Establishing Pattern Sequences Using Stochastic Trees and Bayesian Belief Networks With an Application to Security Patterns
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Matovič, Viktor [Faculty of Informatics and Inform↗
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ESnet Requirements Review Program Through the IRI Lens: A Meta-Analysis of Workflow Patterns Across DOE Office of Science Programs (Final Report)
The Department of Energy (DOE) ensures America’s security and prosperity by addressing its energy, environmental, and nuclear challenges through transformative science and technology solutions. The DOE’s Office of Science (SC) delivers groundbreaking scientific discoveries and major scientific tools that transform our understanding of nature and advance the energy, economic, and national security of the United States. The SC’s programs advance DOE mission science across a wide range of disciplines and have developed the research infrastructure needed to remain at the forefront of scientific discovery. The DOE SC’s world-class research infrastructure — exemplified by the 28 SC scientific user facilities — provides the research community with premier observational, experimental, computational, and network capabilities. Each user facility is designed to provide unique capabilities to advance core DOE mission science for its sponsor SC program and to stimulate a rich discovery and innovation ecosystem. Research communities gather and flourish around each user facility, bringing together diverse perspectives. A hallmark of many facilities is the large population of students, postdoctoral researchers, and early-career scientists who contribute as full-fledged users. These facility staff and users collaborate over years to devise new approaches to utilizing the user facility’s core capabilities. The history of the SC user facilities has many examples of wildly inventive researchers challenging operational orthodoxy to pioneer new vistas of discovery; for example, the use of the synchrotron X-ray light sources for study of proteins and other large biological molecules. This continual reinvention of the practice of science — as users and staff forge novel approaches expressed in research workflows — unlocks new discoveries and propels scientific progress. Within this research ecosystem, the high-performance computing (HPC) and networking user facilities stewarded by SC’s Advanced Scientific Computing Research (ASCR) program play a dynamic cross-cutting role, enabling complex workflows demanding high performance data, networking, and computing solutions. The DOE SC’s three HPC user facilities and the Energy Sciences Network (ESnet) high-performance research network serve all of the SC’s programs as well as the global research community. Argonne Leadership Computing Facility (ALCF), the National Energy Research Scientific Computing Center (NERSC), and Oak Ridge Leadership Computing Facility (OLCF) conceive, build, and provide access to a range of supercomputing, advanced computing, and large-scale data-infrastructure platforms, while ESnet interconnects DOE SC research infrastructure and enables seamless exchange of scientific data. All four facilities operate testbeds to expand the frontiers of computing and networking research. Together, the ASCR facilities enterprise seeks to understand and meet the needs and requirements across SC and DOE domain science programs and priority efforts, highlighted by the formal requirements reviews (RRs) methodology. In recent years, the research communities around the SC user facilities have begun experimenting with and demanding solutions integrated with HPC and data infrastructure. This rise of integrated-science approaches is documented in many community and high-level government reports. At the dawn of the era of exascale science and the acceleration of artificial intelligence (AI) innovation, there is a broad need for integrated computational, data, and networking solutions. In response to these drivers, DOE has developed a vision for an Integrated Research Infrastructure (IRI): To empower researchers to meld DOE’s world-class research tools, infrastructure, and user facilities seamlessly and securely in novel ways to radically accelerate discovery and innovation.
