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A conservative, consistent, and scalable meshfree mimetic method

Mimetic methods discretize divergence by restricting the Gauss theorem to mesh cells. Because point clouds lack such geometric entities, construction of a compatible meshfree divergence remains a challenge. In this work, we define an abstract Meshfree Mimetic Divergence (MMD) operator on point clouds by contraction of field and virtual face moments. This MMD satisfies a discrete divergence theorem, provides a discrete local conservation principle, and is first-order accurate. We consider two MMD instantiations. The first one assumes a background mesh and uses generalized moving least squares (GMLS) to obtain the necessary field and face moments. This MMD instance is appropriate for settings where a mesh is available but its quality is insufficient for a robust and accurate mesh-based discretization. The second MMD operator retains the GMLS field moments but defines virtual face moments using computationally efficient weighted graph-Laplacian equations. This MMD instance does not require a background grid and is appropriate for applications where mesh generation creates a computational bottleneck. It allows one to trade an expensive mesh generation problem for a scalable algebraic one, without sacrificing compatibility with the divergence operator. We demonstrate the approach by using the MMD operator to obtain a virtual finite-volume discretization of conservation laws on point clouds. Finally, numerical results in the paper confirm the mimetic properties of the method and show that it behaves similarly to standard finite volume methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Three-dimensional phenotyping of peach tree-crown architecture utilizing terrestrial laser scanning

Tree training systems for temperate fruit have been developed throughout history by pomologists to improve light interception, fruit yield, and fruit quality. These training systems direct crown and branch growth to specific configurations. Quantifying crown architecture could aid the selection of trees that require less pruning or that naturally excel in specific growing/training system conditions. Regarding peaches [Prunus persica (L.) Batsch], access tools such as branching indices have been developed to characterize tree-crown architecture. However, the required branching data (BD) to develop these indices are difficult to collect. Traditionally, BD have been collected manually, but this process is tedious, time-consuming, and prone to human error. These barriers can be circumnavigated by utilizing terrestrial laser scanning (TLS) to obtain a digital twin of the real tree. TLS generates three-dimensional (3D) point clouds of the tree crown, wherein every point contains 3D coordinates (x, y, z). To facilitate the use of these tools for peach, we selected 16 young peach trees scanned in 2021 and 2022. These 16 trees were then modeled and quantified using the open-source software TreeQSM. As a result, “in silico” branching and biometric data for the young peach trees were calculated to demonstrate the capabilities of TLS phenotyping of peach tree-crown architecture. The comparison and analysis of field measurements (in situ) and in silico BD, biometric data, and quantitative structural model branch uncertainty data were utilized to determine the reconstructive model’s reliability as a source substitute for field measurements. Mean average deviation when comparing young tree (YT) height was approx. 5.93%, with crown volume was approx. 13.26% across both 2021 and 2022. All point clouds of the YTs in 2022 showed residuals lower than 12 mm to cylinders fitted to all branches, and mean surface coverage greater than 40% for both the trunk and primary branching orders.

09 BIOMASS FUELS↗

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗

Haar-Like Wavelets on Hierarchical Trees

Here, discrete wavelet methods, originally formulated in the setting of regularly sampled signals, can be adapted to data defined on a point cloud if some multiresolution structure is imposed on the cloud. A wide variety of hierarchical clustering algorithms can be used for this purpose, and the multiresolution structure obtained can be encoded by a hierarchical tree of subsets of the cloud. Prior work introduced the use of Haar-like bases defined with respect to such trees for approximation and learning tasks on unstructured data. This paper builds on that work in two directions. First, we present an algorithm for constructing Haar-like bases on general discrete hierarchical trees. Second, with an eye towards data compression, we present thresholding techniques for data defined on a point cloud with error controlled in the $L$ $\infty$ norm and in a Hölder-type norm. In a concluding trio of numerical examples, we apply our methods to compress a point cloud dataset, study the tightness of the $L$ $\infty$ error bound, and use thresholding to identify MNIST classifiers with good generalizability.

