Julia Programming Language Research Articles

Predicer: abstract stochastic optimisation model framework for multi-market operation

An open-source modelling framework Predicer, standing for Predictive Decider, for multi-market day-ahead market operation purposes is described in this paper. The Predicer model uses scenario-based stochastic optimisation to obtain decision variables and bid matrixes for energy and reserve markets by maximising the risk-adjusted expected value of the profit during the model time frame. The modelled energy system structure is abstract, that is, based on basic elements such as nodes representing different energy types and processes representing flows between nodes. The abstract model structure enables user to construct arbitrary energy systems and define links between assets, commodities, energy markets and reserve markets. Predicer model can include properties such as unit ramp rates, online units, dynamic energy storages, market realisation and market bidding requirements. The aggregation of unit-based energy and reserve opportunities into a virtual power plant allows the asset owner to make optimized portfolio-level bids for different market products. The model scenarios consist of user defined forecasts for market prices, renewable energy supply, energy demand and other system related time series. Predicer is implemented in Julia programming language and uses the JuMP optimisation package.

Tuning and interpretation of electronic transport properties with

Electronic transport coefficients such as the electrical conductivity, the termo-power, and the charge carrier concentration are routinely measured in a variety of application areas such as electronics or thermoelectric power-generation and cooling. Using fitting procedures, those measurements are used to infer microscopic features of the samples. The code ▪ facilitates the estimation of electronic structure parameters such as the effective masses and band energies improving the current approach by increasing the complexity of the band structure representation. The software is designed with a server-client architecture to enhance performance and scalability. The server is implemented in the Julia programming language. We illustrate the design and the efficiency of the code with selected applications, which are relevant to the optimization of thermoelectric materials. Program summaryProgram Title:▪CPC Library link to program files:https://doi.org/10.17632/494nj6ftbv.1Developer's repository link:https://github.com/marcofornari/etransport.gitLicensing provisions: GPLv3Programming language: Julia, Python.Nature of problem: Electronic transport measurements are routinely used to link the functional properties exploited in electronics and energy sciences applications with the underlying electronic structure of the material under investigation. Experimentalists collect data of derived and integrated physical quantities, from which they estimate properties and parameters, e.g., nature of the conduction mechanisms and effective mass. The interpretation is based on simplistic models that rarely represent the complexity of the band structure. The code ▪ improves the current state of the art and facilitates the estimation of effective masses and energies from experimental measurements of electrical conductivity, Seebeck coefficients, and carrier concentration using a multi-valley anisotropic parabolic band structure as a model for the unknown real band structure. Experimental data can be imported and visualized to facilitate the comparison with theoretical analysis.Solution method: The Boltzmann equation within the relaxation-time approximation is used to compute the electronic transport tensors from the electronic density of states characterized in terms of a set of effective masses tensors mi⁎ and critical energies ϵi. Numerical and analytical techniques are adopted to integrate the Boltzmann equation efficiently. By tuning the features of the density of states, temperature, Fermi level, and the functional expression for the relaxation time, the software streamlines the reconstruction of the underlying electronic properties from experimental data.Additional comments including restrictions and unusual features: The software is designed with a server-client architecture to enhance performance and scalability. The server is implemented in the Julia programming language as a stand-alone library. It performs all the numerical operations to compute the transport tensors from a set of multi-valley parabolic band structures. The client is implemented either as a command-line user interface (CLI) or a graphical user interface (GUI) written in the Python programming language. The communications between the server and clients are handled by a REST API, where the data are exchanged using JSON payloads.

Physics‐Informed Gas Lifting Oil Well Modelling using Neural Ordinary Differential Equations

AbstractModelling of oil well systems is important for a wide range of petroleum scientific and oil industrial processes. Considering the uncertainty of the measurements and the demand for empirical knowledge, a purely first‐principle model and a black‐box model based on data are not sufficient for accurately describing an oil well system. Thus, there is a growing body of literature that recognizes the importance of data‐driven methods combined with physical knowledge. However, the application of combination methods for dynamic nonlinear systems is still challenging. In this work, we demonstrate the application of a physics‐informed neural network to a gas lifting oil well system. The neural ordinary differential equation is the main tool for the modeling and the simulation is examined in Julia programming language. The advantage and drawbacks of the physics‐informed data‐driven method are analyzed.

