coupling effects of strain, temperature and strain rate were constructed, respectively, by using the regression method and the parameter inverse optimization identification method. For the purposes of comparing and verifying the reliability of the predictions of the two established constitutive models, the correlation coefficient (R), average absolute relative error (AARE), and relative error (RE) were adopted. The results show that both the optimized A-T model and the optimized JC model have high prediction accuracy. Compared to the optimized JC model, the optimized A-T model demonstrated a higher correlation coefficient, by 0.003, and a lower average absolute relative error, by 1.43%. Furthermore, the relative error distribution of the optimized A-T model was found to be more concentrated than that of the optimized JC model. These results suggest that the A-T model is more appropriate than the JC model for characterizing the high-temperature deformation behavior of Ti6Al4V alloy.

Impact of land use on water quality in buffer zones at different scales in the Poyang Lake, middle reaches of the Yangtze River basin

The water quality of Poyang Lake (PYL) is significantly influenced by land use which is a crucial factor that can exhibit complex changes in the environment and can serve as an indicator of the intensity of human activity. Therefore, this study analyzed the spatial and temporal distribution characteristics of nutrients and investigated the effects of land-use factors on water quality in the PYL during 2016–2019. The main conclusions are as follows: (1) Although there was some variation in the accuracy of the water quality inversion models (random forest (RF), support vector machine (SVM), and multiple statistical regression models), they were homogeneous. In particular, ammonia nitrogen (NH3-N) concentration from band (B) 2 and B2–B10 regression model was more consistent with each other. In contrast, the overall concentration levels from the combined B9/(B2–B4) triple-band regression model were relatively low, with approximately 0.03 mg/L in most areas of PYL. (2) The optimal inversion method varied for different water quality parameters. For instance, RF obtained better inversion of total phosphorus (TP) and total nitrogen (TN), with the fitting coefficient (r2) of 0.78 and 0.81, respectively; SVM had higher accuracy in the inversion of permanganate index (CODMn), with r2 of approximately 0.61; the accuracy of multi-band combined regression model in the inversion of each water quality parameter was at a higher level. (3) The influence of land use on water quality at different scales of buffer zone was different. In general, the correlation between water quality parameters and land use was higher at large spatial scales (1000–5000 m) than at small spatial scales (100 m, 500 m). A common feature of all hydrological stations was the significant negative correlation between crops, buildings, and water quality at all buffer scales. This study is of great practical significance for promoting water environment management and water quality health in the PYL.

Novel procedure to determine the stress-strain relation of Lithium-ion Batteries through indentation test

This study proposes a novel approach to convert the load–depth curve measured in the experimental indentation test into stress–strain curves. Due to the lack of the tensile test results for the cylindrical lithium-ion battery (LIB) cell, a combination of the analytical analysis and the inverse optimization approach is first conducted as a reference point to determine the elastoplastic constitutive equation, which can predict the response of cylindrical LIB cell cells under the cylindrical indenter. The obtained load-depth curves from the robust optimization algorithm are in good agreement with the experimental loading–unloading curves. This novel approach includes a new definition of the contact area between the cylindrical indenter and the cylindrical LIB cell. Finite element models validate the measured contact area values from the analytical approach. The analytical approach in this study can accurately capture the stress–strain curve validated with optimization results. Afterward, different single indentation tests are conducted to estimate the reduction of Young’s modulus through the increasing indentation depth. Noteworthy, a definition of the indentation strain can physically interpret the indentation strain in the case of two crossed cylinders. The cell voltage is measured during the indentation test to detect the internal short circuit in the LIB cell. In homogenized modeling, the damage of the LIB cell is considered, which is an essential indicator of the internal short circuit of a LIB cell and possible thermal runaway.

