Hyper-Differential Sensitivity Analysis: Managing High Dimensional Uncertainty in Large-Scale Optimization.
Abstract not provided.
Hart, Joseph Lee↗
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Results for “high dimensionality”
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Reliable Measures of Spread in High Dimensional Latent Spaces
Understanding geometric properties of the latent spaces of natural language processing models allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model’s latent space, or how fully the available latent space is being used. We demonstrate that the commonly used measures of data spread, average cosine similarity and a partition function min/max ratio I (V), do not provide reliable metrics to compare the use of latent space across data distributions. We propose and examine six alternative measures of data spread, all of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.
97 MATHEMATICS AND COMPUTING↗
Fast Gaussian process regression for high dimensional functions with derivative information
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Sorokin, Aleksei Gregory [Sandia National Laborato↗
Contour-Based Sampling Methods in High-Dimensional Space
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Engineering - Aeronautics↗
Data driven discovery and quantification of hyperspectral leaf reflectance phenotypes across a maize diversity panel
Abstract Estimates of plant traits derived from hyperspectral reflectance data have the potential to efficiently substitute for traits, which are time or labor intensive to manually score. Typical workflows for estimating plant traits from hyperspectral reflectance data employ supervised classification models that can require substantial ground truth datasets for training. We explore the potential of an unsupervised approach, autoencoders, to extract meaningful traits from plant hyperspectral reflectance data using measurements of the reflectance of 2151 individual wavelengths of light from the leaves of maize ( Zea mays ) plants harvested from 1658 field plots in a replicated field trial. A subset of autoencoder‐derived variables exhibited significant repeatability, indicating that a substantial proportion of the total variance in these variables was explained by difference between maize genotypes, while other autoencoder variables appear to capture variation resulting from changes in leaf reflectance between different batches of data collection. Several of the repeatable latent variables were significantly correlated with other traits scored from the same maize field experiment, including one autoencoder‐derived latent variable (LV8) that predicted plant chlorophyll content modestly better than a supervised model trained on the same data. In at least one case, genome‐wide association study hits for variation in autoencoder‐derived variables were proximal to genes with known or plausible links to leaf phenotypes expected to alter hyperspectral reflectance. In aggregate, these results suggest that an unsupervised, autoencoder‐based approach can identify meaningful and genetically controlled variation in high‐dimensional, high‐throughput phenotyping data and link identified variables back to known plant traits of interest.
Tross, Michael C.↗
Safe and Robust Binary Classification and Fault Detection Using Reinforcement Learning
In this paper, we propose a learning-based method utilizing the Soft Actor-Critic (SAC) algorithm to train a binary Support Vector Machine (SVM) classifier. This classifier is designed to identify valid input spaces in high-dimensional, highly constrained systems while minimizing the total runtime of offline simulations. The simulations adapt their runtime based on the likelihood that a given training input will be informative to the classifier. Furthermore, we introduce a method for using the trained SAC model to predict whether a desired system input is likely to violate constraints, along with a technique to adjust the input as necessary. Additionally, we explore the potential of this model to detect faults or adversarial attacks within the system. The effectiveness of our approach is demonstrated through various simulations of challenging classification problems and a constrained quadrotor model.
Netter, Josh [Georgia Institute of Technology, Atl↗
Graph Neural Networks for Particle Reconstruction in High Energy Physics detectors
Pattern recognition problems in high energy physics are notably different from traditional machine learning applications in computer vision. Reconstruction algorithms identify and measure the kinematic properties of particles produced in high energy collisions and recorded with complex detector systems. Two critical applications are the reconstruction of charged particle trajectories in tracking detectors and the reconstruction of particle showers in calorimeters. These two problems have unique challenges and characteristics, but both have high dimensionality, high degree of sparsity, and complex geometric layouts. Graph Neural Networks (GNNs) are a relatively new class of deep learning architectures which can deal with such data effectively, allowing scientists to incorporate domain knowledge in a graph structure and learn powerful representations leveraging that structure to identify patterns of interest. In this work we demonstrate the applicability of GNNs to these two diverse particle reconstruction problems.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DNTTD (Distributed Non-Negative Tensor Train Decomposition)
The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exa flops also come the extra-large high-dimensional data generated by high performance computing. High-dimensional data is presented as multidimensional arrays, aka tensors. The presence of latent (not directly observable) structures in the tensor allows a unique representation and compression of the data by classical tensor factorization techniques. However, the classical tensor methods are not always stable or they can be exponential in their memory requirements, which makes them not suitable for high-dimensional tensors. Tensor train (TT) is a state-of-the-art tensor network introduced for factorization of high-dimensional tensors. TT transforms the initial high-dimensional tensor in a network of three-dimensional tensors that requires only a linear storage. Many real-world data, such as, density, temperature, population, probability, etc., are non-negative and for an easy interpretation, the algorithms preserving non-negativity are preferred. Here, we introduce a distributed non-negative tensor-train and demonstrate its scalability and the compression on synthetic and real world big datasets.
Bhattarai, Manish↗
Affinity propagation clustering of full-field, high-spatial-dimensional measurements for robust output-only modal identification: A proof-of-concept study
Determination of the model order is a challenging problem in system identification, especially in output-only or operational modal identification where some modes are weakly excited. While existing methods such as the stabilization diagram method (spectral information) are effective, they do not scale to high-dimensional data, which is usually needed for high-fidelity characterization of structural dynamics and has been made available in the emerging full-field measurement techniques using optical methods such as photogrammetry and laser vibrometers. In this proof-of-concept study we present a new non-parametric, data-driven approach for robust output-only identification of high-spatial-dimensional modal parameters of basic structures by efficiently processing and interactively exploiting the full-field measurement (i.e., very dense spatial measurement points). Specifically, we first over-estimate the system model once, producing a pool of candidate modes associated with their modal frequencies and full-field, high-spatial-dimensional mode shapes. This is accomplished by a data-driven method termed affinity propagation clustering (APC), where the active clusters, which are the active modes in our formulations, emerge from the "message-passing" procedure and does not require a pre-determination of the cluster number (mode or model order). Next, rather than using the spectral information to distinguish the physical and spurious modes in the stabilization diagram method, we exploit and visualize the spatial, full-field mode shape associated with each candidate mode to do so. We conduct extensive experiments on basic structural models with comparisons to a few existing methods. The results indicate that the new method is computationally efficient for identifying high-spatial-dimensional modal parameters, and robust to identify weak modes by exploiting the full-field measurement. We also discuss its applicability and limitations for structures with complex geometry (shapes).
