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Adaptive random search algorithm utilizing boundary cost-function hypersurfaces measurement to implement Pontryagin maximum principle, discussing hybrid computer use, iterative solution and convergence properties
Random-search algorithm employs local and global properties to solve two-point boundary value problem in Pontryagin maximum principle for either fixed or variable end-time problems. Mixed boundary value problem is transformed to an initial value problem. Mapping between initial and terminal values utilizes hybrid computer.
A novel problem in computational materials modeling is addressed: “Are the computational microstructure reconstruction techniques reliable enough to replace experiments?” Here, “reliable” computations are associated with producing “expected” reconstructions that are adequately close to the experimental data. The output of computational techniques can deviate from the experimental measurements because of the epistemic uncertainties in the algorithms. In this work, an analytical formulation for quantification of epistemic uncertainties in a microstructure reconstruction algorithm based on Markov random field is presented. The method is used to predict the large-scale spatial distribution of a microstructure given an experimental input measured over a small spatial domain. However, small variations are observed on the microstructural features of the synthesized samples due to the Markov random field algorithm. The proposed analytical technique aims to quantify these uncertainties and estimate their propagation to the macroscale material properties to provide a significant understanding on how reliable it is to replace the experiments with the Markov random field model to predict microstructural maps over large spatial domains.
Theoretical and observational studies suggest that between-event variability in the median ground motions of larger ( M≥5 ) earthquakes is controlled primarily by the dynamic properties of the earthquake source, such as Brune-type stress drop. Analogous results remain equivocal for smaller events due to the lack of comprehensive and overlapping ground-motion and source-parameter datasets in this regime. Here in this paper, we investigate the relationship between peak ground acceleration (PGA) and dynamic stress drop for a new dataset of 5297 earthquakes that occurred in the San Francisco Bay area from 2002 through 2016. For each event, we measure PGA on horizontal-component channels of stations within 100 km and estimate stress drop from P-wave spectra recorded on vertical-component channels of the same stations. We then develop a nonparametric ground-motion prediction equation (GMPE) applicable for the moderate (M 1–4) earthquakes in our study region, using a mixed-effects generalization of the Random Forest algorithm. We use the Random Forest GMPE to model the joint influence of magnitude, distance, and near-site effects on observed PGA. We observe a strong correlation between dynamic stress drop and the residual PGA of each event, with the events with higher-than-expected PGA associated with higher values of stress drop. The strength of this correlation increases as a function of magnitude but remains significant even for smaller magnitude events with corner frequencies that approach the observable bandwidth of the acceleration records. Mainshock events are characterized by systematically higher stress drop and PGA than aftershocks of equivalent magnitude. Coherent local variations in the distribution of dynamic stress drop provide observational constraints to support the future development of nonergodic GMPEs that account for variations in median stress drop at different source locations.
Optimal stock level with algorithm for random distribution
This innovation is a variation of a simulated-annealing optimization algorithm that uses a recursive-branching structure to parallelize the search of a parameter space for the globally optimal solution to an objective. The algorithm has been demonstrated to be more effective at searching a parameter space than traditional simulated-annealing methods for a particular problem of interest, and it can readily be applied to a wide variety of optimization problems, including those with a parameter space having both discrete-value parameters (combinatorial) and continuous-variable parameters. It can take the place of a conventional simulated- annealing, Monte-Carlo, or random- walk algorithm. In a conventional simulated-annealing (SA) algorithm, a starting configuration is randomly selected within the parameter space. The algorithm randomly selects another configuration from the parameter space and evaluates the objective function for that configuration. If the objective function value is better than the previous value, the new configuration is adopted as the new point of interest in the parameter space. If the objective function value is worse than the previous value, the new configuration may be adopted, with a probability determined by a temperature parameter, used in analogy to annealing in metals. As the optimization continues, the region of the parameter space from which new configurations can be selected shrinks, and in conjunction with lowering the annealing temperature (and thus lowering the probability for adopting configurations in parameter space with worse objective functions), the algorithm can converge on the globally optimal configuration. The Recursive Branching Simulated Annealing (RBSA) algorithm shares some features with the SA algorithm, notably including the basic principles that a starting configuration is randomly selected from within the parameter space, the algorithm tests other configurations with the goal of finding the globally optimal solution, and the region from which new configurations can be selected shrinks as the search continues. The key difference between these algorithms is that in the SA algorithm, a single path, or trajectory, is taken in parameter space, from the starting point to the globally optimal solution, while in the RBSA algorithm, many trajectories are taken; by exploring multiple regions of the parameter space simultaneously, the algorithm has been shown to converge on the globally optimal solution about an order of magnitude faster than when using conventional algorithms. Novel features of the RBSA algorithm include: 1. More efficient searching of the parameter space due to the branching structure, in which multiple random configurations are generated and multiple promising regions of the parameter space are explored; 2. The implementation of a trust region for each parameter in the parameter space, which provides a natural way of enforcing upper- and lower-bound constraints on the parameters; and 3. The optional use of a constrained gradient- search optimization, performed on the continuous variables around each branch s configuration in parameter space to improve search efficiency by allowing for fast fine-tuning of the continuous variables within the trust region at that configuration point.