42 ENGINEERING↗
Resilience Design Patterns: A Structured Approach to Resilience at Extreme Scale (V.2.0)
Reliability is a serious concern for future extreme-scale high-performance computing (HPC) systems. Projections based on the current generation of HPC systems and technology roadmaps suggest the prevalence of very high fault rates in future systems. The errors resulting from these faults will propagate and generate various kinds of failures, which may result in outcomes ranging from result corruptions to catastrophic application crashes. Therefore, the resilience challenge for extreme-scale HPC systems requires coordination between various hardware and software technologies that are capable of handling a broad set of fault models at accelerated fault rates. Also, due to practical limits on power consumption in future HPC systems, they are likely to embrace innovative architectures, increasing the levels of hardware and software complexities. Therefore, the techniques that seek to improve resilience must navigate the complex trade-off space between resilience and the overheads to power consumption and performance. While the HPC community has developed various resilience solutions, application-level techniques as well as system-based solutions, the solution space of HPC resilience techniques remains fragmented. There are no formal methods to integrate the various HPC resilience techniques into composite solutions, nor are there methods to holistically evaluate the adequacy and efficacy of such solutions in terms of their protection coverage, and their performance & power efficiency characteristics. Additionally, few implementations of current resilience solutions are portable to newer architectures and software environments that will be deployed on future systems. We developed a new structured approach to the management of HPC resilience using the concept of resilience-based design patterns. In general, a design pattern is a repeatable solution to a commonly occurring problem. We identified the well-known solutions that are commonly used to deal with faults, errors and failures in HPC systems. In the initial design patterns specification (version 1.0), we described the various solutions, which address specific problems in the design of resilient HPC environments, in the form of patterns. Each pattern describes a problem caused by a fault, error or failure event in an HPC environment, and then describes the core of the solution of the problem in such a way that this solution may be adapted to different systems and implemented at different layers of the system stack. The catalog of these resilience design patterns provides designers with a collection of design elements. To construct complete resilience solutions using combinations of various patterns, we defined a framework that enhances HPC designers' understanding of the important constraints and the opportunities for the design patterns to be implemented and deployed at various layers of the system stack. The design framework is also useful for establishing interfaces and mechanisms to coordinate flexible fault management across hardware and software components, as well as to consider the trade-off between performance, resilience, and power consumption when constructing a solution. The resilience design patterns specification version 1.1 included more detailed explanations of the pattern solutions, the context in which the patterns are applicable, and the implications for hardware or software design. It also provided several additional examples and detailed case studies to demonstrate the use of patterns to build realistic solutions. In version 1.2 of the specification document, we have improved the pattern descriptions, including graphical representations of the pattern components. These improvements are largely based on critical comments, feedback and suggestions received from pattern experts and readers of the previous versions of the specification. The pattern classification has been modified to further clarify the relationships between pattern categories. This version of the specification also introduces a pattern language for resilience design patterns. The pattern language presents the patterns in the catalog as a network, revealing the relations among the resilience patterns. The language provides designers with the means to explore alternative techniques for handling a specific fault model that may have different efficiency and complexity characteristics. Using the pattern language also enables the design and implementation of comprehensive resilience solutions as a set of interconnected resilience patterns that can be instantiated across layers of the system stack. The overall goal of this work is to provide hardware and software designers, as well as the users and operators of HPC systems, a systematic methodology for the design and evaluation of resilience technologies in HPC systems that keep scientific applications running to a correct solution in a timely and cost-efficient manner despite frequent faults, errors, and failures of various types. Version 2.0 expands the resilience design pattern classification and catalog to include self-stabilization patterns and reliability, availability and performance models for each structural pattern.
97 MATHEMATICS AND COMPUTING↗
Chemical mixture exposure patterns and obesity among U.S. adults in NHANES 2005–2012
The effect of chemical exposure on obesity has raised great concerns. Real-world chemical exposure always imposes mixture impacts, however their exposure patterns and the corresponding associations with obesity have not been fully evaluated. To discover obesity-related mixed chemical exposure patterns in the general U.S. population. Sparse Decompositional Regression (SDR), a model adapted from sparse representation learning technique, was developed to identify exposure patterns of chemical mixtures with exclusion (non-targeted model) and inclusion (targeted model) of health outcomes. We assessed the relationships between the identified chemical mixture patterns and obesity-related indexes. We also conducted a comprehensive evaluation of this SDR model by comparing to the existing models, including generalized linear regression model (GLM), principal component analysis (PCA), and Bayesian kernel machine regression (BKMR). Eight core exposure patterns were identified using the non-targeted SDR model. Patterns of high levels of MEP, high levels of naphthalene metabolites (ΣOH-Nap), and a pattern of high exposure levels of MCOP, MCNP, and MCPP were positively associated with obesity. Patterns of high levels of BP3, and a pattern of higher mixed levels of MPB, PPB, and MEP were found to have negative associations. Associations were strengthened using the targeted SDR model. In the single chemical analysis by GLM, BP3, MBP, PPB, MCOP, and MCNP showed significant associations with obesity or body indexes. The SDR model exceeded the performance of PCA in pattern identification. Both SDR and BKMR identified a positive contribution of ΣOH-Nap and MCOP, as well as a negative contribution of BP3 and PPB to obesity. Our study identified five core exposure patterns of chemical mixtures significantly associated with obesity using the newly developed SDR model. The SDR model could open a new avenue for assessing health effects of environmental mixture contaminants.
