Traditional Stochastic Approaches Research Articles

Data‐Worth Analysis for Heterogeneous Subsurface Structure Identification With a Stochastic Deep Learning Framework

AbstractReliable characterization of subsurface structures is essential for earth sciences and related applications. Data assimilation‐based identification frameworks can reasonably estimate subsurface structures using available lithological (e.g., borehole core, well log) and dynamic (e.g., hydraulic head, solute concentration) observations. However, a reasonable selection of the observation type and frequency is essential for accurate structure identification. To achieve this, we extended a recently developed stage‐wise stochastic deep learning inversion framework by coupling it with non‐isothermal flow and transport simulations. With the extended framework, the worth of three common observations (hydraulic head, concentration, and temperature) are compared under different observation noise and frequency. The framework combines the emerging deep‐learning (DL)‐based framework with the traditional stochastic approaches. This combination makes it possible to simultaneously compare the ability of these two methods to assimilate observation data. Our results show that including at least one type of dynamic observation strongly improves subsurface structure identifiability and reduces the uncertainty. However, the DL‐based framework is able to identify subsurface structures more accurately than stochastic identification methods under the same scenarios. Assimilation of certain types of dynamic observations could reduce the prediction error for related dynamic responses, but not necessarily for other uncorrelated dynamic responses. Observation data worth is affected by the observation noise and frequency. High observation noise increases the uncertainty of the prediction and reduces the estimation accuracy. However, the higher observation frequency can significantly improve the temporal dynamic information of observations. This information can compensate for negative impacts of high observation noise.

Integrating stochastic programs and decision trees in capacitated barge planning with uncertain container arrivals

In this paper, we propose an approach that combines optimization techniques with machine learning to improve capacitated barge planning with uncertain container arrivals. The main idea is to use the predictions of a decision tree in the scenario generation of a 2-stage stochastic program to plan the barge calls (i.e. visits) of a barge operator. The predictions of container arrivals help to generate more accurate scenarios, which in turn leads to more informed decisions and less costs. The approach is tested with an iterative method of periodic planning and simulation for a one year duration so that the long term performance is evaluated. A computational experiment is conducted using the historical data of an inland terminal and the Port of Rotterdam. The results show that the proposed approach improves total costs up to 2.07% over the traditional stochastic approach, and up to 4.57% over the current method used in industry.

Foundations of semialgebraic gene-environment networks

Gene-environment network studies rely on data originating from different disciplines such as chemistry, biology, psychology or social sciences. Sophisticated regulatory models are required for a deeper investigation of the unknown and hidden functional relationships between genetic and environmental factors. At the same time, various kinds of uncertainty can arise and interfere with the system's evolution. The aim of this study is to go beyond traditional stochastic approaches and to propose a novel framework of semialgebraic gene-environment networks. Foundation is laid for future research, methodology and application. This approach is a natural extension of interconnected systems based on stochastic, polyhedral, ellipsoidal or fuzzy (linguistic) uncertainty. It allows for a reconstruction of the underlying network from uncertain (semialgebraic) data sets and for a prediction of the uncertain futures states of the system. In addition, aspects of network pruning for large regulatory systems in genome-wide studies are discussed leading to mixed-integer programming (MIP) and continuous programming.

An Accelerated Edge Cloud System for Energy Data Stream Processing Based on Adaptive Incremental Deep Learning Scheme