An improved band design framework for atmospheric pollutant detection and its application to the design of satellites for CO2 observation

High-precision atmospheric remote sensing observation is one of the most challenging tasks in the key fields of earth observation. The accurate accounting for technical indicators such as the working spectral band, spectral resolution, and signal-to-noise ratio (SNR) of high-precision atmospheric observation satellites is an urgent research task. To address this need, this paper proposes a band design framework (BDF) that can replace airborne detection experiments to some extent and reduce the workload of satellite design. First, based on the HITRAN database, the absorption spectra of gases in the target gas absorption window are extracted as a band dataset. Then, membership functions are designed based on a trapezoid distribution, the monitoring factor α is introduced according to the importance of strong and weak absorption channels to obtain the improved fuzzy comprehensive evaluation (IFCE) model. Subsequently, the IFCE model is used to screen the band dataset. Finally, the bands are optimized based on the SCIATRAN model, sensitivity analysis and optimal inversion algorithm, and the BDF-IFCE band design method for remote sensing detection of gaseous atmospheric pollutants is established based on the improved fuzzy synthetic evaluation model. The BDF-IFCE method is applied to design the CO2 sensor detection band and two absorption windows are successfully identified (6170–6270 cm−1 and 6290–6380 cm−1). With a restricted range of aerosol AODs, detection accuracy of 3–4 ppm can be achieved with a signal-to-noise ratio of ∼300. The test results are the same as the band setting of existing atmospheric sensors, indicating that this method is effective and feasible in designing the CO2 remote sensor detection band.

IKOL: Inverse Kinematics Optimization Layer for 3D Human Pose and Shape Estimation via Gauss-Newton Differentiation

This paper presents an inverse kinematic optimization layer (IKOL) for 3D human pose and shape estimation that leverages the strength of both optimization- and regression-based methods within an end-to-end framework. IKOL involves a nonconvex optimization that establishes an implicit mapping from an image’s 3D keypoints and body shapes to the relative body-part rotations. The 3D keypoints and the body shapes are the inputs and the relative body-part rotations are the solutions. However, this procedure is implicit and hard to make differentiable. So, to overcome this issue, we designed a Gauss-Newton differentiation (GN-Diff) procedure to differentiate IKOL. GN-Diff iteratively linearizes the nonconvex objective function to obtain Gauss-Newton directions with closed form solutions. Then, an automatic differentiation procedure is directly applied to generate a Jacobian matrix for end-to-end training. Notably, the GN-Diff procedure works fast because it does not rely on a time-consuming implicit differentiation procedure. The twist rotation and shape parameters are learned from the neural networks and, as a result, IKOL has a much lower computational overhead than most existing optimization-based methods. Additionally, compared to existing regression-based methods, IKOL provides a more accurate mesh-image correspondence. This is because it iteratively reduces the distance between the keypoints and also enhances the reliability of the pose structures. Extensive experiments demonstrate the superiority of our proposed framework over a wide range of 3D human pose and shape estimation methods. Code is available at https://github.com/Juzezhang/IKOL

A Unified Inverse Design and Optimization Workflow for the Miura-oRing Metastructure

Abstract Origami structures are often attractive for a broad range of applications in engineering, design, and robotics because of their useful characteristics such as reconfigurable geometry, tunable stiffness, and energy absorption capacity. Although a range of algorithms and software is available for origami design and folding analysis, they are generally isolated from other computational tools. To contribute to filling this research gap, we propose a unified parametric origami design workflow based on grasshopper combined with a multi-objective optimization process. To this end, first, a parametric model for a ring-shaped fourfold origami structure, called the Miura-oRing metastructure, is developed based on appropriate geometric parameters. Its nonlinear folding process is then simulated according to geometric compatibility conditions and given constraints. Simultaneously, modal analysis is iteratively performed, using SAP2000 through C# scripts, to obtain relationships for the structural configuration, mass, and stiffness of the origami structure. Finally, an inverse design process based on a fitting cylindrical annulus is carried out using Octopus, considering the spatial fit, mass, and stiffness of the Miura-oRing. A comparison is made between the obtained results and those of the origami simulator and the physical models to validate the performance of the proposed method. After balancing the three objectives of inverse design, a recommended range of parameters is prescribed for the Miura-oRing for a given set of dimensions. This study provides a workflow that integrates geometry, kinematics, and structural performance, enabling the design of origami structures with desirable geometric, kinematic, and structural characteristics.

