Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “analysis and visualization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Collaborative Exploration of Scientific Datasets Using Immersive and Statistical Visualization: Preprint

We discuss the value of collaborative, immersive visualization for the exploration of scientific datasets and review techniques and tools that have been developed and deployed at the National Renewable Energy Laboratory (NREL). We believe that collaborative visualizations linking statistical interfaces and graphics on laptops and high-performance computing (HPC) with 3D visualizations on immersive displays (head-mounted displays and large-scale immersive environments) enable scientific workflows that further rapid exploration of large, high-dimensional datasets by teams of analysts. We present a framework, PlottyVR, that blends statistical tools, general-purpose programming environments, and simulation with 3D visualizations. To contextualize this framework, we propose a categorization and loose taxonomy of collaborative visualization and analysis techniques. Finally, we describe how scientists and engineers have adopted this framework to investigate large, complex datasets.

collaborative visualization↗

Collaborative Exploration of Scientific Datasets Using Immersive and Statistical Visualization

We discuss the value of collaborative, immersive visualization for the exploration of scientific datasets and review techniques and tools that have been developed and deployed at the National Renewable Energy Laboratory (NREL). We believe that collaborative visualizations linking statistical interfaces and graphics on laptops and high-performance computing (HPC) with 3D visualizations on immersive displays (head-mounted displays and large-scale immersive environments) enable scientific workflows that further rapid exploration of large, high-dimensional datasets by teams of analysts. We present a framework, PlottyVR, that blends statistical tools, general-purpose programming environments, and simulation with 3D visualizations. To contextualize this framework, we propose a categorization and loose taxonomy of collaborative visualization and analysis techniques. Finally, we describe how scientists and engineers have adopted this framework to investigate large, complex datasets.

collaborative visualization↗

Extremely Scalable Distributed Computation of Contour Trees via Pre-Simplification

Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains challenging due to scalability limitations. Recent developments in distributed hierarchical contour trees have addressed these challenges by enabling scalable computation across distributed systems. Building on these structures, advanced analytical tasks—such as volumetric branch decomposition and contour extraction—have been introduced to facilitate large-scale scientific analysis. Despite these advancements, such analytical tasks substantially increase memory usage, which hampers scalability. In this paper, we propose a pre-simplification strategy to significantly reduce the memory overhead associated with analytical tasks on distributed hierarchical contour trees. We demonstrate enhanced scalability through strong scaling experiments, constructing the largest known contour tree—comprising over half a trillion nodes with complex topology—in under 15 minutes on a dataset containing 550 billion elements.

Li, Mingzhe [University of Utah]↗

elm-diagnostics

elm-diagnostics is a Python package for computing diagnostic analyses and visualizations for the E3SM Land Model (ELM) component and is meant to support new feature development in ELM. The tool reads model history files and performs quantitative analyses including budget-closure checking, variable transformations, temporal aggregations, and statistical summaries to support model evaluation, validation, and scientific interpretation. The framework is designed for extensibility, with modular architecture enabling straightforward addition of new diagnostic methods, derived variables, analysis types, visualization approaches, and model-specific adaptations

Hoffman, Matt [Los Alamos National Laboratory]↗

Sim-Situ: A Framework for the Faithful Simulation of in situ Processing

The amount of data generated by numerical simulations in various scientific domains led to a fundamental redesign of how the analysis and visualization of simulation outputs are performed. The throughput and capacity of storage subsystems have not evolved as fast as the computing power in extreme-scale supercomputers, making the classical post-hoc approach highly inefficient. In situ processing has then emerged as a solution in which simulation and data analysis/visualization are intertwined for better performance and greater interactivity.Determining the best allocation, i.e., how many resources to allocate to simulation and analysis respectively, mapping, i.e., where and at which frequency to run the analysis/visualization, and data transfer mode is a complex task whose performance assessment is crucial to the efficient execution of in situ processing. However, such a performance evaluation of different strategies usually relies either on directly running them on the targeted execution environments, which can rapidly become extremely time- and resource-consuming, or on resorting to simplified models of the components of an in situ application, which can lack of realism. In both cases, the validity of the performance evaluation is limited.In this paper, we present Sim-Situ, a simulation-based framework for the faithful performance evaluation of in situ processing strategies. We designed Sim-Situ to reflect the typical features of in situ processing systems. Thanks to its modular design, Sim-situ has the necessary flexibility to easily and faithfully evaluate the behavior and performance of various allocation, mapping, and data transfer strategies. We illustrate the simulation capabilities of Sim-Situ on a Molecular Dynamics use case. We study the impact of different strategies on performance and show how users can leverage Sim-Situ to determine interesting tradeoffs when adding analysis/visualization components to their application.