97 MATHEMATICS AND COMPUTING↗

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗

Automated Approach to Accurate, Precise, and Fast Detector Simulation and Reconstruction

Detector simulation and reconstruction are a significant computational bottleneck in particle physics. Here, we develop particle-flow neural-assisted simulations (parnassus) to address this challenge. Our deep learning model takes as input a point cloud (particles impinging on a detector) and produces a point cloud (reconstructed particles). By combining detector simulations and reconstruction into one step, we aim to minimize resource utilization and enable fast surrogate models suitable for application both inside and outside large collaborations. We demonstrate this approach using a publicly available dataset of jets passed through the full simulation and reconstruction pipeline of the Compact Muon Solenoid (CMS) experiment. We show that parnassus accurately mimics the CMS particle flow algorithm on the (statistically) same events it was trained on and can generalize to jet momentum and type outside of the training distribution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Kinematics reconstruction in solenoidal spectrometers operated in active target mode

Here, we discuss the reconstruction of low-energy nuclear reaction kinematics from charged-particle tracks in solenoidal spectrometers working in Active Target Time Projection Chamber mode. In this operation mode, reaction products are tracked within the active gas medium of the Active Target with a three dimensional space point cloud. We have inferred the reaction kinematics from the point cloud using an algorithm based on a linear quadratic estimator (Kalman filter). The performance of this algorithm has been evaluated using experimental data from nuclear reactions measured with the Active Target Time Projection Chamber (AT-TPC) detector.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Probing criticality with deep learning in relativistic heavy-ion collisions

Systems with different interactions could develop the same critical behavior due to the underlying symmetry and universality. Using this principle of universality, we can embed critical correlations modeled on the 3D Ising model into the simulated data of heavy-ion collisions, hiding weak signals of a few inter-particle correlations within a large particle cloud. Employing a point cloud network with dynamical edge convolution, we are able to identify events with critical fluctuations through supervised learning, and pick out a large fraction of signal particles used for decision-making in each single event.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Accurate surface estimation from high-resolution 3D microwave images

Active millimeter and microwave imaging techniques can be used to create a high-resolution 3D image volume of a target’s reflectivity. Millimeter-wave imaging is commonly used for personnel security screening and numerous other applications. Backprojection based image reconstruction techniques form a 3D complex-valued volume. The complex-valued volume is commonly reduced to a real-valued volume by taking the magnitude. For anomaly detection and cross image registration of an object it is beneficial to generate an accurate representation of an object’s surface. Extracting a smooth and accurate surface from a magnitude only image is challenging. One difficulty is the magnitude image has limited resolution in the depth direction which normally limits precision to a moderate fraction of the depth resolution. Another difficulty is that the magnitude of the image depends heavily on the geometry and orientation of the object being imaged. The phase information in a complex-valued image volume provides a means to decouple the magnitude of the image from the geometry of an object and provide precision much finer than the depth resolution would indicate. This enables the generation of a smooth and accurate point cloud representation of the surface of an imaged object. A method to extract a point cloud from the phase information in a 3D complex-valued millimeter-wave image volume is developed and results with simulated and experimental data are presented.

Clark, Richard T.↗

Comprehension of Spatial Constraints by Neural Logic Learning from a Single RGB-D Scan

Autonomous industrial assembly relies on the precise measurement of spatial constraints as designed by computer-aided design (CAD) software such as SolidWorks. This paper proposes a framework for an intelligent industrial robot to understand the spatial constraints for model assembly. An extended generative adversary network (GAN) with a 3D long short-term memory (LSTM) network was designed to composite 3D point clouds from a single RGB-D scan. The spatial constraints of the segmented point clouds are identified by a neural-logic network that incorporates general knowledge of spatial constraints in terms of first-order logic. The model was designed to comprehend a complete set of spatial constraints that are consistent with industrial CAD software, including left, right, above, below, front, behind, parallel, perpendicular, concentric, and coincident relations. The accuracy of 3D model composition and spatial constraint identification was evaluated by the RGB-D scans and 3D models in the ABC dataset. The proposed model achieved 57.23% intersection over union (IoU) in 3D model composition, and over 99% in comprehending all spatial constraints.