54 ENVIRONMENTAL SCIENCES↗
Super-Resolution Photothermal Patterning in Conductive Polymers Enabled by Thermally Activated Solubility
Doping induced solubility control (DISC) patterning is a recently developed technique which uses the change in polymer solubility upon doping, along with an optical dedoping process, to achieve high resolution optical patterning. DISC patterning is remarkable because the process resolution exceeds the linear Abbe’s diffraction limit, however, no mechanism has been proposed to explain such high resolution. Here, we use diffraction to spatially modulate the light intensity and determine the dissolution rate, revealing a superlinear dependence on light intensity, which yields features that are sharper than the profile of the writing photomask. This rate law is independent of wavelength, indicating that patterning resolution is not dominated by an optical dedoping reaction, as was previously proposed. Instead we show here that the optical patterning mechanism is primarily controlled by the thermal profile generated by the laser. To quantify this effect, the thermal profile and dissolution rate are modeled using a finite-element model and compared against patterned line cross sections as a function of wavelength, laser intensity, and dwell time. Our model reveals that although the laser-generated thermal profile is broadened considerably beyond the lasers resolution, the highly temperature dependent dissolution rate results in selective dissolution near the peak of the thermal profile. Therefore, the key factor in achieving super-resolution patterning is a strongly temperature dependent dissolution rate|a common feature of many polymers. In addition to suggesting several routes to improved resolution, our model also demonstrates that doping is not required for optical patterning of conjugated polymers, as was previously believed. Instead, we demonstrate that superlinear resolution optical patterning is attainable in any conjugated polymer simply by tuning the solvent quality during patterning, thus extending the applicability of our method to a wide class of materials. Here, we demonstrate the generality of photothermal patterning by writing sub-400 nm features into undoped Pff-BT4T-2OD.
36 MATERIALS SCIENCE↗
QPatLib v1.0 — Measurement-based quantum simulation Pauli string unitary pattern collections
This Zenodo record accompanies the paper “Scalable Measurement-Based Quantum Simulation Patterns for Benchmarking” arXiv.2605.12502 and provides QPatLib v1.0 measurement-pattern datasets in human-readable JSONL together with a ZIP archive of OpenQASM 3.0 circuits used for validation and reproducibility. The patterns and circuits implement Pauli string unitaries for benchmark cases. Cases include all possible string combinations for less than 6 qubits and strings used in Hamiltonians for certain diatomic molecules for 6 or more qubits. Format: Each pattern_*.jsonl file is containins measurement patterns for all subsets for a given model/instance and subset strategy: it begins with a preamble containing model metadata, subset definitions, provenance, and (when feasible) full-pattern test results, followed by one pattern entry per subset. Each subset entry includes a required pattern_ascii field storing the measurement pattern in the measurement-calculus/Graphix standard with signal shifting, written left-to-right in the canonical order nodes → edges → measurements (with signal dependencies) → byproduct corrections (X/Z). The circuits are included as circuit_files.zip. Patterns in this record were validated against the corresponding circuits and checked for causal flow. Codes for generating these patterns can be found at QPatLib repository on Github
Graphix↗
Predicting multi-nodal in-nozzle particle interactions in high-viscosity fluid mediums for acoustophoretic direct-ink writing of line-patterned composites
Patterned functional materials offer improved properties (electrical, thermal, etc.) over their bulk counterparts in many applications, including energy storage, flexible electronics, and sensors. However, manufacturing approaches for patterning materials over large areas with features on the order of hundreds of microns or less are limited. Acoustophoresis, which uses acoustic forces to control particle arrangement in a fluid medium, is a pathway to address this challenge. This process is dependent on particle and fluid properties and enables patterning of a broad range of materials. Herein, a model with experimental validation is presented to demonstrate that acoustophoresis can be combined with direct-ink writing (DIW) to fabricate line patterns over large cm-scale areas. An in-nozzle particle interaction model was developed to investigate the impact of processing conditions on multi-nodal acoustophoretic DIW. The model predicts patterned line widths within a factor of two relative to experimental results for a high viscosity case study. Here, the model was used to investigate the impact of frequency, particle loading, particle radius, and acoustic pressure on line width and patterning time, providing critical feedback regarding the processing conditions suitable for a target application. Model results illustrate that frequency has the greatest impact on line patterns: increasing from 1 to 3 MHz resulted in a greater than 65% reduction in line width and a greater than 85% reduction in patterning time. Additionally, experiments were conducted with an alumina-epoxy ink and a ~21 cm 2 area pattern was rastered in ~5.5 minutes, demonstrating a path towards large-area line-patterned composite fabrication.