Honoré, Valentin↗

Toward Unified Autonomous Scattering Experiments: A Cross-Facility Case Study at ALS and PETRA III

Autonomous experiments rely on the integration of control, data acquisition, analysis, and decision-making frameworks. While such systems have been demonstrated at individual facilities, adapting them to additional instruments remains challenging due to differences in local infrastructure. We present a modular workflow that connects existing open-source tools for data access (Tiled), workflow orchestration (Prefect), analysis and visualization (pyFAI, Plotly Dash), and Gaussian-process-based adaptive sampling (gpCAM) into a unified framework for autonomous scattering experiments. The same configuration operates across two synchrotron beamlines (ALS 7.3.3 and PETRA III P03) with only minimal facility-specific adjustments, as shown in proof-of-concept demonstrations. This validates that a consistent design emphasizing modularity and shared interfaces can ease deployment across diverse experimental environments. The resulting framework provides a flexible foundation for extending autonomous control and analysis capabilities beyond a single beamline or instrument.

47 OTHER INSTRUMENTATION↗

Introducing Molecular Hypernetworks for Discovery in Multidimensional Metabolomics Data

Orthogonal separations of data from high-resolution mass spectrometry can provide insight into sample composition and address challenges of complete annotation of molecules in untargeted metabolomics. “Molecular networks” (MNs), as used in the Global Natural Products Social Molecular Networking platform, are a prominent strategy for exploring and visualizing molecular relationships and improving annotation. MNs are mathematical graphs showing the relationships between measured multidimensional data features. MNs also show promise for using network science algorithms to automatically identify targets for annotation candidates and to dereplicate features associated with a single molecular identity. Here, this paper introduces “molecular hypernetworks” (MHNs) as more complex MN models able to natively represent multiway relationships among observations. Compared to MNs, MHNs can more parsimoniously represent the inherent complexity present among groups of observations, initially supporting improved exploratory data analysis and visualization. MHNs also promise to increase confidence in annotation propagation, for both human and analytical processing. We first illustrate MHNs with simple examples, and build them from liquid chromatography- and ion mobility spectrometry-separated MS data. We then describe a method to construct MHNs directly from existing MNs as their “clique reconstructions”, demonstrating their utility by comparing examples of previously published graph-based MNs to their respective MHNs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

LatticeAnalytics: Strut-Level Visualization and Inspection of Additively Manufactured Lattice Structures

Additive manufacturing (AM) is revolutionizing the production of custom components with complex internal geometries, essential for high-performance applications in diverse fields such as medicine and defense. These AM parts optimize strength while minimizing weight by utilizing internal lattice structures consisting of large quantities of small interconnected struts. However, the complexity of these structures, combined with the challenges of using X-ray Computed Tomography (XCT) data, makes validation of part reliability difficult. This ultimately inhibits the development of novel parts for our collaborating material scientists. Here, we introduce LatticeAnalytics, a novel framework specifically designed for visual inspection of defects in these lattice structures. Our framework offers an end-to-end solution that includes the data management of XCT scans, enables remote access for geographically dispersed teams through a web-based dashboard, and incorporates novel visualizations. Our analysis is facilitated by a coarse alignment between the lattice’s nominal model, a spatial graph, and the XCT data. We employ a simple VR-based approach for fast and rough alignment, followed by an offline registration and identification of the struts. With the nodes and struts aligned and identified in the volume, our framework allows querying of subvolumes containing a single strut at multiple resolutions. This avoids computation over the entire lattice and also allow for easy parallelization of down-stream computations, such as strut-specific metrics. To depict a fast overview of the strut quality, we introduce two innovative visual encodings, crucial for our collaborators’ research in creating novel AM parts: the Contour View and the Roughness Map, which depict critical geometrical and surface features of individual struts in standardized two 2D views. We evaluated the integrated system through expert interviews. The feedback confirms the framework’s practicality and its effectiveness in enhancing current inspection workflows. It solves major bottlenecks for our collaborators, ultimately helping them create novel parts with advanced properties.

