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Get Non-Real: Randomized Sketching for High-Dimensional Non-Real Valued Data (Final Report)

In our final report for DE-C0022186, we describe the work we did on this grant towards the goals we proposed. Our first goal was characterizing fundamental limits for sketching of discrete high-dimensional matrices with low-dimensional structures. Our second main goal was designing algorithms for data reconstruction from sketches. We focus on approaches that are either specifically designed for non-real-valued data (binary, finite field) or that will translate more readily to that setting.

97 MATHEMATICS AND COMPUTING

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING

G-Mapper: Learning a Cover in the Mapper Construction

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a “nice” Mapper graph. This paper focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on G-means clustering, which searches for the optimal number of clusters in 𝑘-means by iteratively applying the Anderson–Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the given data. In conclusion, experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets, while also running significantly faster than a previous iterative method.

G-means clustering

Tutorial: Machine-Learning-Based CREASE-2D Analysis of 2D SAXS Profiles to Characterize Anisotropic Nanostructures in Soft Materials

We present a tutorial to guide users on how to extend the Computational Reverse Engineering Analysis of Scattering Experiments-2D (CREASE-2D) framework to interpret their experimental two-dimensional small-angle scattering (SAS) data from soft materials (e.g., polymers, peptide amphiphiles, biomolecular fibrils). Unlike most traditional SAS analysis approaches, which typically rely on azimuthally averaged onedimensional (1D) profiles, CREASE-2D utilizes the complete 2D scattering profile to reveal information about anisotropy in the structure. In past applications, CREASE has provided insights into complex structural features, including the cross-sectional shapes of assembled nanostructures and dispersity in these features, which are difficult to discern with existing analytical models. While (1D- ) CREASE has been applied to SANS and SAXS data, this tutorial shares the steps for implementing CREASE-2D using an example of a dipeptide solution system, for which we have SAXS data. We present details for these steps involved in using CREASE-2D to interpret SAXS profiles: how to preprocess SAXS data, define relevant structural features, generate three-dimensional real-space structures for specific values of these features, train a machine learning (ML) surrogate model to predict scattering profiles for given structural features, and optimize these features using genetic algorithms (GA). Then, we use these steps to interpret complex 2DSAXS data collected from dipeptide solutions that, in microscopy images, exhibit nanoscale structures that could be elliptical tubes/ flat tapes/cylinders or a combination of these cross sections. Open-source codes, computational hardware, and software requirements, as well as the strengths and limitations of this protocol, are also presented. We expect researchers working with (soft) biomaterials, peptide amphiphiles, amphiphilic polymer solutions, polymer nanocomposites, and blends of particles/polymers will find this CREASE-2D method and this tutorial of use.

CREASE

Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning

Abstract Diverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discretized compositions and possible neighbor-to-neighbor transitions. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and order in procedurally generated simplex grids, keeping the algorithm $${\mathcal{O}}(N)$$ O ( N ) , with minimal memory, enabling rapid construction of graphs with billions of transitions in seconds. Additionally, we demonstrate how such graph representations can be combined to homogeneously express complex path-planning problems, while facilitating efficient deployment of existing high-performance gradient descent, graph traversal, and other optimization algorithms.

Krajewski, Adam M. (ORCID:0000000222660099)

CVEVOLVE

CVEvolve is an agentic AI system for autonomous algorithm discovery for scientific data processing. It creates workflows where large language model agents freely set up and configure development environments and evaluation harnesses, develop and improve data processing algorithms with designed exploration-exploitation balancing mechanisms, log history and findings in a structured database, and run holdout testing to ensure algorithm generalizability. CVEvolve offers a zero-code interface and does not require users to provide structured data and evaluation scripts.