Virtual data-based generative optimization using domain-adaptive designable data augmentation (DADDA): Application to electric vehicle design

In the field of virtual product development, product performance is evaluated at an early stage through metamodel-based optimization using simulation, reducing development time and cost, and improving product quality. However, it takes a lot of time to construct a simulation model. The model must go through calibration and validation process to reduce errors with actual systems. This study proposes a novel engineering design process that can perform virtual data-based generative optimization by adapting the design domain of existing systems to those of new systems without requiring many simulations. A domain-adaptive designable data augmentation (DADDA) algorithm is proposed using inverse generator-implemented data augmentation, domain adaptation, and design optimization techniques. The DADDA algorithm can quickly provide optimal design variables for new systems compared to the genetic algorithm-based approximate optimization. The proposed process was applied to electric vehicle design. Driving responses and design variables related to safety performance were selected, and a small amount of training data was obtained using Modelica-based electric vehicle. As a result, it was shown that DADDA could significantly reduce the time required to derive optimal design variables by approximately 53% compared with the existing method. In addition, it is possible to derive the optimal performance for a new electric vehicle, which is approximately 21% better than that of an existing vehicle.

Fast image processing method for coal particle cluster box dimension measurement and its application in diffusion coefficient testing

The diffusion coefficient is the key parameter used to characterize methane diffusion behavior in coal. The commonly used analytical solutions for diffusion coefficients require simplifying the particle shape to regular shapes, which greatly deviates from the actual shape of coal particles. The influence of coal particle shape on the diffusion coefficient is currently not well understood. Based on image processing techniques and inverse problem-based numerical simulation, a new method is proposed in this paper to determine the diffusion coefficients of irregular coal particles, and a feasible solution for quantitatively assessing the influence of particle shapes on the diffusion coefficient is provided. The implementation of this method is based on two aspects: the fast quantitative characterization of the shape features of coal particle clusters and inverse problem-based numerical simulation to solve the diffusion coefficient of irregularly shaped coal particles. First, image processing technology is used to quickly and accurately extract the 2D projection contour of batch particles, and an algorithm based on fractal theory is designed to obtain the box dimension of batch contours, which achieves the quantitative characterization for the shape features of coal particle clusters. At the same time, a comparison with Fraclab is conducted to validate the scientific effectiveness of the box dimension algorithm. Then, 3 coal particles with representative fractal dimensions are selected and their diffusion coefficients are obtained using the inverse problem numerical method. The results indicate that the desorption curves obtained through inverse problem optimization for the 3 particles are excellently consistent with the experimental data, with fitting degrees R2 all exceeding 99%. Therefore, the diffusion coefficients can be effectively obtained. Meanwhile, the influence of shape on the diffusion coefficient is analyzed quantitatively. The results show that the diffusion coefficient increases with the box dimension of the contour, and the particle shape has a considerable impact on determining the gas diffusion coefficient.

Use of artificial intelligence to automatically predict the optimal patient-specific inversion time for late gadolinium enhancement imaging. Tool development and clinical validation

