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At least 739 records · Page 41

Global Sensitivity Analysis of a Reactive Transport Model for Mineral Scale Formation During Hydraulic Fracturing

Injection of water-based hydraulic fracturing fluid (HFF) into tight shale gas/oil formations can increase formation permeability and enhance production rates, but this process frequently causes mineral scale formation that can occlude pore space and hinder flow. To identify the most important factors that control the formation of mineral scales, we applied a novel global sensitivity analysis method—distance-based generalized sensitivity analysis (DGSA)—to a reactive transport model (RTM) that was previously built and calibrated to simulate precipitation of barite [BaSO4] and iron (hydr)oxide [Fe(OH) 3 ] in shale matrices and on fracture surfaces. Reactive transport simulations were run with model parameters randomly sampled based on assigned uncertainties. Modeling results for barite and Fe(OH)3 formation were clustered using machine-learning algorithms. A list of ranked critical input parameters was obtained after statistical quantification of cumulative distribution functions of input parameters. We found that barite formation is most sensitive to the rate of sulfate ion generation, which is determined by the pyrite dissolution rate coefficient and oxidant availability. In addition, barite formation is sensitive to the initial amounts of barite in HFF and shale, followed by barite thermodynamics/kinetics. For Fe(OH) 3 formation, the ranked factors are Fe(OH)3 precipitation rate coefficients, initial HFF pH, initial Fe(OH) 3 amount in HFF, and oxidant availability. Overall, our results provide insights into managing mineral scale formation during hydraulic fracturing to enhance production. Meanwhile, this study serves as an example of global sensitivity analysis of RTMs using the efficient, straightforward, and open-source DGSA method.

58 GEOSCIENCES↗

Computationally Efficient Decompositions of Oblique Projection Matrices

Oblique projection matrices arise in problems in weighted least squares, signal processing, and optimization. While these matrices can be potentially very large, their low-rank structure can be exploited for efficient computation. Here, we propose fast and scalable algorithms for computing their eigendecomposition and singular value decomposition (SVD). Numerical experiments that compare our proposed approaches to existing methods, including randomized SVD, are presented. In addition, we test their accuracy on linear systems from equality constrained optimization problems.

97 MATHEMATICS AND COMPUTING↗

Using GANs with adaptive training data to search for new molecules

The process of drug discovery involves a search over the space of all possible chemical compounds. Generative Adversarial Networks (GANs) provide a valuable tool towards exploring chemical space and optimizing known compounds for a desired functionality. Standard approaches to training GANs, however, can result in mode collapse, in which the generator primarily produces samples closely related to a small subset of the training data. In contrast, the search for novel compounds necessitates exploration beyond the original data. In this work, we present an approach to training GANs that promotes incremental exploration and limits the impacts of mode collapse using concepts from Genetic Algorithms. In our approach, valid samples from the generator are used to replace samples from the training data. We consider both random and guided selection along with recombination during replacement. By tracking the number of novel compounds produced during training, we show that updates to the training data drastically outperform the traditional approach, increasing potential applications for GANs in drug discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A square root formulation for the combined state-parameter estimator with application to the identification of sailplane performance

A square root formulation is presented for the discrete combined state parameter estimation problem with linear plant dynamics, Gaussian random disturbances, and constant but uncertain parameters. The estimator is a combination of the classical Kalman filter and a maximum likelihood algorithm which maximizes the parameter log-likelihood function using a first order search routine.

Froidevaux, M. R.↗

An approximate methods approach to probabilistic structural analysis

A major research and technology program in Probabilistic Structural Analysis Methods (PSAM) is currently being sponsored by the NASA Lewis Research Center with Southwest Research Institute as the prime contractor. This program is motivated by the need to accurately predict structural response in an environment where the loadings, the material properties, and even the structure may be considered random. The heart of PSAM is a software package which combines advanced structural analysis codes with a fast probability integration (FPI) algorithm for the efficient calculation of stochastic structural response. The basic idea of PAAM is simple: make an approximate calculation of system response, including calculation of the associated probabilities, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The deterministic solution resulting should give a reasonable and realistic description of performance-limiting system responses, although some error will be inevitable. If the simple model has correctly captured the basic mechanics of the system, however, including the proper functional dependence of stress, frequency, etc. on design parameters, then the response sensitivities calculated may be of significantly higher accuracy.