Miao, Haichao [Lawrence Livermore National Laborat↗

GENESPACE R Package (GENESPACE) v1.0

In short, the GENESPACE pipeline conducts analysis of orthology networks, constrained within syntenic regions. Since analyses are limited to local tests conducted within syntenic blocks, GENESPACE is agnostic to ploidy, duplicated regions, inversions or other whole-genome chromosomal complexities that are common across many evolutionary lineages. This advantage allows for evolutionary tests in polyploids (e.g. switchgrass, manuscript in review), species with ancient, but retained whole-genome duplications (e.g. pecan, manuscript in prep), high levels of tandem array proliferation (e.g. eukalypts, manuscript in review) and many other factors that can confound comparative genomic analyses. The major advances of GENESPACE are three-fold: First, this is the first R package to integrate visualization and analysis of large-scale comparative genomics. R, which offers a high-level environment for graphical and statistical exploration of data, is often speed- and memory-limited and not used for computationally intensive tasks such as comparative genomics. The highly efficient C++ scripts used in GENESPACE (via data.table) permit a much faster and computationally lightweight implementation of comparative genomics than is currently available. Second, the pipeline itself is novel. To the best of our knowledge, no other program accomplishes synteny-constrained and ploidy-agnostic comparative genomics. Since nearly all plants and many animals have a history of whole-genome duplications, this is a major and necessary advance to the field. Third, GENESPACE offers high-level and intuitive multi-genome graphical outputs. The dotplots and 'riparian' plots produced herein, which are produced entirely through original R code, are publication-ready and easily customizable.

Schmutz, Jeremy↗

Demonstrating the viability of Lagrangian in situ reduction on supercomputers

Performing exploratory analysis and visualization of large-scale time-varying computational science applications is challenging due to inaccuracies that arise from under-resolved data. In recent years, Lagrangian representations of the vector field computed using in situ processing are being increasingly researched and have emerged as a potential solution to enable exploration. However, prior works have offered limited estimates of the encumbrance on the simulation code as they consider “theoretical” in situ environments. Further, the effectiveness of this approach varies based on the nature of the vector field, benefitting from an in-depth investigation for each application area. With this study, an extended version of Sane et al. (2021), we contribute an evaluation of Lagrangian analysis viability and efficacy for simulation codes executing at scale on a supercomputer. We investigated previously unexplored cosmology and seismology applications as well as conducted a performance benchmarking study by using a hydrodynamics mini-application targeting exascale computing. Here, to inform encumbrance, we integrated in situ infrastructure with simulation codes, and evaluated Lagrangian in situ reduction in representative homogeneous and heterogeneous HPC environments. To inform post hoc accuracy, we conducted a statistical analysis across a range of spatiotemporal configurations as well as a qualitative evaluation. Additionally, our study contributes cost estimates for distributed-memory post hoc reconstruction. In all, we demonstrate viability for each application — data reduction to less than 1% of the total data via Lagrangian representations, while maintaining accurate reconstruction and requiring under 10% of total execution time in over 90% of our experiments.

97 MATHEMATICS AND COMPUTING↗

Sensitivity Analysis of Drivers Water Shortage in the Los Angeles Region During Drought