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): This research was partly funded by the Italian Ministry of Health Introduction With the worldwide diffusion of cardiac magnetic resonance (CMR), demand on image quality has grown. CMR late gadolinium enhancement (LGE) imaging provides critical diagnostic and prognostic information, and guides management. The identification of optimal Inversion Time (TI), a time-sensitive parameter closely linked to contrast kinetics, is pivotal for correct myocardium nulling. However, determining the optimal TI can be challenging in some diseases and for less experienced operators. Purpose To develop and test an artificial intelligence tool to automatically predict the personalised optimal TI in LGE imaging. Methods The tool, named THAITI, consists of a Random Forest regression model. It considers, as input parameters, patient-specific TI determinants (age, gender, weight, height, kidney function, heart rate) and CMR scan-specific TI determinants (B0, contrast type and dose, time elapsed from contrast injection). THAITI was trained on 219 patients (3585 images) with mixed conditions who underwent CMR (1.5T; Gadobutrol; averaged, MOCO, free-breathing true-FISP IR [1]) for clinical reasons. The dataset was split with a 90–10 policy: 90% of data for training, and 10% for testing. THAITI’s hyperparameters were optimised by embedding k-fold cross validation into an evolutionary computation algorithm, and the best performing model was finally evaluated on the test set. A graphical user interface was also developed. Clinical validation was performed on 55 consecutive patients, randomised to experimental (THAITI-set TI) vs control (operator-set TI) group. Image quality was assessed blindly by 2 independent experienced operators by a 4-points Likert scale, and by means of the contrast/enhancement ratio (CER) (i.e., signal intensity of enhanced/remote myocardium ratio). Results In the testing set, the TI predicted by THAITI differed from the ground truth by ≥ 5ms in 16% of cases. At clinical validation, myocardial nulling quality did not differ between the experimental vs the control group either by CER or visual assessment, with an overall "optimal" or "good" nulling in 96% vs 93%, respectively. Conclusions Using main determinants of contrast kinetics, THAITI efficiently predicted the optimal TI for CMR-LGE imaging. The tool works as a stand-alone on laptops/mobile devices, not requiring adjunctive scanner technology and thus has great potential for diffusion, including in small or recently opened CMR services, and in low-resource settings. Additional development is ongoing to increase generalisability (multi-vendor, multi-sequence, multi-contrast) and to test its potential to further improve CMR-LGE image quality and reduce the need for repeated imaging for inexperienced operators. Figure 1. Top: THAITI interface. Bottom: examples of experimental group CMR-LGE imaging. Table 1. Control vs experimental group. Data expressed as absolute number (%), mean ± SD, median [IQR]. ⧧ T-test; * Chi-square.

Fast inversion method for seepage parameters of core earth-rock dam based on LHS-SSA-MKELM fusion surrogate model

The inversion of seepage parameters is an important research topic in the safety evaluation of earth-rock dams. Core earth-rock dam is a commonly used structural type in earth-rock dams. Most of the existing inversion methods focus on concrete dams, and few of them are aimed at earth-rock dams. These methods have the problems of slow inversion speed or low accuracy. Aiming at the above problems, this paper proposes a novel fast inversion method for the seepage parameters of core earth-rock dams based on the LHS-SSA-MKELM fusion surrogate model. The proposed fusion inversion model optimizes the selection of combination models based on the surrogate model framework, making it more suitable for the inversion calculation of seepage parameters in earth-rock dams. First, based on the seepage theory of earth-rock dams, the finite element numerical simulation model of core earth-rock dam seepage is constructed. The Latin Hypercube Sampling (LHS) method is used to obtain the parameter sample dataset according to the range of the seepage parameters, and the sample dataset is substituted into the finite element model to obtain the corresponding theoretical seepage pressure of different datasets. Then, the Mixed Kernel Extreme Learning Machine (MKELM) is used to establish the mapping relationship between seepage parameters and the theoretical seepage pressure. The MKELM parameters were optimized by using the Sparrow Search Algorithm (SSA) to further improve the accuracy of the surrogate model. Finally, taking the minimum error between the theoretical value and the measured value of the surrogate model as the objective function, the SSA algorithm is used to derive the optimal inversion value of seepage parameters. The results of engineering examples show that the mean absolute percentage error between the measured value of the core earth-rock dam seepage pressure and the simulated value after inversion is only 4.958%. In addition, the average inversion time of the proposed surrogate model is only 6.6 s, which greatly reduces the time-consuming problem of numerical simulation. The proposed method provides a new way for accurate and fast inversion of seepage parameters of core earth-rock dams after long-term operation.

Implicit function characterization of the curvilinear mask to realize parametric optical proximity correction with a neighborhood parallel tabu search.