Mcclung, R. C.↗

Microgravity and Charge Transfer in the Neuronal Membrane: Implications for Computational Neurobiology

Evidence from natural and artificial membranes indicates that the neural membrane is a liquid crystal. A liquid-to-gel phase transition caused by the application of superposed electromagnetic fields to the outer membrane surface releases spin-correlated electron pairs which propagate through a charge transfer complex. The propagation generates Rydberg atoms in the lipid bilayer lattice. In the present model, charge density configurations in promoted orbitals interact as cellular automata and perform computations in Hilbert space. Due to the small binding energies of promoted orbitals, their automata are highly sensitive to microgravitational perturbations. It is proposed that spacetime is classical on the Rydberg scale, but formed of contiguous moving segments, each of which displays topological equivalence. This stochasticity is reflected in randomized Riemannian tensor values. Spacetime segments interact with charge automata as components of a computational process. At the termination of the algorithm, an orbital of high probability density is embedded in a more stabilized microscopic spacetime. This state permits the opening of an ion channel and the conversion of a quantum algorithm into a macroscopic frequency code.

Wallace, Ron↗

MONACO: accurate biological network alignment through optimal neighborhood matching between focal nodes

Motivation: Alignment of protein–protein interaction networks can be used for the unsupervised prediction of functional modules, such as protein complexes and signaling pathways, that are conserved across different species. To date, various algorithms have been proposed for biological network alignment, many of which attempt to incorporate topological similarity between the networks into the alignment process with the goal of constructing accurate and biologically meaningful alignments. Especially, random walk models have been shown to be effective for quantifying the global topological relatedness between nodes that belong to different networks by diffusing node-level similarity along the interaction edges. However, these schemes are not ideal for capturing the local topological similarity between nodes. Results: Here, we propose MONACO, a novel and versatile network alignment algorithm that finds highly accurate pairwise and multiple network alignments through the iterative optimal matching of ‘local’ neighborhoods around focal nodes. Extensive performance assessment based on real networks as well as synthetic networks, for which the ground truth is known, demonstrates that MONACO clearly and consistently outperforms all other state-of-the-art network alignment algorithms that we have tested, in terms of accuracy, coherence and topological quality of the aligned network regions. Furthermore, despite the sharply enhanced alignment accuracy, MONACO remains computationally efficient and it scales well with increasing size and number of networks.

97 MATHEMATICS AND COMPUTING↗

A mathematical assessment of the isolation random forest method for anomaly detection in big data

We present the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection, proposed by Liu F.T., Ting K.M. and Zhou Z. H. in their seminal work as a heuristic method for anomaly detection in Big Data. We prove that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved, using the Law of Large Numbers. Here, a couple of counterexamples are presented to show that the method is inconclusive and no certificate of quality can be given, when using it as a means to detect anomalies. Hence, an alternative version of the method is proposed whose mathematical foundation is fully justified. Furthermore, a criterion for choosing the number of sampled trees needed to guarantee confidence intervals of the numerical results is presented. Finally, numerical experiments are presented to compare the performance of the classic method with the proposed one.

97 MATHEMATICS AND COMPUTING↗

Reinforcement learning in discrete action space applied to inverse defect design

Abstract Reinforcement learning (RL) algorithms that include Monte Carlo Tree Search (MCTS) have found tremendous success in computer games such as Go, Shiga and Chess. Such learning algorithms have demonstrated super-human capabilities in navigating through an exhaustive discrete action search space. Motivated by their success in computer games, we demonstrate that RL can be applied to inverse materials design problems. We deploy RL for a representative case of the optimal atomic scale inverse design of extended defects via rearrangement of chalcogen (e.g. S) vacancies in 2D transition metal dichalcogenides (e.g. MoS 2 ). These defect rearrangements and their dynamics are important from the perspective of tunable phase transition in 2D materials i.e. 2H (semi-conducting) to 1T (metallic) in MoS 2 . We demonstrate the ability of MCTS interfaced with a reactive molecular dynamics simulator to efficiently sample the defect phase space and perform inverse design—starting from randomly distributed S vacancies, the optimal defect rearrangement of defects corresponds a line defect of S vacancies. We compare MCTS performance with evolutionary optimization i.e. genetic algorithms and show that MCTS converges to a better optimal solution (lower objective) and in fewer evaluations compared to GA. We also comprehensively evaluate and discuss the effect of MCTS hyperparameters on the convergence to solution. Overall, our study demonstrates the effectives of using RL approaches that operate in discrete action space for inverse defect design problems.