A technique for the digital simulation of multicorrelated Gaussian random processes is described. This technique is based upon generating discrete frequency functions which correspond to the Fourier transform of the desired random processes, and then using the fast Fourier transform (FFT) algorithm to obtain the actual random processes. The main advantage of this method of simulation over other methods is computation time; it appears to be more than an order of magnitude faster than present methods of simulation. One of the main uses of multicorrelated simulated random processes is in solving nonlinear random vibration problems by numerical integration of the governing differential equations. The response of a nonlinear string to a distributed noise input is presented as an example.
We report that the automated enforcement system (AES) is an effective way of supplementing traditional traffic enforcement, and the traffic violation data from AES can also be effectively used for safety research. In this study, traffic violation data were used to analyze the influencing factors associated with traffic violations and to predict the probability of violations at intersections. The potential factors influencing violations include 24 independent factors related to time, space, traffic and weather. Results from a logistic model showed that the midday period, weekends, residential districts, collector roads, congested traffic conditions, high traffic flow, lower wind speed and low temperature would increase the probability of traffic violations. The probability of violations was predicted by the random forest algorithm, which was proven to be the best traffic violation prediction model among logistic regression, Gaussian naive Bayes, and support vector machine. Moreover, the proximity weighted synthetic oversampling technique (ProWSyn) method was applied to reduce the impact of the imbalance ratio (IR) and improve the model’s prediction performance. The receiver operating characteristics (ROC) curves and Precision-Recall (PR) curves illustrated that the random forest algorithm using oversampling data had the best classifier prediction performance than undersampling data. The area under curve (AUC) and out-of-bag (OOB) error with IR = 1 reached 0.914 and 0.0787, which showed the better performance of the random forest algorithm using ProWSyn in dealing with imbalanced traffic violation data.
This paper discusses the application of evolutionary random-search algorithms (Simulated Annealing and Genetic Algorithms) to the problem of spacecraft design under performance uncertainty. Traditionally, spacecraft performance uncertainty has been measured by reliability. Published algorithms for reliability optimization are seldom used in practice because they oversimplify reality. The algorithm developed here uses random-search optimization to allow us to model the problem more realistically. Monte Carlo simulations are used to evaluate the objective function for each trial design solution. These methods have been applied to the Gravity Probe-B (GP-B) spacecraft being developed at Stanford University for launch in 1999, Results of the algorithm developed here for GP-13 are shown, and their implications for design optimization by evolutionary algorithms are discussed.
Motion planning remains a fundamental problem in robotics. Sampling-based algorithms use randomization to allow efficient solutions to this complex problem. As mobile robots and autonomous vehicles become more prevalent in everyday life, motion planning must be applied to increasingly challenging scenarios. Safety has become a paramount concern in motion planning for ensuring robotic applications enrich human lives. To date, many motion planning techniques to increase safety in the face of uncertain and dynamic environments have been developed. This dissertation first addresses distributional safety of Rapidly-Exploring Random Trees (RRT) through our algorithm W-Safe RRT. To acknowledge distributional uncertainty and poor modeling, W-Safe RRT uses the Wasserstein metric to provide a probabilistic bound on the distributional distance between a robot and obstacles. Human-interpretable environmental agent classification allows online safety margin adaptation. We propose and analyze an integrating region method for online classification that increases actor labeling accuracy based on behavioral feature values when compared to state of the art methods. The method performs class assignments based on local maximum likelihood in a created behavioral feature-space, allowing a notion of classification uncertainty. Model-based methods with safety guarantees can quickly become computationally in tractable, especially with multiple agents, higher dimensions, and plentiful unknowns. Sampling based algorithms have been parallelized for computation with multi-core computers and GPUs. We consider the use of quantum algorithms and computers for sampling-based motion planning for the first time. Quantum computing performs operations on superpositions of states and can solve certain problems much more efficiently than classical computers, but introduces previously unseen challenges. With Quantum-RRT, we recast the motion planning problem into a database-search structure and use Quantum Amplitude Amplification to find reachable states in the database with a quadratic performance increase over classical methods. We address two error sources with this method: quantum measurement and quantum oracle errors. We then extend this method to Parallel Quantum-RRT, which uses a manager-worker architecture with multiple parallel quantum workers to increase database search efficiency. We compare algorithm architectures and characterize probabilities of multiple workers finding solutions. Lastly, we test in simulation the quantum algorithms against classical versions in a wide variety of scenarios, concluding that a similar parallelization improvement is to be found in the quantum case as was found in the parallelization of classical RRT.