The code and detailed step-by-step instructions for generating the model output data, processing results, and analysis and plotting are provided at https://github.com/IMMM-SFA/Ferencz_et_al_2026_ER_Water. The PyArtes model is a python adaptation of the Artes model. PyArtes uses many of the same input data and optimization model architecture as Artes. Documentation for the PyArtes model is provided in the Supplement to the paper. The primary data product are simulated monthly water shortages for indoor and outdoor demand under a large ensemble of drought scenarios (>13,000). The droughts are hypothetical and are not based on historical time series data of supply sources - though historical data did help inform ranges explored for supply parameters. Demands are informed by recent 2017-2021 water supply data. Demands used for the model can be accessed at https://github.com/IMMM-SFA/Ferencz_et_al_2026_ER_Water. Simulations resolve demand for over 90 water providers in the study region. The results report 36 months of water shortage data for each indoor and outdoor demand node. The study also developed a multilayer perceptron (MLP) neural network trained on a subset of the simulated shortage ensemble to emulate worst annual water shortage for a given set of parameter multipliers -- provided the parameter values fall within the ranges sampled in the ensemble. Emulated water shortages for synthetic ensembles are in the MLP-generated shortages folder. The MLP model was used to generate larger ensembles to support Sobol analysis that would have been extremely computationally expensive to simulate. Datasets provided in this repository*: Simulated shortages. These results are used for the analysis for Figures 5, 8, and 9 in the paper, and also to train the MLP emulator. .zip file containing outputs for the 13,312 scenario ensemble. Separate .csv files for indoor and outdoor shortage for each scenario. Rows = demand ids (~100), Columns = months (36) Units = acre-feet/month of shortage (shortage = monthly demand - supply). 1 acft = 1233.48 m^3 .csv files of aggregated shortages derived from the 13,312 ensemble Rows = scenarios (13,312), Columns = demand ids (~100) Units = acre-feet/year (either worst annual shortage or total shortage over the 3-year drought) .csv file of the parameter multipliers scenarios for the ensemble .csv file of the parameter ranges and baseline values the multipliers were applied to MLP-generated shortages. These results are used for Figures 4, 6, and 7 in the paper. mwd higher folder: scenario ensembles, emulated worst year total shortages (acft), and Sobol results Emulated shortages. Rows = scenarios, columns = demand ids, units acft Sobol results. Rows = demand ids, columns Sobol (S1, ST, or 95% confidence interval) value for each parameter mwd lower folder: scenario ensembles, emulated worst year total shortages (acft), and Sobol results same organization as mwd higher MLP performance: performance metrics (R^2, RMSE, BIAS, MAPE) for the testing subset (20% or 2,662 scenarios) and simulated vs emulated worst year shortage (acre-feet/year) for every demand node, MWD wholesale regions, and the entire study region (LAC). Supporting data for figures. Figure plotting scripts in the associated GitHub repo. These files support analysis and visualization. Geospatial Data used for plotting simulated water shortages and Sobol results. Dictionary of full names for demand nodes in the model and estimates of water supply by source type informed by Artes input files and California Urban Water Management Planning data: https://water.ca.gov/Programs/Water-Use-And-Efficiency/Urban-Water-Use-Efficiency/Urban-Water-Management-Plans *Readme files provided for each folder.

drought↗

A Data Processing Pipeline To Extract A Knowledge Graph From Heterogeneous Data For Socio-technical Analysis Of Critical Infrastructure Influence

The code is written in Python and consists of the following pipeline that is implemented in Apache Airflow. This pipeline intends to understand the companies that are directly or indirectly involved with a type of critical infrastructure system at some point in that system's lifecycle. The pipeline takes a configuration file that specifies a list of initial companies to consider, a geographic region of interest, and a set of SEC form types as well as other data sources (e.g. CrunchBase) from which to extract entities and relations. There are four main components to this pipeline as currently implemented: Entity Extraction, Network Construction, Analysis, and Visualization. First, Entity Extraction, is implemented as the `topear-extract_organizations` Apache Airflow workflow. Given an initial query that specifies a geographic region of interest and a time interval, the software will extract CI facilities of interest and organizations that have a direct influence relationship to those facilities (e.g. ownership). During the course of the LDRD, we focused on Electric Vehicle charging stations and this information is available via the Department of Energy (DOE) database on fueling stations maintained by NREL. Within the context of the DOE CESER project, we have focused on Battery Energy Storage Systems (BESS). Second, the Network Extraction component will iteratively construct a social network graph given the set of organizations and people extracted in the previous step. Organizations (and eventually People if desired) are then fed as a query to the `topgear-construct_social_network` Apache Airflow workflow which given a set of initial companies and data sets (e.g. SEC EDGAR form types, OpenCorporates, Crunchbase). This Airflow workflow will iteratively query such data sources to discover relationships with new organizations and people. For example, this module can iteratively query SEC EDGAR for metadata that documents the number of each type of form for the given set of companies and their location. This forms metadata represents a catalog of data sources from SEC EDGAR for the extracted social network knowledge graph. The pipeline then downloads these forms from the website and saves them in a build directory for further processing. These documents are then parsed for entities and relations. Again, we note that in additional to SEC data sources, this step can also pull in information on organizations via API services such as CrunchBase and OpenCorporates or bulk data sources. At the end of this step, the resultant social network, the Critical Infrastructure network, and the edges that encode relationships between organizations and CI facilities, form the Adversarial Socio-Technical Network (ASTN) that informs the analysis. Third, the Analysis component processes these generated ASTN. Previously, that has included the ability to compare prevalence of different vendors for a given infrastructure component type across different regions as well as identify common public and private investors across those vendors. This was demonstrated for EV Charging Stations across several different metropolitan areas within an IEEE PES GridEdge publication. More recently, we have looked at ways to identify infrastructure owners and operators of BESS with the most nameplate capacity across different states as well as other indictors of risk resulting from changes in ownership over time. Finally, the Visualization component consists of an HTML/CSS/JS framework by which users can interact geospatial, operational, and organizational relationships across a given portfolio of Critical Infrastructure facilities. The objective is to provide a library of UI/UX modules that can be repurposed for stakeholder-specific dashboards. All of the modules are related via a common event model that enables UI actions in one view to percolate across the other views.