42 ENGINEERING↗

Machine Learning for Improving Surface-Layer-Flux Estimates

Abstract Flows in the atmospheric boundary layer are turbulent, characterized by a large Reynolds number, the existence of a roughness sublayer and the absence of a well-defined viscous layer. Exchanges with the surface are therefore dominated by turbulent fluxes. In numerical models for atmospheric flows, turbulent fluxes must be specified at the surface; however, surface fluxes are not known a priori and therefore must be parametrized. Atmospheric flow models, including global circulation, limited area models, and large-eddy simulation, employ Monin–Obukhov similarity theory (MOST) to parametrize surface fluxes. The MOST approach is a semi-empirical formulation that accounts for atmospheric stability effects through universal stability functions. The stability functions are determined based on limited observations using simple regression as a function of the non-dimensional stability parameter representing a ratio of distance from the surface and the Obukhov length scale (Obukhov in Trudy Inst Theor Geofiz AN SSSR 1:95–115, 1946), $$z/L$$ z / L . However, simple regression cannot capture the relationship between governing parameters and surface-layer structure under the wide range of conditions to which MOST is commonly applied. We therefore develop, train, and test two machine-learning models, an artificial neural network (ANN) and random forest (RF), to estimate surface fluxes of momentum, sensible heat, and moisture based on surface and near-surface observations. To train and test these machine-learning algorithms, we use several years of observations from the Cabauw mast in the Netherlands and from the National Oceanic and Atmospheric Administration’s Field Research Division tower in Idaho. The RF and ANN models outperform MOST. Even when we train the RF and ANN on one set of data and apply them to the second set, they provide more accurate estimates of all of the fluxes compared to MOST. Estimates of sensible heat and moisture fluxes are significantly improved, and model interpretability techniques highlight the logical physical relationships we expect in surface-layer processes.

Meteorology & Atmospheric Sciences↗

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

The problem of a spatially discontinuous diffusion coefficient (D(x)) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow properties. To date, mass-transfer particle-tracking (MTPT) methods, a family of Lagrangian methods in which diffusion is jointly simulated by random walk and diffusive mass transfers, have been unable to solve this problem. This manuscript presents a new mass-transfer (MT) algorithm that enables MTPT methods to accurately solve the problem of discontinuous D(x). To achieve this, we derive a semi-analytical solution to the discontinuous D(x) problem by employing a predictor-corrector approach, and we use this semi-analytical solution as the weighting function in a reformulated MT algorithm. Furthermore, this semi-analytical solution is generalized for cases with multiple 1D interfaces as well as for 2D cases, including a 2 × 2 tiling of 4 subdomains that corresponds to a numerically-generated diffusion field. The solutions generated by this new mass-transfer algorithm closely agree with an analytical 1D solution or, in more complicated cases, trusted numerical results, demonstrating the success of our proposed approach.

42 ENGINEERING↗

SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has two parameters: subsampling size and the number of subsamples. When the subsampling size increases with fixed total sample size, the accuracy of our algorithm goes up and then down. When the number of subsamples increases, the accuracy of our algorithm keeps going up. We demonstrate how to use our algorithm step by step and compare our algorithm with threshold sparse Bayesian regression (TSBR) for the discovery of differential equations. We show that our algorithm produces better results. We also discuss the merits of discovering differential equations from data and demonstrate how to discover models with random initial and boundary condition as well as models with bifurcations. The numerical examples are: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary condition, and (4) fish-harvesting problem with bifurcations.

97 MATHEMATICS AND COMPUTING↗

Machine learning enhanced predictions of ICRF heating: Overcoming numerical limitations via data curation

In this work, we present the development of robust surrogate models for Ion Cyclotron Range of Frequencies (ICRF) and High-Harmonic Fast Wave (HHFW) heating predictions in fusion plasmas. Building upon our previous efforts to achieve real-time capable models, we identify the cause of the outliers found using TORIC in certain HHFW heating scenarios. The outliers are observed to be spurious ion Bernstein wave (IBW)-like modes caused by a wavelength control algorithm designed to address challenging scenarios with high perpendicular wavenumbers. The effect arises from the modulation in the perpendicular susceptibility, which can induce sign reversal and IBW-like propagation for scenarios featuring normalized ion Larmor radius λ i ≫ 1. We use TORIC with this algorithm disabled to generate a novel HHFW-NSTX database that is free of outliers. Surrogate models trained on this database, including Random Forest Regressor (RFR), Multi-Layer Perceptrons, and Gaussian Process Regressors (GPR), demonstrate the ability to accurately predict HHFW heating profiles, with regression scores of R 2 ∈[0.93−0.99]. Additionally we demonstrate that it is possible to generalize predictions beyond training data by the use of both RFR and GPR models, enabling the prediction of scenarios previously limited to the original model. GPR models also provide uncertainty quantification, offering insights into model confidence. This work introduces a comprehensive Verification, Validation, and Uncertainty Quantification methodology for surrogate modeling, applicable not only to ICRF heating but also to other RF heating challenges and fusion physics problems. Beyond accelerated inference, these models show effective extrapolation capabilities, providing an alternative for addressing numerical challenges.

Artificial neural networks↗

Computing Sparse Tensor Decompositions via Chapel and C++/MPI Interoperability without Intermediate I/O

We extend an existing approach for efficient use of shared mapped memory across Chapel and C++ for graph data stored as 1-D arrays to sparse tensor data stored using a combination of 2-D and 1-D arrays. We describe the specific extensions that provide use of shared mapped memory tensor data for a particular C++ tensor decomposition tool called GentenMPI. We then demonstrate our approach on several real-world datasets, providing timing results that illustrate minimal overhead incurred using this approach. Finally, we extend our work to improve memory usage and provide convenient random access to sparse shared mapped memory tensor elements in Chapel, while still being capable of leveraging high performance implementations of tensor algorithms in C++.

