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Uncovering differential equations from data with hidden variables

arXiv.org Machine Learning

Examples include meteorology, biology, and physics. The usual way to model deterministic dynamical systems is by using (partial) differential equations. Typically, differential equations models for a given dynamical system are derived using apriori insights into the problem at hand; then the model is validated using empirical observations. In an era in which massive data-sets pertaining to different fields of science are widely available, an interesting problem is whether it is possible for a useful differential equations model to be learned directly from data, without any major modeling effort required by the researcher. Our goal in this paper is to develop a general methodology for building such differential equations models in contexts in which not all relevant variables are observed, that is, in cases in which the main variable of interest depends on other variables of which no measurements are available. As a concrete example, consider the following problem. RTE, the electricity transmission system operator of France, uses high-level simulations of hourly temperature series to study the impact different climate scenarios have on electricity consumption, and hence on the French electrical power grid.


Value of Information Analysis via Active Learning and Knowledge Sharing in Error-Controlled Adaptive Kriging

arXiv.org Machine Learning

Large uncertainties in many phenomena of interest have challenged the reliability of pertaining decisions. Collecting additional information to better characterize involved uncertainties is among decision alternatives. Value of information (VoI) analysis is a mathematical decision framework that quantifies expected potential benefits of new data and assists with optimal allocation of resources for information collection. However, a primary challenge facing VoI analysis is the very high computational cost of the underlying Bayesian inference especially for equality-type information. This paper proposes the first surrogate-based framework for VoI analysis. Instead of modeling the limit state functions describing events of interest for decision making, which is commonly pursued in surrogate model-based reliability methods, the proposed framework models system responses. This approach affords sharing equality-type information from observations among surrogate models to update likelihoods of multiple events of interest. Moreover, two knowledge sharing schemes called model and training points sharing are proposed to most effectively take advantage of the knowledge offered by costly model evaluations. Both schemes are integrated with an error rate-based adaptive training approach to efficiently generate accurate Kriging surrogate models. The proposed VoI analysis framework is applied for an optimal decision-making problem involving load testing of a truss bridge. While state-of-the-art methods based on importance sampling and adaptive Kriging Monte Carlo simulation are unable to solve this problem, the proposed method is shown to offer accurate and robust estimates of VoI with a limited number of model evaluations. Therefore, the proposed method facilitates the application of VoI for complex decision problems.


Japanese authorities urging foreign nationals to be aware of drone regulations

The Japan Times

Japanese authorities are introducing a variety of measures to prevent the wrongful use of drones, which has been increasing due to many people being unfamiliar with regulations, especially tourists from abroad. Under the civil aeronautics law, a drone of 200 grams or more cannot be operated in airspace around airports or residential areas without permission from the government. In addition, the law regulating the use of drones bans flights in airspace near designated important places such as the Prime Minister's Office, the Imperial Palace and nuclear power plants. Foreign tourists and others unfamiliar with the laws continue to violate them. In 2019, 14 foreign nationals had their cases sent to prosecutors, as of Nov. 20.


Forecasting Industrial Aging Processes with Machine Learning Methods

arXiv.org Machine Learning

By accurately predicting industrial aging processes (IAPs), it is possible to schedule maintenance events further in advance, thereby ensuring a cost-efficient and reliable operation of the plant. So far, these degradation processes were usually described by mechanistic models or simple empirical prediction models. In this paper, we evaluate a wider range of data-driven models for this task, comparing some traditional stateless models (linear and kernel ridge regression, feed-forward neural networks) to more complex recurrent neural networks (echo state networks and LSTMs). To examine how much historical data is needed to train each of the models, we first examine their performance on a synthetic dataset with known dynamics. Next, the models are tested on real-world data from a large scale chemical plant. Our results show that LSTMs produce near perfect predictions when trained on a large enough dataset, while linear models may generalize better given small datasets with changing conditions.


Extracting dispersion curves from ambient noise correlations using deep learning

arXiv.org Machine Learning

We present a machine-learning approach to classifying the phases of surface wave dispersion curves. Standard FTAN analysis of surfaces observed on an array of receivers is converted to an image, of which, each pixel is classified as fundamental mode, first overtone, or noise. We use a convolutional neural network (U-net) architecture with a supervised learning objective and incorporate transfer learning. The training is initially performed with synthetic data to learn coarse structure, followed by fine-tuning of the network using approximately 10% of the real data based on human classification. The results show that the machine classification is nearly identical to the human picked phases. Expanding the method to process multiple images at once did not improve the performance. The developed technique will faciliate automated processing of large dispersion curve datasets.


