Optimization-based model calibration of marginal and joint output distributions utilizing analytical gradients

The fully analytic gradient of the second-order Møller-Plesset perturbation theory (MP2) with the resolution-of-the-identity (RI) approximation in the fragment molecular orbital (FMO) framework is derived and implemented using a hybrid multilevel parallel programming model, a combination of the general distributed data interface (GDDI) and the OpenMP API. The FMO/MP2 analytic gradient contains three parts, i.e., the internal fragment component, the electrostatic potential (ESP) component, and the response terms. The RI approximation is applied to the internal fragment MP2 gradient term, whose MP2 densities and monomer MP2 Lagrangians are shared with the ESP and the response terms. The FMO/RI-MP2 analytic gradient implementation is validated against the numerical gradient (with errors ∼10-6-10-5 Hartree/Bohr) and the energy conservation in molecular dynamics (MD) simulations using NVE ensembles. The RI approximation introduces an error of ∼10-5 Hartree/Bohr with a speedup of 4.0-8.0× compared with the currently available GDDI FMO/MP2 gradient. The node linear scaling of the fragmentation framework due to multilevel parallelism is well-preserved and is demonstrated in single-point gradient calculations of large water clusters (e.g., 1120 and 2165 molecules) using 300-800 KNL compute nodes with a parallel efficiency of more than 90%.

Some Thoughts About Data Type, Distribution, and Statistical Significance

In this article, we derive a simple and accurate expression for the change in timing yield due to a change in the gate delay distribution. It is based on analytical bounds that we have derived for the moments of the circuit and path delay. Based on this, we propose computationally efficient algorithms for (1) discrete gate sizing and (2) simultaneous gate sizing and threshold voltage ( V T ) assignment so that the circuit meets a timing yield specification under parameter variations. The use of this analytical yield gradient within a gradient-based timing yield optimization algorithm results in a significant improvement in the runtime as compared to the numerical method, while achieving the same final yield. It also allows us to explore a larger search space in each iteration more efficiently, which is required in the case of simultaneous resizing and V T assignment. We also propose heuristics for resizing/changing the V T of multiple gates in each iteration. This makes it possible to optimize the timing yield for large circuits. Results on ITC ’99 benchmarks show that the proposed multinode resizing algorithm results in a significant improvement in the runtime with a marginal average area penalty and no cost to the final yield achieved.

Identifying informative energy data in Bayesian calibration of building energy models

This paper presents a novel and efficient nonlinear model developed for analysis of reinforced concrete slabs under monotonic loading. The model accounts for the presence of reinforcing steel and its influence on the micro-cracks formation and propagation; as well as tension stiffening due to steel-concrete residual bond. In the finite element analysis (FEA), the principal barrier encountered in large-scale parametric investigations, with thousands of potential parameter’s combinations and modeling executions, it is essential to adopt the fastest and most accurate FEA model. In this regard, the use of shell elements for nonlinear reinforced concrete slab modeling was found to yield superior, far more-efficient solutions that can bring within seconds a higher accuracy than a time consuming, poorly calibrated solid models. Linear-elastic behavior is described with the constant linear-statics moment trajectories, which represent the absence of material and section properties deterioration and nonlinear responses. In contrast, the proposed nonlinear FEA study investigated the material’s fourth dimension behavior and model synthesis, calibration, optimization, and efficiency. A summary of the suggested parameters for the proposed time-efficient nonlinear modeling of reinforced concrete slabs under monotonic loading is introduced. It is extremely valuable for large-scale parametric investigations of slabs nonlinearity under monotonic loading up to failure in which the proposed model was compared with many models; all revealing its superior accuracy.

Through the use of computer simulations, Labovitz's (1970) examination of the effects of randomly stretching measurement scales on the correlation between these stretched scales and an equal distance scoring system are reformulated and extended. Specifically, we examine the effects of the number of rank categories (C) for rank-order variables on the product moment correlation (r) between stretched scales and an equal distance scoring system. The stretched scales are drawn from three types of distributions: (1) the uniform distribution (i.e., the one used by Labovitz), (2) the normal distribution, and (3) a skewed distribution (log-normal distribution). We find that the average correlation (r) between the equal distance scoring system and the stretched scale is quite high for both the uniform and normal distributions, and that I increases with C only when C is greater than four or five. Thus, contrary to suggestions in the literature, I is not a monotonic function of C. More importantly, for the skewed distribution, is a monotonically decreasing function of C and is substantially smaller than r's based on uniform and normal distributions. The implications of these findings for the use of Pearson's r with rank-order values are discussed.

