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At least 271 records · Page 15

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗

Domain Knowledge Guided Bayesian Optimization For Autonomous Alignment Of Complex Scientific Instruments

Bayesian Optimization (BO) is a powerful tool for optimizing complex non-linear systems. However, its performance degrades in high-dimensional problems with tightly coupled parameters and highly asymmetric objective landscapes, where rewards are sparse. In such needle-in-a-haystack scenarios, even advanced methods like trust-region BO (TurBO) often lead to unsatisfactory results. We propose a domain knowledge guided Bayesian Optimization approach, which leverages physical insight to fundamentally simplify the search problem by transforming coordinates to decouple input features and align the active subspaces with the primary search axes. We demonstrate this approach's efficacy on a challenging 12-dimensional, 6-crystal Split-and-Delay optical system, where conventional approaches, including standard BO, TuRBO and multi-objective BO, consistently led to unsatisfactory results. When combined with an reverse annealing exploration strategy, this approach reliably converges to the global optimum. The coordinate transformation itself is the key to this success, significantly accelerating the search by aligning input co-ordinate axes with the problem's active subspaces. As increasingly complex scientific instruments, from large telescopes to new spectrometers at X-ray Free Electron Lasers are deployed, the demand for robust high-dimensional optimization grows. Our results demonstrate a generalizable paradigm: leveraging physical insight to transform high-dimensional, coupled optimization problems into simpler representations can enable rapid and robust automated tuning for consistent high performance while still retaining current optimization algorithms.

FOS: Computer and information sciences↗

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

97 MATHEMATICS AND COMPUTING↗

Improving near real-time precipitation estimation using a U-Net convolutional neural network and geographical information

Reliable near real-time precipitation estimates are essential for monitoring and managing of natural disasters such as floods. Quality of inputs and capability of the retrieval algorithm are two important aspects for developing satellite-based precipitation datasets. Most retrieval algorithms utilize infrared (IR) information as their input due to its fine spatiotemporal resolution and near-instantaneous availability. However, their sole reliance on IR information limits their capability to learn different mechanisms of precipitation during training, resulting in less accurate estimates. Moreover, recent advances in the field of machine learning offer attractive opportunities to improve the precipitation retrieval algorithms. This work investigates the effectiveness of adding geographical information (i.e. latitude and longitude) to IR information and the application of a U-Net-based convolutional neural network for improving the accuracy of retrieval algorithms. This research suggests that applying an appropriate CNN architecture on geographical and IR information provides an opportunity to improve the satellite-based precipitation products.

42 ENGINEERING↗

JPL basic research review

Current status, projected goals, and results of 49 research and advanced development programs at the Jet Propulsion Laboratory are reported in abstract form. Areas of investigation include: aerodynamics and fluid mechanics, applied mathematics and computer sciences, environment protection, materials science, propulsion, electric and solar power, guidance and navigation, communication and information sciences, general physics, and chemistry.

Source record↗

A universal variational quantum eigensolver for non-Hermitian systems

Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional $$O(log_{2}{N})$$ O ( l o g 2 N ) quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications.

97 MATHEMATICS AND COMPUTING↗

Coarse-grain cluster analysis of tensors with application to climate biome identification

A tensor provides a concise way to codify the interdependence of complex data. Treating a tensor as a d-way array, each entry records the interaction between the different indices. Clustering provides a way to parse the complexity of the data into more readily understandable information. Clustering methods are heavily dependent on the algorithm of choice, as well as the chosen hyperparameters of the algorithm. However, their sensitivity to data scales is largely unknown. In this work, we apply the discrete wavelet transform to analyze the effects of coarse-graining on clustering tensor data. We are particularly interested in understanding how scale affects clustering of the Earth's climate system. The discrete wavelet transform allows classification of the Earth's climate across a multitude of spatial-temporal scales. The discrete wavelet transform is used to produce an ensemble of classification estimates, as opposed to a single classification. Each element of the ensemble is a clustering at a different spatial-temporal scale. Information theoretic approaches are used to identify important scale lengths in clustering the L15 Climate Datset. We also discover a sub-collection of the ensemble that spans the majority of the variance observed, allowing for efficient consensus clustering techniques that can be used to identify climate biomes.