Wang, Dali↗

Oak Ridge National Laboratory Building Envelope Library (ORNOBEL)

The Oak Ridge National Laboratory Building Envelope Library (ORNOBEL) is a collection of dense exterior building-facade point clouds acquired using a survey-grade terrestrial laser scanner. Each file represents an individual facade from a building on the Oak Ridge National Laboratory (ORNL) campus or in Knoxville, Tennessee, with an average point-cloud resolution of approximately 3 mm. The points in each facade are semantically labeled into three classes: (1) window/door, representing openings in the building envelope; (2) wall, representing planar opaque envelope surfaces; and (3) other, representing the remaining facade-adjacent elements, architectural features, and protrusions. ORNOBEL supports the development, training, and evaluation of advanced deep-learning methods for automated building-envelope segmentation, geometric reconstruction, and building information modeling (BIM).

Maldonado Puente, Bryan [ORNL] (ORCID:000000033880↗

Aerial Captured Data and Processed Models in Beaumont-Port Arthur Region in Feb and Oct, 2023

Our Co-design team is from the University of Texas, working on a Department of Energy-funded project focused on the Beaumont-Port Arthur area. As part of this project, we will be developing climate-resilient design solutions for areas of the region. More on www.caee.utexas.edu.We used a DJI Mavic 2 Pro to capture aerial photos in Beaumont-Port Arthur, TX, in February 2023, including:I. Beaumont Soccer ClubII. Corps’ Port Arthur Resident OfficeIII. Halbouty Pump Station comprises its vicinityIV. Lamar University (Including Exxon Power Plants close to Lamar Univ.)V. MLK Boulevard for aerial images of the industry and the ship channelVI. Salt Water Barrier (include some aerial images about the Big Thicket)Aerial photos taken were through DroneDeploy autonomous flight, and models were processed through the DroneDeploy engine as well. All aerial photos are in .JPG format and contained in zipped files for each location.The processed data package including 3D models, geospatial data, mappings, point clouds, and the animation video of Halbouty Pump Station has various file types:- The Adobe Suite gives you great software to open .Tif files.- You can use LASUtility (Windows), ESRI ArcGIS Pro (Windows), or Blaze3D (Windows, Linux) to open a LAS file and view the data it contains.- Open an .OBJ file with a large number of free and commercial applications. Some examples include Microsoft 3D Builder, Apple Preview, Blender, and Autodesk.- You may use ArcGIS, Merkaartor, Blender (with the Google Earth Importer plug-in), Global Mapper, and Marble to open .KML files.- The .tfw world file is a text file used to georeference the GeoTIFF raster images, like the orthomosaic and the DSM. You need suitable software like ArcView to open a .TFW file.This dataset provides researchers with sufficient geometric data and the status quo of the land surface at the locations mentioned above. This dataset could streamline researchers' decision-making processes and enhance the design as well.In October 2023, we had our follow-up data collection, including:I. Beaumont Soccer ClubII. Shipping and Receiving Center at Lamar UniversityAfter the aerial collection, we obtained aerial photos of those two locations mentioned above, as well as processed data (such as point clouds and models).

2D mapping↗

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Bayesian optimization↗

Grain size estimation in fluvial gravel bars using uncrewed aerial vehicles: A comparison between methods based on imagery and topography

Abstract Grain size assessments are necessary for understanding the various geomorphological, hydrological and ecological processes that occur within rivers. Recent research has shown that the application of Structure‐from‐Motion (SfM) photogrammetry to imagery from uncrewed aerial vehicles (UAVs) shows promise for rapidly characterising grain sizes along rivers in comparison to traditional field‐based methods. Here, we evaluated the applicability of different methods for estimating grain sizes in gravel bars along a study reach in the Olentangy River in Columbus, Ohio. We collected imagery of these gravel bars with a UAV and processed those images with SfM photogrammetry software to produce three‐dimensional point clouds and orthomosaics. Our evaluation compared statistical models calibrated on topographic roughness, which was computed from the point clouds, and to those based on image texture, which was computed from the orthomosaics. Our results showed that statistical models calibrated on image texture were more accurate than those based on topographic roughness. This might be because of site‐specific patterns of grain size, shape and imbrication. Such patterns would have complicated the detection of topographic signatures associated with individual grains. Our work illustrates that UAV‐SfM approaches show potential to be used as an accessible method for characterising surface grain sizes along rivers at higher spatial and temporal resolutions than those provided by traditional methods.