We investigate stochastic microcracks of a heterogeneous microstructure as the primary mechanism determining the non‐shock ignition probability of octahydro‐1,3,5,7‐tetranitro‐1,2,3,5‐tetrazocine‐based polymer‐bonded explosives. To quantify the ignition probability, we modify the viscoelastic cracking constitutive model by considering randomly distributed microcracks and combine this model with the hot‐spot model and the Monte Carlo method. This method is validated by using a standard Steven test simulation, and we quantify how the microcrack stochasticity affects the ignition probability. The high‐temperature region clearly changes compared with the case of single microcrack size. The discrepancy in the mechanical response of each element due to the heterogeneous microcracks causes a shear deformation, which increases the temperature. The difference between a uniform distribution and a normal distribution in microcrack size is also discussed. For a given impact velocity, the ignition probability for the normal microcrack size distribution exceeds that for the uniform microcrack size distribution. Although the two distributions have the same mean and variance, the real range in microcrack size corresponding to the normal distribution exceeds that for the uniform distribution. The results show that the sample radius does not significantly affect the ignition probability, whereas the opposite is true for the sample thickness. The ignition‐probability curve is obtained in these cases. For sample dimensions of φ70 mm×13 mm, φ98 mm×13 mm, φ140 mm×13 mm, and φ98 mm×26 mm, the impact velocity thresholds corresponding to ignition probabilities in the range 0 %–99 % are 41.0–43.7, 41.0–44.3, 40.0–44.6, and 62.0–67.2 m/s, respectively, which is consistent with experimental results.

The goal of model calibration is to improve the predictive capability of a computational model by estimating the unknown input variables of the model. Optimization-based model calibration (OBMC) is a probabilistic way to estimate the unknown input variables through the use of optimization techniques. Performing optimization in a probabilistic sense requires a high computational cost to obtain statistics about the outputs at every iteration of the optimization. To improve optimization efficiency, this paper proposes a sequential optimization-based model calibration approach that makes use of first an efficient, and then a highly accurate probabilistic assessment method, in sequence. At the earlier stage of the sequential optimizations, approximate integration methods are used to accelerate the probabilistic assessment process. As a calibration metric, the moment matching metric is devised to use the obtained statistics of the outputs. When the optimization reaches near-convergence, a more accurate method, such as a sampling method with an accurate surrogate model, is substituted for the probabilistic assessment. Thus, this paper provides an efficient and accurate procedure for optimization-based model calibration. Two engineering applications, model calibration of a shallow strip footing model and an automotive steering wheel-column model, are presented to demonstrate the effectiveness of the proposed method.

The presence of errors in water quality and hydrologic variables can significantly impair the calibration of water quality models. To enhance the estimation of model parameters, it is important to accurately identify data errors during the calibration process. However, this task is challenging due to the complex interactions between model parameter uncertainty and data uncertainty. Existing methods for incorporating data uncertainty in model calibration have limitations, such as high-dimensional computation or the inability to handle stochastic errors.To address these challenges, a novel method called Bayesian Error Analysis with Reordering (BEAR) has been developed. Given that the data uncertainty arises from the data itself and is independent of the model calibration or simulation, the cumulative distribution function (CDF) of the data error can be estimated ahead and regarded as the prior information of Bayesian inference. Then the values of data error series only depend on their ranks in the CDF. BEAR method transforms the values of data error series into their ranks in the CDF. This transformation enables the effective identification of input and/or output data errors in water quality calibration.The innovation of the BEAR method can be attributed to several key aspects:1) Modification of the secant method to handle the non-linear transformation from input to output, ensuring the correspondence between the rank of input data error and the residual error of the model.2) Decomposition of model simulations to calculate the delay between each input and its corresponding output.3) Utilization of the Autoregressive model to account for the correlation of residual errors.4) Selection of an appropriate updating logic to minimize the compensation effects among multiple sources of data uncertainty.Overall, the BEAR method demonstrates flexibility and adaptability to various environmental modelling scenarios, making it a valuable tool for improving model specification under conditions of data uncertainty.

First-order nonadiabatic coupling (NAC) matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice of methods. However, the lack of many-electron wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. Because of this, various variants of NAC-TDDFT have been proposed in the literature from different standing points, including the Hellmann-Feynman-like expression and auxiliary/pseudo-wave function (AWF)-, equation-of-motion (EOM)-, and time-dependent perturbation theory (TDPT)-based formulations. Based on critical analyses, the following conclusions are made here: (1) The Hellmann-Feynman-like expression, which is rooted in exact wave function theory, is hardly useful due to huge demand on basis sets. (2) Although most popular, the AWF variants of NAC-TDDFT are not theoretically founded and become ambiguous particularly for the fo-NACMEs between two excited states, although they do agree with the EOM and TDPT variants under the Tamm-Dancoff approximation. (3) The TDPT variant of NAC-TDDFT is theoretically most rigorous but suffers from numerical instabilities on the one hand and does not differ to a significant extent from the EOM variant on the other hand. (4) As such, the EOM variant of NAC-TDDFT for the fo-NACMEs between the ground and excited states and between two excited states is solely the right choice in practice. These formal analyses are fully supported by numerical experimentations, taking azulene as a showcase. The proper implementation of the EOM variant of NAC-TDDFT is also highlighted, showing that the fo-NACMEs between the ground and excited states and between two excited states are computationally very much the same as the analytic energy gradients of DFT and TDDFT, respectively. Possible future developments of the EOM variant of NAC-TDDFT are also highlighted. Its extensions to spin-adapted open-shell TDDFT and proper treatment of spin-orbit couplings (which are another source of force for electronically nonadiabatic processes) are particularly warranted in the near future.