The curvilinear mask structures provide significant benefits in improving lithographic resolution. Curvilinear masks, as opposed to rectilinear masks, have a wider range of structure types that can be used precisely to correct the contour of diffraction at sharp technological nodes. However, the curvilinear structure also makes the inverse design of mask in optical proximity correction (OPC) flow difficult. The current OPC of curvilinear masks uses pixel-based inverse optimization, which is extremely computationally intensive and takes up a lot of design data storage space. This paper proposes an implicit function to represent a large number of curve types with a small number of parameters to reduce computational complexity and the R&D cycle. Therefore, the ultra-high dimensional pixel-based OPC problem is transformed into a low-dimensional parameter search problem in the critical diffraction area of the mask pattern. The tabu search algorithm and neighborhood parallel computing strategy are then used to quickly search for optimal characterized parameters. The results of the simulation show that the parametric curvilinear OPC method achieves a higher image fidelity than that of rectilinear OPC. At the same time, it addresses the shortcomings of the traditional pixelated curvilinear mask OPC method, including high computational complexity, low manufacturability, and storage space occupancy.

Inverse planning optimization with lead block effectively suppresses dose to the mandible in high-dose-rate brachytherapy for tongue cancer

PurposeIn this study, we developed in-house software to evaluate the effect of the lead block (LB)-inserted spacer on the mandibular dose in interstitial brachytherapy (ISBT) for tongue cancer. In addition, an inverse planning algorithm for LB attenuation was developed, and its performance in mandibular dose reduction was evaluated.MethodsTreatment plans of 30 patients with tongue cancer treated with ISBT were evaluated. The prescribed dose was 54 Gy/9 fractions. An in-house software was developed to calculate the dose distribution based on the American Association of Physicists in Medicine (AAPM) Task Group No.43 (TG-43) formalism. The mandibular dose was calculated with consideration of the LB attenuation. The attenuation coefficient of the lead was computed using the PHITS Monte Carlo simulation. The software further optimized the treatment plans using an attraction–repulsion model (ARM) to account for the LB attenuation.ResultsCompared to the calculation in water, the D2 cc of the mandible changed by − 2.4 ± 2.3 Gy (range, − 8.6 to − 0.1 Gy) when the LB attenuation was considered. The ARM optimization with consideration of the LB resulted in a − 2.4 ± 2.4 Gy (range, − 8.2 to 0.0 Gy) change in mandibular D2 cc.ConclusionsThis study enabled the evaluation of the dose distribution with consideration of the LB attenuation. The ARM optimization with lead attenuation further reduced the mandibular dose.

Modeling biochar-soil depth dependency on fecal coliform straining under subsurface drip irrigation

Biochar has several benefits for soil, including improved flow and retention properties that decrease bacterial transport. To improve understanding of the underlying mechanisms and optimal irrigation strategies for contaminated gray water, we conducted a lysimeter study exploring impacts of biochar level (0, 0.5, and 1% w/w) and 30-days irrigation regime (0.003 and 0.0064 cm h−1). Biochar did not change hydraulic properties but at maximum allowable depletion (MAD) of 30, 50, and 70% biochar had a large impact on fecal coliform retention. At 15–25 cm depth where the subsurface dripper was located, 1% biochar-treated soil had 1.5 times greater retention than the controls. A combination of the lower irrigation rate (0.003 vs. 0.0064 cm h−1) and the greater biochar (1% vs. 0.5%) had greater impacts on bacteria inactivation and retention than the MAD levels. Nevertheless, adding 1% biochar resulted in a 2-fold increase of bacteria retention for 30% MAD and low flow rate than greater flow rates and MAD levels (50 and 70%). Our results provided novel data for inverse optimization to explore bacteria retention by differences in bacteria attachment, straining, survival or growth. Close to the irrigation dripper, straining was the pronounced mechanism under the best performing treatment of 1% biochar and 30% MAD. Therefore, we recommend application of biochar at the rate of 1% where wastewater is used for subsurface drip irrigation.