IMPLEMENTASI PENYELESAIAN PERSAMAAN BURGERS DENGAN METODE BEDA HINGGA DALAM BAHASA PEMROGRAMAN JULIA

Burgers equation is a partial differential equation used to modelling several events related to fluids. Burgers equation was firstly introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. This study discusses solving Burgers equations with finite difference method. In this study, several parameters have been known for the Burgers equation and several cases of partitions are used in finite difference method. The result shows that the more partitions used, the numerical result obtained will be closer to the exact values. In this study, calculations are numerically carried out with the help of Julia programming language.

A GPU-parallelized interpolation-based fast multipole method for the relativistic space-charge field calculation

The fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for the computation of the relativistic space-charge field. Different to the quasi-electrostatic model, our FMM is formulated in the lab-frame and can be applied without the assistance of the Lorentz transformation. In particular, we derive a modified admissibility condition which can effectively control the interpolation error of the proposed FMM. The algorithms and their GPU parallelization are discussed in detail. A package containing serial and GPU-parallelized solvers is implemented in the Julia programming language. The GPU-parallelized solver can reach a speedup of more than a hundred compared to the execution on a single CPU core.

Polynomial NARX-based nonlinear model predictive control of modular chemical systems

The design of control systems for modular chemical systems typically requires the identification of nonlinear dynamic models. Mechanistic models for modular chemical systems are typically of high order, which results in high online computational cost when the models are incorporated into the nonlinear model predictive control (NMPC) formulations developed for explicitly taking constraints into account. This article proposes the use of a particular class of nonlinear input–output models, polynomial nonlinear-autoregressive-with-exogenous-inputs (NARX) models, in the NMPC formulations. A machine learning algorithm, elastic net, is used to select which terms to include within the NARX polynomial series representation. The approach for constructing sparse predictive models and their use in real-time implementable NMPC are demonstrated in a two-input two-output chemical reactor case study. The Julia programming language is used to solve the NMPC optimization problem, resulting in low online computational cost.

Ordinary fractional differential equations to show results of oscillations, using the graphical and numerical approximation in the Julia programming language

The present study developed at a documentary and explanatory level, which aims to assume through an illustrative approach in the Julia programming language, the representation of oscillating results in solutions of fractional ordinary differential equations, among these topics the solutions stand out in: Systems of differential equations equations, differential equations of partial fractions and the differential equations of fractional lags. In this sense, this scientific article assumes the recent foundations in this field and serves as foundations for future research contributions.

A complex systems model of breast cancer etiology: The Paradigm II Model.

Complex systems models of breast cancer have previously focused on prediction of prognosis and clinical events for individual women. There is a need for understanding breast cancer at the population level for public health decision-making, for identifying gaps in epidemiologic knowledge and for the education of the public as to the complexity of this most common of cancers. We developed an agent-based model of breast cancer for the women of the state of California using data from the U.S. Census, the California Health Interview Survey, the California Cancer Registry, the National Health and Nutrition Examination Survey and the literature. The model was implemented in the Julia programming language and R computing environment. The Paradigm II model development followed a transdisciplinary process with expertise from multiple relevant disciplinary experts from genetics to epidemiology and sociology with the goal of exploring both upstream determinants at the population level and pathophysiologic etiologic factors at the biologic level. The resulting model reproduces in a reasonable manner the overall age-specific incidence curve for the years 2008-2012 and incidence and relative risks due to specific risk factors such as BRCA1, polygenic risk, alcohol consumption, hormone therapy, breastfeeding, oral contraceptive use and scenarios for environmental toxin exposures. The Paradigm II model illustrates the role of multiple etiologic factors in breast cancer from domains of biology, behavior and the environment. The value of the model is in providing a virtual laboratory to evaluate a wide range of potential interventions into the social, environmental and behavioral determinants of breast cancer at the population level.

Julia for biologists.