Cherukara, MatthewJoseph [Argonne National Laborat

PDB-IHM: A System for Deposition, Curation, Validation, and Dissemination of Integrative Structures

Structures of many large biomolecular assemblies are now being determined using integrative approaches. In these approaches, information derived from multiple experimental and computational methods is combined to compute three-dimensional structures of multi-protein complexes and other macromolecular machines. A standalone prototype data resource for integrative structures called PDB-Dev was built, based on recommendations of the Integrative and Hybrid Methods (IHM) Task Force of the Worldwide Protein Data Bank (wwPDB). This effort included developing data standards and software tools for collecting, curating, validating, visualizing, archiving, and disseminating integrative structures that span diverse spatiotemporal scales and conformational states. Mechanisms have been created to validate integrative structures based on the experimental data underpinning them. Building upon this foundational framework, PDB-Dev has been further expanded to handle large dynamic macromolecular systems and integrative structures that combine, for example, experimental restraints with atomic coordinates computed by machine learning algorithms. Data standards and supporting tools have also been extended to capture information about biomolecular dynamics, such as conformational transitions and related kinetic data derived from biophysical methods. Recently, PDB-Dev was unified with the PDB archive and rebranded as PDB-IHM (pdb-ihm.org), further promoting FAIR (Findable, Accessible, Interoperable, and Reusable) principles of data stewardship for integrative structural biology.

IHMCIF

Unified architecture for quantum lookup tables

Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications depends crucially on gate-efficient implementations of these oracles, which are commonly some reversible versions of the Boolean circuit for a classical lookup table. Here, we present a general parametrized architecture for quantum circuits implementing a lookup table that encompasses all prior work in realizing a continuum of optimal trade-offs between qubits, non-Clifford gates, and error resilience, up to logarithmic factors. Our architecture assumes only local 2D connectivity, yet recovers results, with the appropriate parameters, polylogarithmic error scaling. We also identify regimes, such as simultaneous sublinear scaling, in all parameters. These results enable tailoring implementations of the commonly used lookup table primitive to any given quantum device with constrained resources.

quantum circuits

Learning of networked spreading models from noisy and incomplete data

Recent years have seen a lot of progress in algorithms for learning parameters of spreading dynamics from both full and partial data. Some of the remaining challenges include model selection under the scenarios of unknown network structure, noisy data, missing observations in time, as well as an efficient incorporation of prior information to minimize the number of samples required for an accurate learning. Here, in this work, we introduce a universal learning method based on a scalable dynamic message-passing technique that addresses these challenges often encountered in real data. The algorithm leverages available prior knowledge on the model and on the data, and reconstructs both network structure and parameters of a spreading model. We show that a linear computational complexity of the method with the key model parameters makes the algorithm scalable to large network instances.

97 MATHEMATICS AND COMPUTING

Factorization Machine‐Based Active Learning for Functional Materials Design with Optimal Initial Data

The optimization of functional materials is important to enhance their properties, but their complex geometries pose great challenges to optimization. Data-driven algorithms efficiently navigate such complex design spaces by learning relationships between material structures and performance metrics to discover high-performance functional materials. Surrogate-based active learning, continually improving its surrogate model by iteratively including high-quality data points, has emerged as a cost-effective data-driven approach. Furthermore, it can be coupled with quantum computing to enhance optimization processes, especially when paired with a special form of surrogate model (i.e., quadratic unconstrained binary optimization), formulated by factorization machine (FM). However, current practices often overlook the variability in design space sizes when determining the initial data size for optimization. In this work, we investigate the optimal initial data sizes required for efficient convergence across various design space sizes. By employing averaged piecewise linear regression, we identify initiation points where convergence begins, highlighting the crucial role of employing adequate initial data in achieving efficient optimization. These results contribute to the efficient optimization of functional materials by ensuring faster convergence and reducing computational costs in FM-based active learning.

active learning

Massive compression for high data rate macromolecular crystallography (HDRMX): impact on diffraction data and subsequent structural analysis