$\epsilon$-shotgun: $\epsilon$-greedy Batch Bayesian Optimisation

arXiv.org Machine Learning

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an $\epsilon$-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our $\epsilon$-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability $\epsilon$ -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the $\epsilon$-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.


Information‐Based Machine Learning for Tracer Signature Prediction in Karstic Environments

#artificialintelligence

Karstic groundwater systems are often investigated by a combination of environmental or artificial tracers. One of the major downsides of tracer‐based methods is the limited availability of tracer measurements, especially in data sparse regions. This study presents an approach to systematically evaluate the information content of the available data, to interpret predictions of tracer concentration from machine learning algorithms, and to compare different machine learning algorithms to obtain an objective assessment of their applicability for predicting environmental tracers. There is a large variety of machine learning approaches, but no clear rules exist on which of them to use for this specific problem. In this study, we formulated a framework to choose the appropriate algorithm for this purpose.


Baker Hughes launches AI software to optimise oil and gas production

#artificialintelligence

Oilfield services company Baker Hughes and artificial intelligence (AI) software provider C3.ai have launched an AI-based application that allows well operators to view real-time production data and more accurately predict future production. The application, BHC3 Production Optimization, is the second AI software application developed by Baker Hughes and C3.ai following the announcement of their strategic partnership in June 2019. BHC3 Production Optimization is available to Baker Hughes' oil and gas customers globally. Baker Hughes says it is able to visualise, analyse and optimise upstream oil and gas operations. The software analyses historical and real-time data across production operations then analyses the data using machine learning for anomaly detection, production forecasting, and prescriptive actions that improve production performance.


Tesla up 20% after Panasonic posts first quarterly profit at battery business

The Japan Times

TOKYO/SAN, FRANCISCO – Tesla Inc.'s stock surged 20 percent on Monday in its largest one-day gain since 2013, fueled by a quarterly profit at Panasonic's battery business with the U.S. carmaker and an investor report predicting its shares would rise more than ten-fold by 2024. Shares of Tesla have rallied by over 30 percent since the car maker run by Chief Executive Elon Musk posted its second consecutive quarterly profit last Wednesday, which was viewed as a milestone for the company competing against established heavyweights including General Motors Co. and BMW. The stock is up over 300 percent since early June, helped by Tesla's better-than-expected financial results and ramped up production at its new car factory in Shanghai. Monday's rise came after Panasonic Corp. reported the first quarterly profit in its U.S. battery business with Tesla, which followed years of production troubles and delays. "We are catching up as Tesla is quickly expanding production," Panasonic Chief Financial Officer Hirokazu Umeda told an earnings briefing, referring to battery cell production. "Higher production volume is helping to push down materials costs and erase losses."


Neural network with data augmentation in multi-objective prediction of multi-stage pump

arXiv.org Machine Learning

A multi-objective prediction method of multi-stage pump method based on neural network with data augmentation is proposed. In order to study the highly nonlinear relationship between key design variables and centrifugal pump external characteristic values (head and power), the neural network model (NN) is built in comparison with the quadratic response surface model (RSF), the radial basis Gaussian response surface model (RBF), and the Kriging model (KRG). The numerical model validation experiment of another type of single stage centrifugal pump showed that numerical model based on CFD is quite accurate and fair. All of prediction models are trained by 60 samples under the different combination of three key variables in design range respectively. The accuracy of the head and power based on the four predictions models are analyzed comparing with the CFD simulation values. The results show that the neural network model has better performance in all external characteristic values comparing with other three surrogate models. Finally, a neural network model based on data augmentation (NNDA) is proposed for the reason that simulation cost is too high and data is scarce in mechanical simulation field especially in CFD problems. The model with data augmentation can triple the data by interpolation at each sample point of different attributes. It shows that the performance of neural network model with data augmentation is better than former neural network model. Therefore, the prediction ability of NN is enhanced without more simulation costs. With data augmentation it can be a better prediction model used in solving the optimization problems of multistage pump for next optimization and generalized to finite element analysis optimization problems in future.