Weaver, Gabriel [Idaho National Laboratory (INL), ↗

RCSB Protein Data Bank: Celebrating 50 years of the PDB with new tools for understanding and visualizing biological macromolecules in 3D

We report the Research Collaboratory for Structural Bioinformatics Protein Data Bank (RCSB PDB), funded by the US National Science Foundation, National Institutes of Health, and Department of Energy, has served structural biologists and Protein Data Bank (PDB) data consumers worldwide since 1999. RCSB PDB, a founding member of the Worldwide Protein Data Bank (wwPDB) partnership, is the US data center for the global PDB archive housing biomolecular structure data. RCSB PDB is also responsible for the security of PDB data, as the wwPDB-designated Archive Keeper. Annually, RCSB PDB serves tens of thousands of three-dimensional (3D) macromolecular structure data depositors (using macromolecular crystallography, nuclear magnetic resonance spectroscopy, electron microscopy, and micro-electron diffraction) from all inhabited continents. RCSB PDB makes PDB data available from its research-focused RCSB.org web portal at no charge and without usage restrictions to millions of PDB data consumers working in every nation and territory worldwide. In addition, RCSB PDB operates an outreach and education PDB101.RCSB.org web portal that was used by more than 800,000 educators, students, and members of the public during calendar year 2020. This invited Tools Issue contribution describes (i) how the archive is growing and evolving as new experimental methods generate ever larger and more complex biomolecular structures; (ii) the importance of data standards and data remediation in effective management of the archive and facile integration with more than 50 external data resources; and (iii) new tools and features for 3D structure analysis and visualization made available during the past year via the RCSB.org web portal.

59 BASIC BIOLOGICAL SCIENCES↗

Mapping Rare Earths and Toxics in E-Waste via Hyperspectral Imaging and Machine Learning

Electronic waste (e-waste) presents a mounting challenge to environmental sustainability due to its complex composition, which includes high-value rare earth elements, hazardous organic compounds, and non-recyclable plastics. Accurate and scalable material classification is essential for enabling efficient resource recovery and safe recycling practices. This study introduces a confidence-aware classification pipeline that combines mid-infrared hyperspectral imaging (HSI), spectral angle mapping (SAM), and iterative machine learning to perform pixel-level material identification across e-waste devices. A curated spectral library encompassing artificial materials (e.g., plastic iron oxide, galvanized metals), minerals (e.g., allanite, hematite), and organic compounds (e.g., benzanthracene, toluene) was used to generate pseudo-labels, each assigned a confidence score based on SAM-derived spectral similarity. High-confidence samples from seven consumer electronics—digital cameras, keyboards, laptop fans, modems, motherboards, TV remotes, and speakers—were iteratively expanded and classified using models such as Support Vector Machine (SVM), Random Forest, Gradient Boosting Classifier, Partial Least Squares Discriminant Analysis (PLSDA) and Logistic Regression. The best-performing classifiers achieved macro F1 scores approaching 1.0. Results revealed widespread plastic content (dominated by plastic iron oxide), the presence of rare earth-bearing minerals like cerium-containing allanite, and pervasive detection of hazardous organics such as benzanthracene. Principal Component Analysis (PCA) visualizations and confusion matrices confirmed high separability and robust classification performance. This methodology enables precise, non-destructive, and scalable classification of heterogeneous e-waste streams. It supports automated, hazard-aware sorting in recycling workflows, facilitating selective recovery of critical materials and compliance with circular economy goals. The confidence-aware framework provides a foundation for real-time deployment in industrial settings, offering significant implications for smart e-recycling infrastructure and policy-driven material stewardship.