42 ENGINEERING↗
Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning
The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.
Neural operator↗
Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference
This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.
97 MATHEMATICS AND COMPUTING↗
Convex relaxation for Fokker–Planck equation
We propose an approach to directly estimate the moments or marginals for a high-dimensional equilibrium distribution in statistical mechanics by solving the high-dimensional Fokker–Planck equation in terms of low-order cluster moments or marginals. With this approach, we bypass the exponential complexity of estimating the full high-dimensional distribution and directly solve the simplified partial differential equations for low-order moments/marginals. Moreover, the proposed moment/marginal relaxation is fully convex and can be solved via off-the-shelf solvers. We further propose a time-dependent version of the convex programs to study non-equilibrium dynamics. In a specific setting, we show the proposed method can recover a mean-field-type equilibrium density. Numerical results are provided to demonstrate the performance of the proposed algorithm for high-dimensional systems.
Chen, Yian↗
Broadening the scope of high structural dimensionality nanomaterials using pyridine-based curcuminoids
We present a new heteroditopic ligand (3pyCCMoid) that contains the typical skeleton of a curcuminoid (CCMoid) decorated with two 3-pyridyl groups. The coordination of 3pyCCMoid with ZnII centres results in a set of novel coordination polymers (CPs) that display different architectures and dimensionalities (from 1D to 3D). Our work analyses how synthetic methods and slight changes in the reaction conditions affect the formation of the final materials. Great efforts have been devoted toward understanding the coordination entities that provide high dimensional systems, with emphasis on the characterization of 2D materials, including analyses of different types of substrates, stability and exfoliation in water. Here, we foresee the great use of CCMoids in the field of CPs and emphasize 3pyCCMoid as a new-born linker.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
In Situ Data Analysis Through Physics-informed Tensor Decompositions (LDRD Final Report)
We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of the model data and functions of the simulation data. This novel approach to dimensionality reduction of simulation data provides a means of directly incorporating quantities of interests and invariants associated with conservation principles associated with the simulation data into the low-dimensional model, thus enabling more accurate analysis of the simulation without requiring access to the full set of high-dimensional data. Computational results of applying this approach to two standard low-rank tensor decompositions of data arising from simulation of combustion and plasma physics are presented.
97 MATHEMATICS AND COMPUTING↗
MENT-Flow: maximum-entropy phase space tomography using normalizing flows
Generative models can be trained to reproduce low-dimensional projections of high-dimensional phase space distributions. Normalizing flows are generative models that parameterize invertible transformations, allowing exact probability density evaluation and sampling. Consequently, flows are unbiased entropy estimators and could be used to solve the high-dimensional maximum-entropy tomography (MENT) problem. In this work, we evaluate a flow-based MENT solver (MENT-Flow) against exact maximum-entropy solutions and Minerbo's iterative MENT algorithm in two dimensions.
Hoover, Austin↗
Measurements at peak operational beam current in the SNS beam test facility
Work at the SNS beam test facility has focused on high dimensional and high dynamic range measurements of the medium energy (2.5 Mev) beam distribution. This is motivated by the need to understand and predict beam losses down to one-part-per-million. The initial demonstration of full-and-direct 6D phase space measurement was done at a current of 40 mA transported through the RFQ. Since that demonstration, more detailed studies have been performed at lower transported currents (in the range 30 mA and below). This is due to a hardware change - recent runs utilize the original SNS RFQ, which after a decade of service in the SNS achieves transmission significantly below design (50-60%, vs >80%). A short run in 2023 with a newly-commissioned RFQ enables maximum transmission. Preliminary results from beam distribution measurements during this run are discussed.
Ruisard, Kiersten↗
Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition
This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.
Gaussian random fields↗
From microbial diversity to functional potential using dimensionality reduction
The high dimensionality of microbial diversity data from ‘omics observations can be reduced using Machine Learning, with many recent studies showcasing ML utility for exploratory ecological feature finding and process prediction. Here, we compare the Self Organizing Map (SOM) dimensionality reduction method to the well-documented sample-based Principal Coordinate Analysis (PCoA) and taxa-based Weighted Gene Correlation Network Analysis (WGCNA) using near daily 16S rRNA gene amplicon sequencing data from the 2019 to 2020 MOSAiC International Arctic Drift Expedition. We then map k-means clustering outputs from each method to available metagenomes, extracting functionally distinct seasonal microbial ecotypes in the surface Arctic Ocean. Our results indicate the SOM method better represented expected seasonal transitions and identified a greater number of metabolically distinct functional groups than the more traditional PCoA ordination. Ultimately, we identified four community ecotypes with distinct taxonomic and functional cut-offs driven by seasonality, water mass, and substrate turnover, highlighting the importance of succession in functional diversity for the central Arctic Ocean. These results reinforce ML dimensionality reduction as a meaningful translator in the mining of historical amplicon datasets to address modern mechanistic questions and potentially provide ’omics informed ecotype diversity to leverage in mechanistic biogeochemical models.
Arctic Ocean↗