54 ENVIRONMENTAL SCIENCES↗

Developing Bloom Filters for Web Archives’ Holdings (Final Project Report)

The main goal of the project was to develop a framework for web archives to create Bloom filters based on their holdings of archived web resources. A Bloom filter (BF) is a data structure that, in our scenario, contains hash values of all (or a subset of) URLs, of which an archive has one or more archival copies. Two main use cases fall in scope for this project and are supported by a BF implementation: 1) Sharing of an archive’s holdings (URLs) and 2) Querying the holdings of one or more archives. Since URL strings are hashed before ingested into the BF, the index of an archive is not shared in plain text when the BF is shared with trusted parties. On the other hand, a BF implementation does allow queries for a URL to confirm if an archive indeed has one or more archival copies of that URL. This collaborative project between Los Alamos National Laboratory (LANL) and the Croatian Web Archive (HAW), from the National and University Library in Zagreb (NSK), developed by NSK and University of Zagreb University Computing Center SRCE), aimed at developing software to create BFs, evaluate the scalability of the approach, pilot a search service based on BFs, and design a framework for archives to share their filters with trusted parties. In the remainder of this document, we will report on the work completed with respect to the individual deliverables, outline aspects of future work, and conclude with our recommendations for the use of BFs for the web archiving community.

97 MATHEMATICS AND COMPUTING↗

The Influence of Visual Provenance Representations on Strategies in a Collaborative Hand-off Data Analysis Scenario

Conducting data analysis tasks rarely occur in isolation. Especially in intelligence analysis scenarios where different experts contribute knowledge to a shared understanding, members must communicate how insights develop to establish common ground among collaborators. The use of provenance to communicate analytic sensemaking carries promise by describing the interactions and summarizing the steps taken to reach insights. Yet, no universal guidelines exist for communicating provenance in different settings. Our work here focuses on the presentation of provenance information and the resulting conclusions reached and strategies used by new analysts. In an open-ended, 30-minute, textual exploration scenario, we qualitatively compare how adding different types of provenance information (specifically data coverage and interaction history) affects analysts' confidence in conclusions developed, propensity to repeat work, filtering of data, identification of relevant information, and typical investigation strategies. We see that data coverage (i.e., what was interacted with) provides provenance information without limiting individual investigation freedom. On the other hand, while interaction history (i.e., when something was interacted with) does not significantly encourage more mimicry, it does take more time to comfortably understand, as represented by less confident conclusions and less relevant information-gathering behaviors. In conclusion, our results contribute empirical data towards understanding how provenance summarizations can influence analysis behaviors.

97 MATHEMATICS AND COMPUTING↗

Kinetics-Informed Neural Networks

Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize feed-forward artificial neural networks as basis functions to solve ordinary differential equations (ODEs) constrained by differential algebraic equations (DAEs) that describe microkinetic models (MKMs). We present an algebraic framework for the mathematical description and classification of reaction networks, types of elementary reaction, and chemical species. Under this framework, we demonstrate that the simultaneous training of neural nets and kinetic model parameters in a regularized multi-objective optimization setting leads to the solution of the inverse problem through the estimation of kinetic parameters from synthetic experimental data. We analyze a set of scenarios to establish the extent to which kinetic parameters can be retrieved from transient kinetic data, and assess the robustness of the methodology with respect to statistical noise. Furthermore, this approach to inverse kinetic ODEs can assist in the elucidation of reaction mechanisms based on transient data.

36 MATERIALS SCIENCE↗

Maximizing efficiency of dataset compression for machine learning potentials with information theory

Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets improve model accuracy and generalization but are computationally expensive to produce and train on, while smaller datasets risk discarding rare but important atomic environments and compromising MLIP accuracy/reliability. Here, we develop an information-theoretical framework to quantify the efficiency of dataset compression methods and propose an algorithm that maximizes this efficiency. By framing atomistic dataset compression as an instance of the minimum set cover (MSC) problem over atom-centered environments, our method identifies the smallest subset of structures that contains as much information as possible from the original dataset while pruning redundant information. The approach is extensively demonstrated on the GAP-20 and TM23 datasets and validated on 64 varied datasets from the ColabFit repository. Across all cases, MSC consistently retains outliers, preserves dataset diversity, and reproduces the long-tail distributions of forces even at high compression rates, outperforming other subsampling methods. Furthermore, MLIPs trained on MSC-compressed datasets exhibit reduced error for out-of-distribution data even in low-data regimes. We explain these results using an outlier analysis and show that such quantitative conclusions could not be achieved with conventional dimensionality reduction methods. The algorithm is implemented in the open-source QUESTS package and can be used for several tasks in atomistic modeling, from data subsampling, outlier detection, and training improved MLIPs at a lower cost.