We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.
Dynamic wireless charging (DWC) has emerged as a viable approach to mitigate range anxiety by ensuring continuous and uninterrupted charging for electric vehicles in motion. DWC systems rely on the length of the transmitter, which can be categorized into long-track transmitters and segmented coil arrays. The segmented coil array, favored for its heightened efficiency and reduced electromagnetic interference, stands out as the preferred option. However, in such DWC systems, the need arises to detect the vehicle’s position, specifically to activate the transmitter coils aligned with the receiver pad and de-energize uncoupled transmitter coils. This paper introduces various machine learning algorithms for precise vehicle position determination, accommodating diverse ground clearances of electric vehicles and various speeds. Through testing eight different machine learning algorithms and comparing the results, the random forest algorithm emerged as superior, displaying the lowest error in predicting the actual position.
Low-lying coastal cities, exemplified by Norfolk, Virginia, face the challenge of street flooding caused by rainfall and tides, which strain transportation and sewer systems and can lead to personal and property damage. While high-fidelity, physics-based simulations provide accurate predictions of urban pluvial flooding, their computational complexity renders them unsuitable for real-time applications. Using data from Norfolk rainfall events between 2016 and 2018, this study compares the performance of a previous surrogate model based on a random forest algorithm with two deep learning models: Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The comparison of deep learning to the random forest algorithm is motivated by the desire to utilize a machine learning architecture that allows for the future inclusion of common uncertainty quantification techniques and the effective integration of relevant, multi-modal features.
The Wang–Landau Monte Carlo method [Wang FG, Landau DP. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys Rev Lett. 2001;86:2050-2053; Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. Phys Rev E. 2001;64:056101] has been established as an effective computational approach for studying complex systems. In this study, we review the properties of 6 popular empirical water potentials, including a recently proposed explicit 3-body potential, obtained by applying the Wang–Landau method to the simulation of water clusters. Finally, comparing to numerous classical and first principle calculations, we show that several classical water models can provide a consistent description of the structural and thermodynamical properties of water clusters partially in agreement of ab initio results, although they were designed to reproduce macroscopic properties of water at ambient conditions.
Background: Patient monitoring is vital in all stages of care. In particular, intensive care unit (ICU) patient monitoring has the potential to reduce complications and morbidity, and to increase the quality of care by enabling hospitals to deliver higher-quality, cost-effective patient care, and improve the quality of medical services in the ICU. Objective: We here report the development and validation of ICU length of stay and mortality prediction models. The models will be used in an intelligent ICU patient monitoring module of an Intelligent Remote Patient Monitoring (IRPM) framework that monitors the health status of patients, and generates timely alerts, maneuver guidance, or reports when adverse medical conditions are predicted. Methods: We utilized the publicly available Medical Information Mart for Intensive Care (MIMIC) database to extract ICU stay data for adult patients to build two prediction models: one for mortality prediction and another for ICU length of stay. For the mortality model, we applied six commonly used machine learning (ML) binary classification algorithms for predicting the discharge status (survived or not). For the length of stay model, we applied the same six ML algorithms for binary classification using the median patient population ICU stay of 2.64 days. For the regression-based classification, we used two ML algorithms for predicting the number of days. We built two variations of each prediction model: one using 12 baseline demographic and vital sign features, and the other based on our proposed quantiles approach, in which we use 21 extra features engineered from the baseline vital sign features, including their modified means, standard deviations, and quantile percentages. Results: We could perform predictive modeling with minimal features while maintaining reasonable performance using the quantiles approach. The best accuracy achieved in the mortality model was approximately 89% using the random forest algorithm. The highest accuracy achieved in the length of stay model, based on the population median ICU stay (2.64 days), was approximately 65% using the random forest algorithm. Conclusions: The novelty in our approach is that we built models to predict ICU length of stay and mortality with reasonable accuracy based on a combination of ML and the quantiles approach that utilizes only vital signs available from the patient’s profile without the need to use any external features. This approach is based on feature engineering of the vital signs by including their modified means, standard deviations, and quantile percentages of the original features, which provided a richer dataset to achieve better predictive power in our models.