New higher-count-rate, integrating, large-area X-ray detectors with framing rates as high as 17400 images per second are beginning to be available. These will soon be used for specialized macromolecular crystallography experiments but will require optimal lossy compression algorithms to enable systems to keep up with data throughput. Some information may be lost. Can we minimize this loss with acceptable impact on structural information? To explore this question, we have considered several approaches: summing short sequences of images, binning to create the effect of larger pixels, use of JPEG-2000 lossy wavelet-based compression, and use of Hcompress, which is a Haar-wavelet-based lossy compression borrowed from astronomy. We also explore the effect of the combination of summing, binning, and Hcompress or JPEG-2000. In each of these last two methods one can specify approximately how much one wants the result to be compressed from the starting file size. These provide particularly effective lossy compressions that retain essential information for structure solution from Bragg reflections.

47 OTHER INSTRUMENTATION

Poisson-response Tensor-on-Tensor Regression and Applications

We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed of counts are common data in fields such as inter national relations, social networks, epidemiology, and medical imaging, where events occur across multiple dimensions like time, location, and dyads. PToTR accommodates such tensor responses alongside tensor covariates, providing a versatile tool for multi dimensional data analysis. We propose algorithms for maximum likelihood estimation under a canonical polyadic (CP) structure on the regression coefficient tensor that satisfy the positivity of Poisson parameters and then provide an initial theoretical error analysis for PToTR estimators. We also demonstrate the utility of PToTR through three concrete applications: longitudinal data analysis of the Integrated Crisis Early Warning System database, positron emission tomography (PET) image reconstruction, and change-point detection of communication patterns in longitudinal dyadic data. These applications highlight the versatility of PToTR in addressing complex, structured count data across various domains.

97 MATHEMATICS AND COMPUTING

Uncertainty in inventories for life cycle assessment: State‐of‐the‐art, challenges, and new technologies

Uncertainty is a critical factor that can hinder the quality and potential applications of life cycle assessment (LCA) results. A prominent source of uncertainty stems from the life cycle inventory (LCI) data. Various methodologies exist to estimate the uncertainty associated with LCI data, primarily based on the widely used structured pedigree matrix approach or the computationally intensive Monte Carlo simulation. This perspective review explores how new technologies (e.g., computational algorithms and data collection methods) from data science and related fields can contribute to identifying, quantifying, and reducing uncertainty in LCI modeling. A brief overview of the sources of uncertainty in LCI modeling and how they are addressed in current LCA practice is provided. Additionally, several new technologies are identified, and the potential benefits of their implementation in reducing uncertainties in LCI modeling are discussed. This perspective review concludes by identifying potential areas that require further development for these technologies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Morphological descriptors of nanoparticles: The link between atomistic structures and x-ray absorption spectra

Understanding and quantifying the morphology of nanoparticles are essential for linking their atomic structure to diverse applications and verifying theoretical models. While experimental information on the structure of nanoparticles in the size range below ∼5 nm can be extracted from x-ray absorption spectroscopy using a small number of descriptors—most commonly coordination numbers—developing an understanding of morphology descriptors from experimental data remains a challenge. Here, in this study, we introduce NanoGene, a genetic algorithm-based method for generating structurally diverse nanoparticle models guided by user-defined descriptors. We establish correlations among structural, size-related, and morphological descriptors and demonstrate how experimentally accessible parameters, such as coordination numbers, can be leveraged to infer otherwise inaccessible ones, such as the generalized coordination number or particle oblateness. Principal component and clustering analyses reveal the relative importance of descriptors, with the number of atoms emerging as a key discriminant of the nanoparticle structure. By providing both the methodology and an extensive dataset of nanoparticle geometries, this work offers a practical foundation for descriptor-based analysis and interpretation of experimental observations, bridging the gap between local atomic coordinates and global morphological characterization.