25 ENERGY STORAGE↗
A simple, validated approach for design of two-dimensional periodic particle patterns via acoustophoresis
Two-dimensional patterning of microparticles enables a wide range of functional materials, including patterned energy storage electrodes, flexible electronics, and sensor arrays. Particle patterning via acoustics offers an attractive path to generate a wide variety of 2D periodic patterns that introduce tailorable hierarchical porosity, useful for controlling surface area, transport distances, and other properties. This method is most effective with micron scale particles and patterns of tens to hundreds of microns. To enable systematic exploration of the broad design space for such patterns, this work develops a model of 2D and 3D assembly of particles at high loadings and validates the obtained patterns against both experiments and more computationally intensive modeling techniques. Using this simple model, connections are mapped between input parameters (like actuation conditions, particle volume fraction, material properties) and output geometrical features (like void size and shape, pattern connectivity, and surface area) so that they can be tailored to given applications. The utility of this simple model is illustrated by predicting and then experimentally demonstrating new hierarchical patterns resulting from multiple waves of different frequencies interacting. These multiscale patterns offer the potential to lift the limits on surface area, diffusion distances, and other features.
42 ENGINEERING↗
A conserved gene regulatory network controls root epidermal cell patterning in superrosid species
Summary In superrosid species, root epidermal cells differentiate into root hair cells and nonhair cells. In some superrosids, the root hair cells and nonhair cells are distributed randomly (Type I pattern), and in others, they are arranged in a position‐dependent manner (Type III pattern). The model plant Arabidopsis ( Arabidopsis thaliana ) adopts the Type III pattern, and the gene regulatory network (GRN) that controls this pattern has been defined. However, it is unclear whether the Type III pattern in other species is controlled by a similar GRN as in Arabidopsis, and it is not known how the different patterns evolved. In this study, we analyzed superrosid species Rhodiola rosea , Boehmeria nivea , and Cucumis sativus for their root epidermal cell patterns. Combining phylogenetics, transcriptomics, and cross‐species complementation, we analyzed homologs of the Arabidopsis patterning genes from these species. We identified R. rosea and B. nivea as Type III species and C. sativus as Type I species. We discovered substantial similarities in structure, expression, and function of Arabidopsis patterning gene homologs in R. rosea and B. nivea , and major changes in C. sativus . We propose that in superrosids, diverse Type III species inherited the patterning GRN from a common ancestor, whereas Type I species arose by mutations in multiple lineages.