In this paper, we investigate the possibility of selecting high-redshift Lyman-Break Galaxies (LBG) using current and future broadband wide photometric surveys, such as the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) or the Vera C. Rubin Legacy Survey of Space and Time (LSST), using a Random Forest algorithm. This work is conducted in the context of future large-scale structure spectroscopic surveys like DESI-II, the next phase of the Dark Energy Spectroscopic Instrument (DESI), which will start around 2029.We use deep imaging data from the Hyper Suprime Camera (HSC) and the Canada-France-Hawaii Telescope Large Area U-band Deep Survey (CLAUDS) on the COSMOS and XMM-LSS fields. To predict the selection performance of LBGs with image quality similar to UNIONS, we degrade the u,g,r,i and z bands to UNIONS depth.The Random Forest algorithm is trained with the u,g,r,i and z bands to classify LBGs in the 2.5 < z < 3.5 range.We find that fixing a target density budget of 1,100 deg$^{-2}$, the Random Forest approach gives a density of z > 2 targets of 873 deg$^{-2}$, and a density of 493 deg$^{-2}$ of confirmed LBGs after spectroscopic confirmation with DESI. This UNIONS-like selection was tested in a dedicated spectroscopic observation campaign of 1,000 targets with DESI on the COSMOS field, providing a safe spectroscopic sample with a mean redshift of 3. This sample is used to derive forecasts for DESI-II, assuming a sky coverage of 5,000 deg$^{2}$. We predict uncertainties on Alcock-Paczynski parameters α$_{⊥}$ and α$_{∥}$ to be 0.7% and 1% for 2.6 < z < 3.2, resulting in a potential 2% measurement of the dark energy fraction at high redshift. Additionally, we estimate the uncertainty in local non-Gaussianity and predict σ$_{fNL}$ ≈ 7, which would be comparable to the current best precision achieved by Planck. The latter forecast suggests that achieving the precision required to place stringent constraints on inflationary models (σ$_{fNL}$ ≈ 1) using spectroscopic galaxy surveys necessitates the development of a next-generation (Stage V) spectroscopic survey.
Here, in this paper, we investigate the possibility of selecting high-redshift Lyman-Break Galaxies (LBG) using current and future broadband wide photometric surveys, such as the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) or the Vera C. Rubin Legacy Survey of Space and Time (LSST), using a Random Forest algorithm. This work is conducted in the context of future large-scale structure spectroscopic surveys like DESI-II, the next phase of the Dark Energy Spectroscopic Instrument (DESI), which will start around 2029. We use deep imaging data from the Hyper Suprime Camera (HSC) and the Canada-France-Hawaii Telescope Large Area U-band Deep Survey (CLAUDS) on the COSMOS and XMM-LSS fields. To predict the selection performance of LBGs with image quality similar to UNIONS, we degrade the u,g,r,i and z bands to UNIONS depth. The Random Forest algorithm is trained with the u,g,r,i and z bands to classify LBGs in the 2.5 < z < 3.5 range. We find that fixing a target density budget of 1,100 deg -2 , the Random Forest approach gives a density of z > 2 targets of 873 deg -2 , and a density of 493 deg -2 of confirmed LBGs after spectroscopic confirmation with DESI. This UNIONS-like selection was tested in a dedicated spectroscopic observation campaign of 1,000 targets with DESI on the COSMOS field, providing a safe spectroscopic sample with a mean redshift of 3. This sample is used to derive forecasts for DESI-II, assuming a sky coverage of 5,000 deg 2 . We predict uncertainties on Alcock-Paczynski parameters α ⊥ and α ∥ to be 0.7% and 1% for 2.6 < z < 3.2, resulting in a potential 2% measurement of the dark energy fraction at high redshift. Additionally, we estimate the uncertainty in local non-Gaussianity and predict σ fNL ≈ 7, which would be comparable to the current best precision achieved by Planck. The latter forecast suggests that achieving the precision required to place stringent constraints on inflationary models (σ fNL ≈ 1) using spectroscopic galaxy surveys necessitates the development of a next-generation (Stage V) spectroscopic survey.
Neuromorphic computing has many promises in the future of computing due to its energy efficient and scalable implementation. Here we extend a neural algorithm that is able to solve the diffusion equation PDE by implementing random walks on neuromorphic hardware. Additionally, we introduce four random walk applications that use this spiking neural algorithm. The four applications currently implemented are: generating a random walk to replicate an image, finding a path between two nodes, finding triangles in a graph, and partitioning a graph into two sections. We then made these four applications available to be implemented on software using a graphical user interface (GUI).