Major computational challenges exist in relation to the collection, curation, processing and analysis of large genomic and imaging datasets, as well as the simulation of larger and more realistic models in systems biology. Here we discuss how a relative newcomer among programming languages-Julia-is poised to meet the current and emerging demands in the computational biosciences and beyond. Speed, flexibility, a thriving package ecosystem and readability are major factors that make high-performance computing and data analysis available to an unprecedented degree. We highlight how Julia's design is already enabling new ways of analyzing biological data and systems, and we provide a list of resources that can facilitate the transition into Julian computing.

A modelling testbed to demonstrate the circular economy of water

Climate change poses significant challenges in terms of water scarcity, environmental crisis, and economic uncertainty. This situation drives an increasing need to pursue more sustainable futures and to conserve and maximise the use of resources whenever possible. The EU-funded H2020 NextGen project aimed to boost sustainability using new and novel technologies and approaches implemented within the water cycle, and to maximise the efficient use of water and water-embedded resources. To facilitate and communicate the potential benefits of such technologies, NextGen developed Serious Games (SGs), enabled by underlying System Dynamic Models (SDMs), for demonstrating how interactions between water, energy, and materials/embedded resources within the urban water cycle can be utilised in the context of the Circular Economy of water. As part of a fast-track development process, a testbed dubbed “Toy Town” was developed that encompasses a range of technologies and options that provides a demonstrable framework that can later be refined and modified accordingly for other case studies. The underlying SDM driving the SG is built using the Julia programming language. The testbed incorporates a range of components, including water-saving and water-reuse technologies, stormwater management, and wastewater treatment systems. The SDM acts fundamentally as a mass-balance model tracking over time volumetric flows of water/wastewater and the concentrations/dilution of pollutants/material within the urban water cycle. A variety of water use, water reuse and wastewater treatment components can be tested within this model to maximise the resource potential of the water and material moving through the cycle. The paper focuses on an extreme drought scenario and highlights the benefits of a modelling testbed for exploring potential technological solutions for managing the urban water cycle and how such solutions can be employed in the context of the circular economy of water. The NextGen SG thus has the potential to improve stakeholders’ understanding of the implementation of novel technologies in the water cycle and the benefits that could be accrued by such stakeholder groups.

Julia language features for processing statistical data

The Julia programming language is a specialized language for scientific computing. It is relatively new, so most of the libraries for it are in the active development stage. In this article, the authors consider the possibilities of the language in the field of mathematical statistics. Special emphasis is placed on the technical component, in particular, the process of installing and configuring the software environment is described in detail. Since users of the Julia language are often not professional programmers, technical issues in setting up the software environment can cause difficulties that prevent them from quickly mastering the basic features of the language. The article also describes some features of Julia that distinguish it from other popular languages used for scientific computing. The third part of the article provides an overview of the two main libraries for mathematical statistics. The emphasis is again on the technical side in order to give the reader an idea of the general possibilities of the language in the field of mathematical statistics.

Numeric estimates of the principal eigenvalue of the p-Laplacian using interval arithmetic

We present a numerical algorithm for computing rigorous upper and lower estimates of the principal eigenvalue of the p-Laplacian. To control all possible errors including the rounding errors of the computer arithmetic, we use the interval arithmetic. We implement our algorithm in the Julia programming language using IntervalArithmetic.jl package [12]. See also https://ejde.math.txstate.edu/special/02/b3/abstr.html

A general framework for the rigorous computation of invariant densities and the coarse-fine strategy

In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system through a finite element reduction, by composing the associated transfer operator with a suitable finite dimensional projection (a discretization scheme) as in the well-known Ulam method.We introduce a general framework based on a list of properties (of the system and of the projection) that need to be verified so that we can take advantage of a so-called “coarse-fine” strategy. This strategy is a novel method in which we exploit information coming from a coarser approximation of the system to get useful information on a finer approximation, speeding up the computation. This coarse-fine strategy allows a precise estimation of invariant densities and also allows to estimate rigorously the speed of mixing of the system by the speed of mixing of a coarse approximation of it, which can easily be estimated by the computer.The estimates obtained her e are rigorous, i.e., they come with exact error bounds that are guaranteed to hold and take into account both the discretization and the approximations induced by finite-precision arithmetic.We apply this framework to several discretization schemes and examples of invariant density computation from previous works, obtaining a remarkable reduction in computation time.We have implemented the numerical methods described here in the Julia programming language, and released our implementation publicly as a Julia package.