Circular economy↗

VAIM-CFF: a variational autoencoder inverse mapper solution to Compton form factor extraction from deeply virtual exclusive reactions

We develop a new methodology for extracting Compton form factors (CFFs) from deeply virtual exclusive reactions such as the unpolarized DVCS cross section using a specialized inverse problem solver, a variational autoencoder inverse mapper (VAIM). The VAIM-CFF framework not only allows us access to a fitted solution set possibly containing multiple solutions in the extraction of all 8 CFFs from a single cross section measurement, but also accesses the lost information contained in the forward mapping from CFFs to cross section. We investigate various assumptions and their effects on the predicted CFFs such as cross section organization, number of extracted CFFs, use of uncertainty quantification technique, and inclusion of prior physics information. We then use dimensionality reduction techniques such as principal component analysis to visualize the missing physics information tracked in the latent space of the VAIM framework. Through re-framing the extraction of CFFs as an inverse problem, we gain access to fundamental properties of the problem not comprehensible in standard fitting methodologies: exploring the limits of the information encoded in deeply virtual exclusive experiments.

Accelerator Physics↗

Local bilinear computation of Jacobi sets

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

97 MATHEMATICS AND COMPUTING↗

A Mountaintop View Requires Minimal Sorting: A Faster Contour Tree Algorithm

Consider a scalar field f : M → R, where M is a triangulated simplicial mesh in R d . A level set, or contour, at value v is a connected component of f –1 (v). As v is changed, these contours change topology, merge into each other, or split. Contour trees are concise representations of f that track this contour behavior. The vertices of these trees are the critical points of f, where the gradient is zero. The edges represent changes in the topology of contours. It is a fundamental data structure in data analysis and visualization, and there is significant previous work (both theoretical and practical) on algorithms for constructing contour trees. Suppose M has n vertices, N facets, and t critical points. A classic result of Carr, Snoeyink, and Axen (2000) gives an algorithm that takes O(n log n+Nα(N)) time (where α(·) is the inverse Ackermann function). A further improvement to O(t log t + N) time was given by Chiang et al. All these algorithms involve a global sort of the critical points, a significant computational bottleneck. Unfortunately, lower bounds of Ω(t log t) also exist. We present the first algorithm that can avoid the global sort and has a refined time complexity that depends on the contour tree structure. Intuitively, if the tree is short and fat, we get significant improvements in running time. For a partition of the contour tree into a set of descending paths, P, our algorithm runs in O($\Sigma$ pϵP |p| log |p| + tα(t) + N). This is at most O(t log D + N), where D is the diameter of the contour tree. Moreover, it is O(tα(t) + N) for balanced trees, a significant improvement over the previous complexity. Our algorithm requires numerous ideas: partitioning the contour tree into join and split trees, a local growing procedure to iteratively build contour trees, and the use of heavy path decompositions for the time complexity analysis. There is a crucial use of a family of binomial heaps to maintain priorities, ensuring that any comparison made is between comparable nodes of the contour tree. We also prove lower bounds showing that the $\Sigma$ pϵP |p| log |p| complexity is inherent to computing contour trees.

97 MATHEMATICS AND COMPUTING↗

Open‐Source Anaerobic Digestion Modeling Platform, Anaerobic Digestion Model No. 1 Fast (ADM1F)

An open‐source modeling platform, called Anaerobic Digestion Model No. 1 Fast (ADM1F), is introduced to achieve fast and numerically stable simulations of anaerobic digestion processes. ADM1F is compatible with an iPython interface to facilitate model configuration, simulation, data analysis, and visualization. Faster simulations and more stable results are accomplished by implementing an advanced open‐source library of numerical methods called Portable Extensive Toolkit for Scientific Computation (PETSc) to solve the ADM1 system of equations. Leveraging PETSc, ADM1F can consistently complete a steady‐state simulation under 0.2 s, over 99% faster than a benchmark ADM1 model implemented with MATLAB while achieving agreement of model outputs within 1% of those obtained with the benchmark model. For dynamic simulations, however, ADM1F has a computational speed advantage only when the influent characteristics update more frequently than every 4 h. The ability of ADM1F to be useful as a tool to study anaerobic digestion systems is demonstrated through two example implementations of ADM1F: (1) a two‐phase co‐digestion scenario evaluating the impact of the organic loading rate and the substrate composition on reactor performance and stability, and (2) a conventional digester scenario assessing the effectiveness of recovery strategies after disruptions that led to instability. These examples demonstrate how the high simulation speed and the convenience of the iPython interface allow ADM1F to complete complex analyses within minutes, much faster than computational strategies currently reported in the literature.

anaerobic co-digestion↗