59 BASIC BIOLOGICAL SCIENCES↗
Seasonal and Geographical Variations in Fundamental Weather Patterns during Extreme Precipitation as Identified from Omega Equation Forcing
Abstract We investigate the large-scale weather patterns during extreme precipitation (PEx) events over the conterminous United States (CONUS) by applying a version of the quasigeostrophic (QG) omega equation. This work aims to develop a climatology of the weather patterns most related to PEx events during current climate. Extreme events are examined for each of seven regions defined by consistent annual cycles of precipitation and spanning the CONUS. For the CONUS we train several self-organizing maps (SOM) on a pressure–time series of vertical velocity from each of the advective forcing terms in the QG omega equation for each extreme event. The unsupervised learning of the SOM allows us to identify the most descriptive set of nine patterns in vertical velocity associated with precipitation extremes. This method finds multiple frontal- and cyclone-driven patterns while grouping primarily convective events into one pattern. Frontal events include a synoptic pattern consistent with West Coast atmospheric river events as well as pattern groups linked to developing and to mature (“occluded”) frontal cyclones. The primary patterns found during PEx events vary seasonally and geographically. Frontal cyclone patterns are most common during PEx events during summer in the part of the Great Plains and during winter for the Northeast, Southeast, Pacific Northwest, and Southwest. Convection is the most common pattern during summer in all regions. Except in the Southeast, the annual cycles of monthly number of PEx events and average precipitation match well, partially validating our choice of regions to aggregate PEx events.
Meteorology & Atmospheric Sciences↗
Pangeo-Enabled ESM Pattern Scaling (PEEPS): A customizable dataset of emulated Earth System Model output
Emulation through pattern scaling is a well-established method of rapidly producing climate fields (like temperature or precipitation) from existing Earth System Model (ESM) output that, while inaccurate, is often useful for a variety of downstream purposes. Conducting pattern scaling has historically been a laborious process, in large part due to the increasing volume of ESM output data that has often required downloading and storing locally to train on. Here we describe the Pangeo-Enabled ESM Pattern Scaling (PEEPS) dataset, a repository of trained annual and monthly patterns from CMIP6 outputs. This manuscript describes and validates these updated patterns so that users can save effort calculating and reporting error statistics in manuscripts focused on the use of patterns. The trained patterns are available as NetCDF files on Zenodo for ease of use in the impact community, and are reproducible with the code provided via GitHub in both Jupyter notebook and Python script formats. Because all training data for the PEEPS data set is cloud-based, users do not need to download and house the ESM output data to reproduce the patterns in the zenodo archive, should that be more efficient. Validating the PEEPS data set on the CMIP6 archive for annual and monthly temperature, precipitation, and near-surface relative humidity, pattern scaling performs well over a variety of future scenarios except for regions in which there are strong, potentially nonlinear climate feedbacks. Although pattern scaling is normally conducted on annual mean ESM output data, it works equally well on monthly mean ESM output data. We identify several downstream applications of the PEEPS data set, including impacts assessment and evaluating certain types of Earth system uncertainties.
54 ENVIRONMENTAL SCIENCES↗
3D pattern formation of a protein–membrane suspension
Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane, onto which they interact and form two-dimensional (2D) patterns. It is unclear how the membrane’s continuity and dimensionality impact pattern formation. Here, we address this gap using the MinDE system, a prototypical example of pattern-forming membrane proteins. We show that when the lipid substrate is fragmented into submicrometer-sized diffusive liposomes, adenosine triphosphate-driven protein–protein interactions generate three-dimensional (3D) spatially extended patterns, despite the complete loss of membrane continuity. Remarkably, these 3D patterns emerge at scales four orders of magnitude larger than the individual liposomes. By systematically varying protein concentration, liposome size, and density, we observed and characterized a variety of 3D dynamical patterns not seen on continuous 2D membranes, including traveling waves, dynamical spirals, and a coexistence phase. Simulations and linear stability analysis of a coarse-grained model revealed that the physical properties of the dispersed membrane effectively rescale both the protein–membrane binding rates and diffusion, two key parameters governing pattern formation and wavelength selection. These findings highlight the robustness of Min’s pattern-forming ability, suggesting that protein–membrane suspensions could serve as an adaptable template for studying out-of-equilibrium self-organization in 3D, beyond in vivo contexts.