KomaMRI.jl: An open-source framework for general MRI simulations with GPU acceleration.

To develop an open-source, high-performance, easy-to-use, extensible, cross-platform, and general MRI simulation framework (Koma). Koma was developed using the Julia programming language. Like other MRI simulators, it solves the Bloch equations with CPU and GPU parallelization. The inputs are the scanner parameters, the phantom, and the pulse sequence that is Pulseq-compatible. The raw data is stored in the ISMRMRD format. For the reconstruction, MRIReco.jl is used. A graphical user interface utilizing web technologies was also designed. Two types of experiments were performed: one to compare the quality of the results and the execution speed, and the second to compare its usability. Finally, the use of Koma in quantitative imaging was demonstrated by simulating Magnetic Resonance Fingerprinting (MRF) acquisitions. Koma was compared to two well-known open-source MRI simulators, JEMRIS and MRiLab. Highly accurate results (with mean absolute differences below 0.1% compared to JEMRIS) and better GPU performance than MRiLab were demonstrated. In an experiment with students, Koma was proved to be easy to use, eight times faster on personal computers than JEMRIS, and 65% of test subjects recommended it. The potential for designing acquisition and reconstruction techniques was also shown through the simulation of MRF acquisitions, with conclusions that agree with the literature. Koma's speed and flexibility have the potential to make simulations more accessible for education and research. Koma is expected to be used for designing and testing novel pulse sequences before implementing them in the scanner with Pulseq files, and for creating synthetic data to train machine learning models.

Towards cell scale agent-based models for membrane cytoskeleton interactions.

The cytoskeleton is a dynamic far-from-equilibrium polymer network. It consumes energy to do mechanical work, and it interacts with complex chemical reaction networks in the cytoplasm and cell membrane to organize into various structures. We will discuss how the MEDYAN (medyan.org) model and software can simulate the chemical and mechanical interactions of actin filaments, crosslinks, myosin motor proteins, and membranes at the micrometer length scale and minute time scale. The next generation of MEDYAN is written in the Julia programming language (MEDYAN.jl). It has significant performance improvements including a 10x faster cylinder volume exclusion algorithm and a 10x faster Gillespie implementation for scheduling chemical reaction events. In addition, it includes an HDF5-based snapshot format that stores the full state of the simulation and enables restarts, and detailed linker and filament aging reactions that have reaction rates that adjust to changes to local monomer states, linker states, and linker mechanics. More complex reactions and reaction rates can be added using user-defined reaction callbacks. It also includes a deformable mesh-based membrane model. MEDYAN.jl is being used to study the role of ARP2/3 in the actin structure in the core of an axon growth cone. MEDYAN.jl is also being used to prototype models of membrane cytoskeleton chemical and mechanical interactions, including activation of ARP2/3.

Image-based approximation of derivatives of traditional differential metrics of angular distortion in map projections

ABSTRACT Map projections are imaging procedures used to depict geographic features. We adopt the traditional differential metric and exploit the intrinsic image properties of map projections to establish an image-based differential metric for evaluating distortions in map projections, obtaining an effective, practical, and relatively accurate metric. We use bivariate polynomial functions to approximate the forward and inverse formulae of map projections. Thereafter, the proposed metric is conveniently calculated using the partial derivatives of the approximate forward functions based on polynomial functions, while complicated differential calculations are avoided. Moreover, multiple sampling and image filters mitigate the influence of imaging noise and achieve a high computation precision. Experiments were conducted using the NASA G.Projector mapping software to generate images from more than 200 map projections. Explicit equations of map projections were not required owing to the use of the mapping software. These images were then evaluated using the proposed metric through an implementation in the Julia programming language. The corresponding results confirmed that the proposed metric avoided the drawbacks of the great circle arc metric and provided considerably low errors (1.12° on average) and high consistency (0.999 on average) with respect to the traditional differential metric. Although there were errors, experimental results indicated that feasibility and high usability were achieved by the image-based method for evaluating distortions in small-scale map projections.