Applying fasteners effectively : Technical Information Staff, Industrial Fasteners Institute, Cleveland, Ohio. Electron. Products, March (1966), p. 36

Numerous applications of the Weibull distribution in diverse fields of human endeavor are well known today. Nevertheless, it is not uncommon to find applications of the normal distribution in such fields of studies as agriculture, biology, chemistry, engineering, physics, sociology and others. At the present time we have at our disposal many more refined statistical techniques for analyzing the normal rather than the Weibull data. Consequently, it is important for applied statisticians to know if some of their data which can be described by the Weibull distribution can also be described by the normal distribution. The present investigation of the author reveals that the normal distri,bution can be considered to be a good approximation to the Weibull distribution as long as its shape parameter is in the open interval (3.25, 3.61). This fact enables them to perform a refined statistical analysis of their data. Conversely, they can now easily compute the desired normal cumulative probabilities from the Weibull distribution function, which would be especially helpful for those standard normal deviates whose cumulative probabilities cannot be read from the available tables of normal cumulative probability. In a similar situation they can also use the Weibull distribution to obtain an approximation to any desired normal deviate for a given normal probability which may be better than those obtained by the linear interpolation method.

This study aimed to design an anatomical contour metal three-dimensional (3D)-printed oblique lateral lumbar interbody fusion (OLIF) cage with porous (lattices) structure and embedded screw fixation to enhance bone ingrowth to reduce the risk of cage subsidence and avoid the stress-shielding effect. Finite element (FE) analysis and weight topology optimization (WTO) were used to optimize the structural design of the OLIF cage based on the anatomical contour morphology of patients with osteoporosis. Two oblique embedded fixation screws and lattice design with 65% porosity and average pore size of 750 μm were equipped with the cage structure. The cage was fabricated via metal 3D printing, and static/dynamic compression and compressive-shear tests were performed in accordance with the ASTM F2077-14 standard to evaluate its mechanical resistance. On FE analysis, the OLIF cage with embedded screw model had the most stability, lowest stress values on the endplate, and uniform stress distribution versus standalone cage and fixed with lateral plate under extension, lateral flexion, and rotation. The fatigue test showed that the stiffnesses/endurance limits (pass 5 million dynamic test) were 16,658 N/mm/6000 N for axial load and 19,643 N/mm/2700 N for compression shear. In conclusion, an OLIF cage with embedded fixation screws can be designed by integrating FE and WTO analysis based on the statistical results of endplate morphology. This improves the stability of the OLIF cage to decrease endplate destruction. The complex contour and lattice design of the OLIF cage need to be manufactured via metal 3D printing; the dynamic axial compression and compressive-shear strengths are greater than that of the U.S. Food and Drug Administration (FDA) standard.

In this paper, we evaluate the performance of two Wireless Mesh Network (WMN) architectures considering throughput, delay and fairness index metrics. For simulations, we used a Genetic Algorithm (GA)-based simulation system (called WMN-GA) and ns-3. We compare the performance for two architectures considering normal and uniform distributions, different transmission rates and OLSR protocol. The simulation results show that the throughput and delay are increased, but the fairness index is decreased with increasing of transmission rate. The throughput of Hybrid WMN is higher than Infrastructure/Backbone (I/B) WMN. But, the delay of I/B WMN is higher than Hybrid WMN for normal distribution. The fairness index of normal distribution is higher than uniform distribution.

Inverse simulation is an inverse process of direct simulation. It determines unknown input variables of the direct simulation for a given set of simulation output variables. Uncertainties usually exist, making it difficult to solve inverse simulation problems. The objective of this research is to account for uncertainties in inverse simulation in order to produce high confidence in simulation results. The major approach is the use of the maximum probability density function (PDF), which determines not only unknown deterministic input variables but also the realizations of random input variables. Both types of variables are solved on the condition that the joint probability density of all the random variables is maximum. The proposed methodology is applied to a traffic accident reconstruction problem where the simulation output (accident consequences) is known and the simulation input (velocities of the vehicle at the beginning of crash) is sought.