36 MATERIALS SCIENCE↗
Electrostatically driven pattern formation in mixed charged–neutral multicomponent elastic membranes
Multicomponent crystalline and amorphous elastic shells exhibit heterogeneous surface patterns that provide distinctive functionalities in cellular environments. Such patterning typically arises from the competition between short-range attractive and long-range repulsive interactions in membranes. Here, we demonstrate that the intrinsic competition between electrostatic repulsion and elastic deformation is sufficient to drive spontaneous surface patterning in elastic shells, requiring no additional attractive interactions. Using numerical simulations, we demonstrate pattern formation in mechanically homogeneous membranes with heterogeneous surface charge composition across different topologies, including spheres, discs, and flat periodic membranes. We also examine patterns in crystalline and amorphous shells of coassembled charged and neutral components with different bending rigidities. At low charge fraction, discrete charged surface domains form. At intermediate charge fraction, the competition between electrostatics and elasticity leads to elongated domains (rods) of the charged component, which results in lamellar patterns at nearly equal fraction of the charged and neutral components. At high charge fraction, nanodomains of the neutral component form. Amorphous shells exhibit similar progressions but with disordered structures rather than ordered lamellar patterns. These pattern morphologies are observed in both the closed shells and flat membranes. As salt concentration increases, all patterns coarsen due to the screening of electrostatic interactions.
charge heterogeneity↗
Self-organized patterns at the plasma–liquid anode interface in a helium glow discharge: temporal development and mechanisms
Self-organization at the plasma–liquid anode interface is a commonly observed phenomenon for atmospheric pressure glow plasmas, resulting in patterns with distinctive shapes such as circular ring, star-shaped, and gear-like structures, depending primarily on the discharge current and solution conductivity. Recent studies have shown that the electrode gap distance, solute used for liquid anode solution, and gas composition can also significantly impact pattern formation. Nonetheless, an overarching model or explanation of the key underlying mechanisms consistent with all experimentally observed trends is not yet reported. We propose a key underlying mechanism enabling pattern formation motivated by a detailed parametric study of pattern formation complemented by the temporal development of patterns and consistent with all observed trends. Pattern formation was observed to be on a time scale of 100 μs, similar to the time scales of gas heating and evaporation. It was found that a minimum water evaporation rate of (3.5 ± 0.5) × 10 –6 kg s –1 and reduced electric field in the positive column of 16.6 ± 0.4 Td is required for pattern formation in the investigated cases irrespective of solution conductivity and gas composition for NaCl solutions. Nonetheless, the presence of cations for which the corresponding metal atom has a low ionization energy was identified as a necessary condition for pattern formation. Furthermore, the reported results suggest that the presence of a small amount of metal atoms in the gas phase with low ionization energy enhances the overall ionization rate in the near anode region which triggers pattern formation.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Pattern Dictionary Method for Anomaly Detection
In this paper, we propose a compression-based anomaly detection method for time series and sequence data using a pattern dictionary. The proposed method is capable of learning complex patterns in a training data sequence, using these learned patterns to detect potentially anomalous patterns in a test data sequence. The proposed pattern dictionary method uses a measure of complexity of the test sequence as an anomaly score that can be used to perform stand-alone anomaly detection. We also show that when combined with a universal source coder, the proposed pattern dictionary yields a powerful atypicality detector that is equally applicable to anomaly detection. The pattern dictionary-based atypicality detector uses an anomaly score defined as the difference between the complexity of the test sequence data encoded by the trained pattern dictionary (typical) encoder and the universal (atypical) encoder, respectively. We consider two complexity measures: the number of parsed phrases in the sequence, and the length of the encoded sequence (codelength). Specializing to a particular type of universal encoder, the Tree-Structured Lempel–Ziv (LZ78), we obtain a novel non-asymptotic upper bound, in terms of the Lambert W function, on the number of distinct phrases resulting from the LZ78 parser. This non-asymptotic bound determines the range of anomaly score. As a concrete application, we illustrate the pattern dictionary framework for constructing a baseline of health against which anomalous deviations can be detected.
97 MATHEMATICS AND COMPUTING↗
Algebraic Theory of Patterns as Generalized Symmetries
We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories.