97 MATHEMATICS AND COMPUTING↗

Phasing of a space based segmented submillimeter wavelength telescope using focal plane measurements

As part of a technology development program for realizing a space based submillimeter telescope, two different approaches to the absolute phasing of a segmented primary mirror using focal plane measurements have been implemented for feasibility. The method of optimization by simulated annealing evaluates the image quality of a point spread function after all the telescope segments have been randomly moved. It accepts each iteration which improves the image quality, as well as a random number of iterations which do not, thus keeping the Strehl in the initialization procedure from falling into local maxima. Methods for determining the annealing schedule, and the step size for random segment movements are presented and discussed. Using phase diversity and a model for the telescope imaging system, a nonlinear least squares algorithm has also been implemented which parameterizes each of the segment actuator movements. Using multiple out of focus images, the segment actuator positions are estimated using an iterative procedure. Nonlinear least squares, although computationally intensive, offers a large savings in the actuator movements over simulated annealing and pairwise phasing methods for large numbers of segments. These algorithms have been integrated into a general simulation program which models the behavior of the telescope under anticipated space conditions.

Levine, B. M.↗

Synergistic Retrievals of Ice in High Clouds From Elastic Backscatter Lidar, Ku-band Radar and Submillimeter Wave Radiometer Observations

In this study, we investigate the synergy of elastic backscatter lidar, Ku-band radar, and sub-millimeter-wave radiometer measurements in the retrieval of ice from satellite observations. The synergy is analyzed through the generation of a large dataset of IceWater Content (IWC) profiles and simulated lidar, radar and radiometer observations. The characteristics of the instruments e.g. frequencies, sensitivities, etc. are set based on the expected characteristics of instruments of the Atmosphere Observing System (AOS) mission. A hold-out validation methodology is used to assess the accuracy of the IWC profiles retrieved from various combinations of observations from the three instruments. Specifically, the IWC and associated observations are randomly divided into two datasets, one for training and the other for evaluation. The training dataset is used to train the retrieval algorithm, while the evaluation dataset is used to assess the retrieval performance. The dataset of IWC profiles is derived from CloudSat reflectivity and CALIOP lidar observations. The retrieval of the ice water content IWC profiles from the computed observations is achieved in two steps. In the first step, a class, out of 18 potential classes characterized by different vertical distribution of IWC, is estimated from the observations. The 18 classes are predetermined based on the k-Means clustering algorithm. In the second step, the IWC profile is estimated using an Ensemble Kalman Smoother (EKS) algorithm that uses the estimated class as a priori information. The results of the study show that the synergy of lidar, radar, and radiometer observations is significant in the retrieval of the IWC profiles. Nevertheless, it should be mentioned that this synergy was found under idealized conditions, and additional work might be required to materialize it in practice. The inclusion of the lidar backscatter observations in the retrieval process has a larger impact on the retrieval performance than the inclusion of the radar observations. As ice clouds have a significant impact on atmospheric radiative processes, this work is relevant to ongoing efforts to reduce uncertainties in climate analyses and projections.

Mircea Grecu↗

Resilient Observer Design for Cyber-Physical Systems with Data-Driven Measurement Pruning

Resilient observer design for Cyber-Physical Systems (CPS) in the presence of adversarial false data injection attacks (FDIA) is an active area of research. The existing state-of-the-art algorithms tend to break down as more and more knowledge of the system is built into the attack model; also as the percentage of attacked nodes increases. From the view of optimization theory, the problem is often cast as a classical error correction problem for which a theoretical limit of has been established as the maximum percentage attacked nodes for which state recovery is guaranteed. Beyond this limit, the performance of -minimization based schemes, for instance, deteriorates rapidly. Similar performance degradation occurs for other types of resilient observers beyond certain percentages of attacked nodes. In order to increase the corresponding percentage of attacked nodes for which state recoveries can be guaranteed, researchers have begun to incorporate prior information into the underlying resilient observer design framework. For the most pragmatic cases, this prior information is often obtained through a data-driven machine learning process. Existing results have shown a strong positive correlation between the maximum attacked percentages that can be tolerated and the accuracy of the data-driven model. Motivated by these results, this chapter examines the case for pruning algorithms designed to improve the Positive Prediction Value (PPV) of the resulting prior information, given stochastic uncertainty characteristics of the underlying machine learning model. Theoretical quantification of the achievable improvement is given. Simulation results show that the pruning algorithm significantly increases the maximum correctable percentage of attacked nodes, even for machine learning model whose prediction power is comparable to the random flip of a coin.

Resilient Observer, Cyber-physical Systems, Data-D↗

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