Wong, Tyler↗

Airborne LiDAR to Improve Canopy Fuels Mapping for Wildfire Modeling

Increasing conflict between wildfire and the built environment has increased the need for more up-to-date and finer resolution canopy fuels data to improve wildfire modeling and associated risk forecasts. The US Forest Service and US Department of the Interior’s LANDFIRE product, which provides 30-m resolution canopy fuels data for the entire US, is one of the most widely used sources of fuels data. However, the last complete mapping effort for LANDFIRE is based on 2016 conditions, and subsequent updates reflect disturbances 1-2 years behind the release year. Airborne systems equipped with Light Detection and Ranging (LiDAR) sensors can be deployed to actively sense canopy structure and estimate canopy fuels data (cover, height, base height, bulk density) at finer resolutions. Canopy base height (CBH) and canopy bulk density (CBD) are difficult to measure both in the field and in LiDAR point clouds. Still, they are important for accurately modeling crown fires, which are often intense and difficult to contain. Additionally, point cloud datasets are large, and calculations require efficient utilization of computational resources. To address these challenges, we are working on an approach that uses openly available National Ecological Observatory Network (NEON) airborne LiDAR data, with calculations processed in the R programming language and parallelized through the lidR package. CBH and CBD are often derived from tree height, diameter at breast height, and species-specific allometries using the Fire and Fuels Extension of the Forest Vegetation Simulator (FFE-FVS). We aim to test if airborne LiDAR can estimate CBH and CBD without the use of empirical equations. Reliable estimates of canopy fuels data directly from airborne LiDAR could streamline quick, fine-resolution updates for use in wildfire behavior models.

54 ENVIRONMENTAL SCIENCES↗

National Center for Airborne Laser Mapping (NCALM) LiDAR, Imagery, and DEM data from five NGEE Arctic Sites, Seward Peninsula, Alaska, August 2021

From August 8 through August 16 of 2021, airborne remote sensing data was collected by the National Center for Airborne Laser Mapping (NCALM) in collaboration with NGEE Arctic scientists. Data was collected around five NGEE Arctic study sites on the Seward Peninsula of Alaska: Teller mm 27, Teller mm 47, Kougarok mm 64, Kougarok mm 86, and Council mm 71. A Robinson R44 II helicopter with a RIEGL VQ-580 II airborne laser scanner was used to collect the LiDAR point cloud data for each study site. A Phase One iXM-RS100F camera was integrated with the Riegl sensor to collect RGB imagery. This data package contains LiDAR point clouds (.las), RGB imagery (tif), 1 m or 50 cm Digital Elevation Models (.tif) generated from the LiDAR data, and shapefiles of the .las tiling system for each site (.shp). Two supplemental documents are also included in the package: 1) a report describing data collection details, GNSS corrections, and processing steps and 2) a document describing the LiDAR Classification used (.pdf). This survey was conducted towards the end of the summer on the Seward Peninsula, and can be paired with data collected in April of 2022 during the snow-on campaign "National Center for Airborne Laser Mapping (NCALM) LiDAR and DEM data from two NGEE Arctic Sites, Seward Peninsula, Alaska, Winter 2022" (Singhania et.al, 2023) (NGA314). The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

Data from "A Bayesian Record Linkage Approach to Applications in Tree Demography Using Overlapping LiDAR Scans"

Processed LiDAR data and environmental covariates from 2015 and 2019 LiDAR scans in the Vicinity of Snodgrass Mountain (Western Colorado, USA), in a geographic subset used in primary analysis for the research paper.This package contains LiDAR-derived canopy height maps for 2015 and 2019, crown polygons derived from the height maps using a segmentation algorithm, and environmental covariates supporting the model of forest growth. Source datasets include August 2015 and August 2019 discrete-return LiDAR point clouds collected by Quantum Geospatial for terrain mapping purposes on behalf of the Colorado Hazard Mapping Program and the Colorado Water Conservation Board. Both datasets adhere to the USGS QL2 quality standard. The point cloud data were processed using the R package lidR to generate a canopy height model representing maximum vegetation height above the ground surface, using a pit-free algorithm.This dataset was compiled to assess how spatial patterns of tree growth in montane and subalpine forests are influenced by water and energy availability. Understanding these growth patterns can provide insight into forest dynamics in the Southern Rocky Mountains under changing climatic conditions.This dataset contains .tif, .csv, and .txt files. This dataset additionally includes a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type.

54 ENVIRONMENTAL SCIENCES↗