77 NANOSCIENCE AND NANOTECHNOLOGY

Collinear limit of the four-point energy correlator in N = 4 supersymmetric Yang-Mills theory

We present a compact formula, expressed in terms of classical polylogarithms up to weight three, for the leading order four-point energy correlator in maximally supersymmetric Yang-Mills theory, in the limit where the four detectors are collinear. This formula is derived by combining a simplified, manifestly dual conformal invariant form of the 1 → 4 splitting function obtained from the square of the tree-level five-particle form factor of stress-tensor multiplet operators, with a novel integration-by-parts algorithm operating directly on Feynman parameter integrals. Our results provide valuable data for exploring the structure of physical observables in perturbation theory, and for calculations of jet substructure observables in quantum chromodynamics. Published by the American Physical Society 2024

Chicherin, Dmitry (ORCID:000000028985084X)

Desmearing two-dimensional small-angle neutron scattering data by central moment expansions

Resolution smearing is a critical challenge in the quantitative analysis of two-dimensional small-angle neutron scattering (SANS) data, particularly in studies of soft-matter flow and deformation using SANS. Here, we present a central moment expansion technique to address smearing in anisotropic scattering spectra, offering a model-free desmearing methodology. By accounting for directional variations in resolution smearing and enhancing computational efficiency, this approach reconstructs desmeared intensity distributions from smeared experimental data. Computational benchmarks using interacting hard-sphere fluids and Gaussian chain models validate the accuracy of the method, while simulated noise analyses confirm its robustness under experimental conditions. Experimental validation using rheological SANS data from shear-induced micellar structures demonstrates the practicality and effectiveness of the proposed algorithm. The desmearing technique provides a powerful tool for advancing the quantitative analysis of anisotropic scattering patterns, enabling precise insights into the interplay between material microstructure and macroscopic flow behavior.

anisotropic scattering spectra

Accelerating GNNs on GPU Sparse Tensor Cores through N:M Sparsity-Oriented Graph Reordering

Recent advancements in GPU hardware support have introduced the capability to leverage N:M sparse patterns for substantial performance gains. Graphs in Graph Neural Networks (GNNs) are typically sparse, but the sparsity is often irregular, not conforming to such sparse patterns. In this paper, we propose a novel graph reordering algorithm, the first of its kind, to reshape irregular graph data into the N:M structured sparse pattern at the tile level, allowing linear-algebra-based graph operations in GNNs to benefit from the N:M sparse hardware. The optimization is lossless, maintaining the accuracy of GNN. It can remove 98-100\% violations of the N:M sparse patterns at the vector level, and increase the proportion of conforming graphs in SuiteSparse collection from 5-9\% to 88.7-93.5\%. On A100 GPUs, the optimization accelerates Sparse Matrix Matrix (SpMM) by up to 43X (2.3X -- 7.5X on average) and speeds up the key graph operations in GNNs on real graphs by as much as 8.6X (3.5X on average).

artificial intelligence, graph neural networks

Time-resolved atomic-resolution Brownian tomography of single nanocrystals reveals size-dependent dynamics

Atomic-resolution structure identification of nanocrystals by graphene liquid cell electron microscopy (GLC-EM) has revealed that small, solubilized platinum nanocrystals consist of an ordered crystalline core surrounded by mobile surface atoms, which dissociate during oxidative etching, resulting in distinct temporal structural states. Requirements imposed by the 3D reconstruction algorithm limit the number of structural states that can be resolved. We introduce a regularized 3D reconstruction algorithm that exploits the redundancy inherent in the experimental data, allowing us to improve the time resolution. Our developments provide a comprehensive molecular picture at unprecedented spatial and temporal resolution of the nonlinear, linear, and fluctuating dynamic phenomena that single nanocrystals undergo during the GLC-EM experiment. We determined atomic structures of 66 temporal structural states, extracted from 15 time trajectories of individual nanocrystals. Large (478 to 698 atoms) and small (<300 atoms) nanocrystals show etching that preserves a stable core, whereas mid-sized (351 to 571 atoms) nanocrystals present dynamics that change the coordination of the core.

Meana-Pañeda, Rubén