97 MATHEMATICS AND COMPUTING↗
Historical Pattern Analysis of Global Geothermal Power Capacity Development: Preprint
Between 1913 and 1958, Italy was the only country with an operational geothermal power plant until New Zealand installed its first plant in 1958. At present, 24 countries are involved in the geothermal power market, and they have a combined installed capacity of 16,127 GW. This study analyzes the historical patterns of geothermal power capacity in the world and in individual countries to investigate the ideal global geothermal development pattern by examining the annual cumulative capacity (ACC) and the annual capacity addition (ACA) graphs of the historical development of geothermal power capacity in 24 countries. First, the global patterns are analyzed using these graphs in five periods (1945-1957, 1958-1976, 1977-1991, 1992-2002, and 2003-2020) that are marked by a series of characteristics of ACA peaks separated by two major troughs. Then, five characteristic patterns are developed in five periods globally. These patterns correspond to the early-stage linear, the first acceleration, the first steady-state linear, the second acceleration, and the second steady-state linear developments. A positive relationship exists between global patterns and the 5-year shifted oil-price curve: two major factors influenced global development: 1) increasing oil prices and increasing awareness of global climate change, and 2) global development of geothermal power. Last, we investigate these patterns in each country. The top ten countries, which comprise 93.3% of the world's total installed capacity are separated into five groups based on the availability and characteristics of patterns globally developed in five periods. Group-1 (the United States) has an installed capacity of 3,794 MW, Group-2 (Mexico and Philippines) 963-1935 MW, Group-3 (New Zealand, Italy, Iceland, and Japan) 601-1,037 MW, and Group-4 (Indonesia, Kenya, and Turkiye) 944-2,356 MW. The remaining 14 countries (6.7%), which are called Group 5, are still in an immature stage and have installed capacities of 7-262 MW and are not involved in pattern analysis. Overall, geothermal power in the world is in its third stage of development, which had its peak development after 1977. A fourth development peak may be expected to occur after this through business-as-usual cases. The biggest barrier to the development of the global geothermal power market is the risk associated with exploration and drilling. If risk mitigation systems and funds are employed, the growth of geothermal power production projects could accelerate.
GEOTHERMAL ENERGY↗
Historical Pattern Analysis of Global Geothermal Power Capacity Development
Between 1913 and 1958, Italy was the only country with an operational geothermal power plant until New Zealand installed its first plant in 1958. At present, 24 countries are involved in the geothermal power market, and they have a combined installed capacity of 16,127 GW. This study analyzes the historical patterns of geothermal power capacity in the world and in individual countries to investigate the ideal global geothermal development pattern by examining the annual cumulative capacity (ACC) and the annual capacity addition (ACA) graphs of the historical development of geothermal power capacity in 24 countries. First, the global patterns are analyzed using these graphs in five periods (1945-1957, 1958-1976, 1977-1991, 1992-2002, and 2003-2020) that are marked by a series of characteristics of ACA peaks separated by two major troughs. Then, five characteristic patterns are developed in five periods globally. These patterns correspond to the early-stage linear, the first acceleration, the first steady-state linear, the second acceleration, and the second steady-state linear developments. A positive relationship exists between global patterns and the 5-year shifted oil-price curve: two major factors influenced global development: 1) increasing oil prices and increasing awareness of global climate change, and 2) global development of geothermal power. Last, we investigate these patterns in each country. The top ten countries, which comprise 93.3% of the world's total installed capacity are separated into five groups based on the availability and characteristics of patterns globally developed in five periods. Group-1 (the United States) has an installed capacity of 3,794 MW, Group-2 (Mexico and Philippines) 963-1935 MW, Group-3 (New Zealand, Italy, Iceland, and Japan) 601-1,037 MW, and Group-4 (Indonesia, Kenya, and Turkiye) 944-2,356 MW. The remaining 14 countries (6.7%), which are called Group 5, are still in an immature stage and have installed capacities of 7-262 MW and are not involved in pattern analysis. Overall, geothermal power in the world is in its third stage of development, which had its peak development after 1977. A fourth development peak may be expected to occur after this through business-as-usual cases. The biggest barrier to the development of the global geothermal power market is the risk associated with exploration and drilling. If risk mitigation systems and funds are employed, the growth of geothermal power production projects could accelerate.
GEOTHERMAL ENERGY↗