As smart metering technology evolves, power suppliers can make low-cost, low-risk estimation of customer-side power consumption by analyzing energy demand data collected in real-time. With advances network infrastructure, smart sensors, and various monitoring technologies, a standardized energy metering infrastructure, called advanced metering infrastructure (AMI), has been introduced and deployed to urban households to allow them to develop efficient power generation plans. Compared to traditional stochastic approaches for time-series data analysis, deep-learning methods have shown superior accuracy on many prediction applications. Because smart meters and infrastructure monitors produce a series of measurements over time, a large amount of data is accumulated, creating a large data stream, which takes much time from data generation to deployment of deep-learning model training. In this article, we propose an accelerated computing system that considers time-variant properties for accurate prediction of energy demand by processing the AMI stream data. The proposed system is a real-time training/inference system that deploys AMI data over a distributed edge cloud. It comprises two core components: an adaptive incremental learning solver and deep-learning acceleration with FPGA-GPU resource scheduling. An adaptive incremental learning scheme adjusts the batch/epoch in training iteration to reduce the time delay of the latest trained model, while trying to prevent biased-training due to the sub-optimal optimizer of incremental learning. In addition, a resource scheduling scheme manages various accelerator resources for accelerated deep-learning processing while minimizing the computational cost. The experimental results demonstrated that our method achieved good performance for adaptive batch size and epoch for incremental learning while guaranteeing a low inference error, a high model score, and queue stability with cost efficient processing.

A novel stochastic method to dispatch microgrids using Monte Carlo scenarios

Stochastic management strategies have proven to achieve cheaper resource scheduling both in large power systems and microgrids, but suffer from high computational requirements with respect to traditional deterministic approaches; therefore, using stochastic formulations in advanced infra-daily operating strategies is quite challenging, especially in isolated hybrid energy systems with limited computational assets. This paper proposes a methodology for the microgrid operation based on a novel two-stage formulation that decomposes the stochastic problem into several deterministic subproblems, whose solutions are afterwards aggregated by the aggregator using simulations and a cost-based rule. In the first stage, every subproblem is solved, then each optimal dispatching is simulated in the second stage to evaluate the corresponding expected operating cost, which is used by the aggregator to select the final optimal scheduling. When compared to traditional methods for a rural microgrid in Uganda, the proposed approach not only achieves interesting savings in operational costs, up to 5%, but also sharply reduces the computational requirements, even more than 5–100 times with respect to traditional stochastic approaches. The paper also proposes a review and first classification of this kind of methodologies, to highlight the novelties of the approach.

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.

Reducing uncertainty in stochastic streamflow generation and reservoir sizing by combining observed, reconstructed and projected streamflow

Reservoir sizing is one of the most important aspects of water resources engineering as the storage in a reservoir must be sufficient to supply water during extended droughts. Typically, observed streamflow is used to stochastically generate multiple realizations of streamflow to estimate the required storage based on the Sequent Peak Algorithm (SQP). The main limitation in this approach is that the parameters of the stochastic model are purely derived from the observed record (limited to less than 80 years of data) which does not have information related to prehistoric droughts. Further, reservoir sizing is typically estimated to meet future increase in water demand, and there is no guarantee that future streamflow over the planning period will be representative of past streamflow records. In this context, reconstructed streamflow records, usually estimated based on tree ring chronologies, provide better estimates of prehistoric droughts, and future streamflow records over the planning period could be obtained from general circulation models (GCMs) which provide 30 year near-term climate change projections. In this study, we developed paleo streamflow records and future streamflow records for 30 years are obtained by forcing the projected precipitation and temperature from the GCMs over a lumped watershed model. We propose combining observed, reconstructed and projected streamflows to generate synthetic streamflow records using a Bayesian framework that provides the posterior distribution of reservoir storage estimates. The performance of the Bayesian framework is compared to a traditional stochastic streamflow generation approach. Findings based on the split-sample validation show that the Bayesian approach yielded generated streamflow traces more representative of future streamflow conditions than the traditional stochastic approach thereby, reducing uncertainty on storage estimates corresponding to higher reliabilities. Potential strategies for improving future streamflow projections and its utility in reservoir sizing and capacity expansion projects are also discussed.

Heterogeneity, nonlinearity and endogenous market volatility

This paper aims to contribute to the literature on the explanatory power of behavior models with heterogeneous agents. The authors present a new nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. An exogenous noise is introduced to the model with the assumption of IID normal innovations of the fundamental value in order to investigate how noisy dynamics interacts with deterministic process. The market is composed of two typical trader types: the rational fundamentalists and the boundedly rational traders governed by greed and fear. The interaction between noise and deterministic element determines the evolution process of the system as key parameters are changed. The authors find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S&P500 index, such as volatility clustering, fat tails (leptokurtosis), autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. The authors also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach.

Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Applicationof a Noisy Mackey–Glass Equation with Heteroskedastic Errors to theParis Stock Exchange Returns Series

Most recent empirical works that apply sophisticated statistical procedures such as a correlation-dimension method have shown that stock returns are highly complex. The estimated correlation dimension is high and there is little evidence of low-dimensional deterministic chaos. Taking the complex behaviour in stock markets into account, we think it is more robust than the traditional stochastic approach to model the observed data by a nonlinear chaotic model disturbed by dynamic noise. In fact, we construct a model having negligible or even zero autocorrelations in the conditional mean, but a rich structure in the conditional variance. The model is a noisy Mackey–Glass equation with errors that follow a GARCH(p,q) process. This model permits us to capture volatility-clustering phenomena. Its characteristic is that volatility clustering is interpreted as an endogenous phenomenon. The main objective of this article is the identification of the underlying process of the Paris Stock Exchange returns series CAC40. To this end, we apply several different tests to detect longmemory components and chaotic structures. Forecasting results for the CAC40 returns series, will conclude this paper.

Scale effects in transmissivity

Heterogeneity accounts for several paradoxes in groundwater flow and solute transport. One of the most striking observations is the emergence of scale effects in transmissivity, that is, the increase in effective transmissivity (or hydraulic conductivity, for that matter) with increasing scale of observation. Traditional stochastic approaches, where transmissivity is treated as a multilog-normal random function, lead to a large-scale effective transmissivity equal to the geometric average of local measurements. We present several field cases in which large-scale transmissivities are indeed larger than the geometric average of local tests. This suggests that the assumption of multilog-normality may not be valid in many cases, even if point T values display a log-normal distribution. We conjecture that scale dependence of T may, in part, be a consequence of high T zones being better connected than average or low T zones, a feature which may occur in many geological environments, but which is not consistent with multinormal log- T fields. We go on to generate a suite of log- T fields with a normal distribution for point values but non-multinormal spatial correlation. In all our fields, high T zones show longer correlations than average of low T zones. By simulating flow through these synthetic fields under simple boundary conditions, and estimating their effective transmissivity values, we conclude that these types of departures from the multilog-normality assumption lead consistently to scale effects.

A characterization of scientometric distributions based on harmonic means

The traditional stochastic approach to scientometric and bibliometric phenomena is based on measuring the absolute number of objects (e.g., publications, topics, citations). These measures reflect underlying rules such as the cumulative advantage principle and lead to classical statistical functions such as arithmetic mean and standard deviation. An alternative measure based on the contribution share of an individual object in the entirety of related objects reveals more about the coherence in the analyzed structure. This approach is connected with (conditional) harmonic means. The analysis of the properties of these statistical functions leads to a special urn-model distribution which has an analogous behaviour to that of the Waring distribution in connection with conditional arithmetic means. The new distribution combines specific properties (long tail, flexibility of the distribution shape) of the two scientometric favourites, the Waring and the negative binomial distribution. Five methods of parameter estimation are presented. The fit and the properties of this special urn-model distribution are illustrated by three scientometric examples, particularly, by two citation rate distributions with different shapes and one publication activity distribution with lacking zero frequencies.

A study of English word category prediction based on neural networks

This paper describes word category prediction based on neural network models for constructing an accurate word recognition system. It is difficult to represent hidden linguistic structure and make an N-gram word prediction model using traditional stochastic approaches. In this paper, two neural network models that can learn hidden linguistic structure are proposed. These models can easily be expanded from Bigram to N-gram networks. They were tested by training experiments with an open English text database. The Trigram word category prediction rates show that neural network models are comparable to stochastic models. Trigram neural network models compress information about 150 times, which is the ratio of the Trigram stochastic model free parameters (893 = 704 969) to the neural network model link weights (4649). In addition, this paper proposes a new method that dynamically controls the training parameters, updating step size and momentum. These techniques are effective for calculating the efficiency of this system.