Categorical Data Structures for Technical Computing

Many mathematical objects can be represented as functors from finitely-presented categoriesCtoSet. For instance, graphs are functors toSetfrom the category with two parallel arrows. Such functors are known informally asC-sets. In this paper, we describe and implement an extension ofC-sets having data attributes with fixed types, such as graphs with labeled vertices or real-valued edge weights. We call such structures acsets, short for attributedC-sets. Derived from previous work on algebraic databases, acsets are a joint generalization of graphs and data frames. They also encompass more elaborate graph-like objects such as wiring diagrams and Petri nets with rate constants. We develop the mathematical theory of acsets and then describe a generic implementation in the Julia programming language, which uses advanced language features to achieve performance comparable with specialized data structures.

Cropbox: a declarative crop modelling framework

AbstractWe introduce Cropbox, a novel modelling framework that supports various aspects of crop modelling in a unique yet concise style. Building a crop model can be easily riddled with technical details looking trivial at first but later becoming major obstacles that hamper the whole development or application process. This is particularly the case when implementing models from scratch without relying on an established framework. Cropbox adopts a declarative approach providing a domain-specific language to reduce technical debt and assist modellers to focus on high-level abstraction formed by relations between variables and enclosing systems, rather than tinkering with low-level implementation details. The syntax of Cropbox framework is based on the Julia programming language and is deliberately constrained to avoid unintended side effects caused by common mistakes while its architecture remains open to extension. We highlight key capabilities of the framework through case studies featuring a leaf gas-exchange model and a whole-plant simulation model. We also illustrate potential extensions for supporting functional-structural plant modelling by demonstrating a 3D root architectural model as an example.

Surrogate-based optimization of multiple-splitters radial compressor for solar hybrid microturbine

In the open literature, there is no clear guidance for design procedure on the number or where best position the splitter leading-edge to improved performance in the radial compressor. A surrogate-based optimization of multiple-splitters radial compressor has been conducted for solar hybrid microturbine in the present studies. Also, the impact of the multiple-splitters leading-edge position on the rotor radial compressor is demonstrated. The radial compressor is compared using air and supercritical carbondioxide ( sCO 2 ) as the working fluid. The optimization problem is solved by applying the surrogate or response surface model using the radial basis function network (RBFN) from the opensource package in the Julia programming language environment. Starting from 65 data points from DoE based on the optimum Latin-hypercube, the optimum candidate design can be predicted with CFD and FE analysis. The results show that for air radial compressors, the optimum position of the small-splitter leading edge is 20% from the outlet rotor, and for the middle-splitter leading position at around 30% from the inlet rotor. Unlike air radial compressors, the sCO 2 radial compressor has the optimum leading-edge position for the middle splitter around 60% from the inlet rotor, and the small splitters are around 30% from the outlet rotor. Finally, compared between the non-splitter and multiple-splitter designs, the total-to-total efficiency at the same pressure ratio is improved by around 2.30% for air radial compressor and 2.25% for sCO 2 radial compressor. Meanwhile, the operating range is increased by 29.0% for air radial compressors and 18.0% for sCO 2 radial compressors.

A Review of Collocation Approximations to Solutions of Differential Equations

This review considers piecewise polynomial functions, that have long been known to be a useful and versatile tool in numerical analysis, for solving problems which have solutions with irregular features, such as steep gradients and oscillatory behaviour. Examples of piecewise polynomial functions used include splines, in particular B-splines, and Hermite functions. Spline functions are useful for obtaining global approximations whilst Hermite functions are useful for approximation over finite elements. Our aim in this review is to study quintic Hermite functions and develop a numerical collocation scheme for solving ODEs and PDEs. This choice of basis functions is further motivated by the fact that we are interested in solving problems having solutions with steep gradients and oscillatory properties, for which this approximation basis seems to be a suitable choice. We derive the quintic Hermite basis and use it to formulate the orthogonal collocation on finite element (OCFE) method. We present the error analysis for third order ODEs and derive both global and nodal error bounds to illustrate the super-convergence property at the nodes. Numerical simulations using the Julia programming language are performed for both ODEs and PDEs and enhance the theoretical results.