36 MATERIALS SCIENCE↗

Support for the Core Research Activities and Studies of the Computer Science and Telecommunications Board (DE-SC0020446 Final Technical Report)

Supported the core operations of the National Academies' Computer Science and Telecommunications Board (CSTB). Helped support planning and conducting of board meetings, identification of priority topics in computer science and other areas of computing and communications technologies, and oversight for CSTB's portfolio of studies and convenings. Activities shaped and overseen included: a workshop on Al for scientific discovery; collaborative work with other Academies units on a study on foundational research gaps and future directions for digital twins; a study on current capabilities, future prospects, and governance of facial recognition technologies, a study on post- exascale computing; a study on fostering responsible computing research, collaborative work with other Academies units on automated research workflows for accelerated scientific discovery; a study on meeting federal cybersecurity workforce needs, and a study of the ecosystem driving information technology innovation.

97 MATHEMATICS AND COMPUTING↗

Educational NASA Computational and Scientific Studies (enCOMPASS)

Educational NASA Computational and Scientific Studies (enCOMPASS) is an educational project of NASA Goddard Space Flight Center aimed at bridging the gap between computational objectives and needs of NASA's scientific research, missions, and projects, and academia's latest advances in applied mathematics and computer science. enCOMPASS achieves this goal via bidirectional collaboration and communication between NASA and academia. Using developed NASA Computational Case Studies in university computer science/engineering and applied mathematics classes is a way of addressing NASA's goals of contributing to the Science, Technology, Education, and Math (STEM) National Objective. The enCOMPASS Web site at http://encompass.gsfc.nasa.gov provides additional information. There are currently nine enCOMPASS case studies developed in areas of earth sciences, planetary sciences, and astrophysics. Some of these case studies have been published in AIP and IEEE's Computing in Science and Engineering magazines. A few university professors have used enCOMPASS case studies in their computational classes and contributed their findings to NASA scientists. In these case studies, after introducing the science area, the specific problem, and related NASA missions, students are first asked to solve a known problem using NASA data and past approaches used and often published in a scientific/research paper. Then, after learning about the NASA application and related computational tools and approaches for solving the proposed problem, students are given a harder problem as a challenge for them to research and develop solutions for. This project provides a model for NASA scientists and engineers on one side, and university students, faculty, and researchers in computer science and applied mathematics on the other side, to learn from each other's areas of work, computational needs and solutions, and the latest advances in research and development. This innovation takes NASA science and engineering applications to computer science and applied mathematics university classes, and makes NASA objectives part of the university curricula. There is great potential for growth and return on investment of this program to the point where every major university in the U.S. would use at least one of these case studies in one of their computational courses, and where every NASA scientist and engineer facing a computational challenge (without having resources or expertise to solve it) would use enCOMPASS to formulate the problem as a case study, provide it to a university, and get back their solutions and ideas.

Memarsadeghi, Nargess↗

A Visual Comparison of Silent Error Propagation

High-performance computing (HPC) systems play a critical role in facilitating scientific discoveries. Their scale and complexity (e.g., the number of computational units and software stack) continue to grow as new systems are expected to process increasingly more data and reduce computing time. However, with more processing elements, the probability that these systems will experience a random bit-flip error that corrupts a program's output also increases, which is often recognized as silent data corruption. Analyzing the resiliency of HPC applications in extreme-scale computing to silent data corruption is crucial but difficult. An HPC application often contains a large number of computation units that need to be tested, and error propagation caused by error corruption is complex and difficult to interpret. Here, to accommodate this challenge, we propose an interactive visualization system that helps HPC researchers understand the resiliency of HPC applications and compare their error propagation. Our system models an application's error propagation to study a program's resiliency by constructing and visualizing its fault tolerance boundary. Coordinating with multiple interactive designs, our system enables domain experts to efficiently explore the complicated spatial and temporal correlation between error propagations. At the end, the system integrated a nonmonotonic error propagation analysis with an adjustable graph propagation visualization to help domain experts examine the details of error propagation and answer such questions as why an error is mitigated or amplified by program execution.

97 MATHEMATICS AND COMPUTING↗

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.

93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