Fast multiplication of random dense matrices with sparse matrices
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms.
Demmel, James↗
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Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications
We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.
Barnafi, Nicolas [University of Chile, Santiago]↗
gLaSDI: Parametric physics-informed greedy latent space dynamics identification
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.
97 MATHEMATICS AND COMPUTING↗
A Data-Driven Pivot-Point-Based Time-Series Feeder Load Disaggregation Method
The load profile at a feeder-head is usually known to utility engineers while the nodal load profiles are not. However, the nodal load profiles are increasingly important for conducting time-series analysis in distribution systems. Therefore, in this paper, we present a pivot-point based, two-stage feeder load disaggregation algorithm using smart meter data. The two stages are load profile selection (LPS) and load profile allocation (LPA). In the LPS stage, a random load profile selection process is first executed to meet the load diversity requirement. Then, a few pairs of pivot points are selected as the matching targets. After that, a matching algorithm will run repetitively to select one load profile at a time for matching the reference load profile at the pivot points. In the LPA stage, the LPS selected load profiles are allocated to each load node on the feeder considering distribution transformer loading limits, load composition, and square-footage. The proposed method is validated using actual data collected in a North Carolina service area. Finally, simulation results show that the proposed method can generate a unique load shape for each load node while match the shape of their aggregated profile with the actual feeder head load profile.
42 ENGINEERING↗
A Hierarchical Feature-Based Methodology to Perform Cervical Cancer Classification
Prevention of cervical cancer could be performed using Pap smear image analysis. This test screens pre-neoplastic changes in the cervical epithelial cells; accurate screening can reduce deaths caused by the disease. Pap smear test analysis is exhaustive and repetitive work performed visually by a cytopathologist. This article proposes a workload-reducing algorithm for cervical cancer detection based on analysis of cell nuclei features within Pap smear images. We investigate eight traditional machine learning methods to perform a hierarchical classification. We propose a hierarchical classification methodology for computer-aided screening of cell lesions, which can recommend fields of view from the microscopy image based on the nuclei detection of cervical cells. We evaluate the performance of several algorithms against the Herlev and CRIC databases, using a varying number of classes during image classification. Results indicate that the hierarchical classification performed best when using Random Forest as the key classifier, particularly when compared with decision trees, k-NN, and the Ridge methods.
60 APPLIED LIFE SCIENCES↗
i- flow: High-dimensional integration and sampling with normalizing flows
In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijective mappings between two distributions. i-flow can also be used to sample random points according to complicated distributions in high dimensions. We compare i-flow to other algorithms for high-dimensional numerical integration and show that i-flow outperforms them for high dimensional correlated integrals. The i-flow code is publicly available on gitlab at https://gitlab.com/i-flow/i-flow.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Estimation of distributions via multilevel Monte Carlo with stratified sampling
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Characterizing and mitigating coherent errors in a trapped ion quantum processor using hidden inverses
Quantum computing testbeds exhibit high-fidelity quantum control over small collections of qubits, enabling performance of precise, repeatable operations followed by measurements. Currently, these noisy intermediate-scale devices can support a sufficient number of sequential operations prior to decoherence such that near term algorithms can be performed with proximate accuracy (like chemical accuracy for quantum chemistry problems). While the results of these algorithms are imperfect, these imperfections can help bootstrap quantum computer testbed development. Demonstrations of these algorithms over the past few years, coupled with the idea that imperfect algorithm performance can be caused by several dominant noise sources in the quantum processor, which can be measured and calibrated during algorithm execution or in post-processing, has led to the use of noise mitigation to improve typical computational results. Conversely, benchmark algorithms coupled with noise mitigation can help diagnose the nature of the noise, whether systematic or purely random. Here, we outline the use of coherent noise mitigation techniques as a characterization tool in trapped-ion testbeds. We perform model-fitting of the noisy data to determine the noise source based on realistic physics focused noise models and demonstrate that systematic noise amplification coupled with error mitigation schemes provides useful data for noise model deduction. Further, in order to connect lower level noise model details with application specific performance of near term algorithms, we experimentally construct the loss landscape of a variational algorithm under various injected noise sources coupled with error mitigation techniques. This type of connection enables application-aware hardware codesign, in which the most important noise sources in specific applications, like quantum chemistry, become foci of improvement in subsequent hardware generations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A mapped dataset of surface ocean acidification indicators in large marine ecosystems of the United States
Mapped monthly data products of surface ocean acidification indicators from 1998 to 2022 on a 0.25° by 0.25° spatial grid have been developed for eleven U.S. large marine ecosystems (LMEs). The data products were constructed using observations from the Surface Ocean CO 2 Atlas, co-located surface ocean properties, and two types of machine learning algorithms: Gaussian mixture models to organize LMEs into clusters of similar environmental variability and random forest regressions (RFRs) that were trained and applied within each cluster to spatiotemporally interpolate the observational data. The data products, called RFR-LMEs, have been averaged into regional timeseries to summarize the status of ocean acidification in U.S. coastal waters, showing a domain-wide carbon dioxide partial pressure increase of 1.4 ± 0.4 μatm yr -1 and pH decrease of 0.0014 ± 0.0004 yr -1 . RFR-LMEs have been evaluated via comparisons to discrete shipboard data, fixed timeseries, and other mapped surface ocean carbon chemistry data products. Regionally averaged timeseries of RFR-LME indicators are provided online through the NOAA National Marine Ecosystem Status web portal.
54 ENVIRONMENTAL SCIENCES↗
How Generalizable is a Machine-Learning Approach for Modeling Hub-Height Turbulence Intensity?
Hub-height turbulence intensity is essential for a variety of wind energy applications. However, simulating it is a challenging task. Simple analytical models have been proposed in the literature, but they all come with significant limitations. Even state-of-the-art numerical weather prediction models, such as the Weather Research and Forecasting model, currently struggle to predict hub-height turbulence intensity. Here, we propose a machine-learning-based approach to predict hub-height turbulence intensity from other hub-height and ground-level atmospheric measurements, using observations from the Perdigao field campaign and the Southern Great Plains atmospheric observatory. We consider a random forest regression model, which we validate first at the site used for training and then under a more robust round-robin approach, and compare its performance to a multivariate linear regression. The random forest successfully outperforms the linear regression in modeling hub-height turbulence intensity, with a normalized root-mean-square error as low as 0.014 when using 30-minute average data. In order to achieve such low root-mean-square error values, the knowledge of hub-height turbulence kinetic energy (which can instead be modeled in the Weather Research and Forecasting model) is needed. Interestingly, we find that the performance of the random forest generalizes well when considering a round-robin validation (i.e., when the algorithm is trained at one site such as Perdigao or Southern Great Plains) and then applied to model hub-height turbulence intensity at the other location.
17 WIND ENERGY↗
Metropolis-style random sampling of quantum gates for the estimation of low-energy observables
In this work, we propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there is an associated average energy. The sampling is done through an accept/reject Metropolis-style algorithm on the quantum gates of the circuit itself. Observables calculated under the canonical ensemble from these samples of circuits are extrapolated from higher energies to the ground state.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Uncertainty Quantification in Scientific ML
The intricate interactions between data sampling, model selection and the inherent randomness in complex systems strongly emphasize the need for a rigorous characterization of ML algorithms. In conventional statistics, uncertainty quantification (UQ) provides this characterization by measuring how accurately a model reflects the physical reality and by studying the impact of different error sources on the prediction.
97 MATHEMATICS AND COMPUTING↗
Predicting Elastic Constants of Refractory Complex Concentrated Alloys Using Machine Learning Approach
Refractory complex concentrated alloys (RCCAs) have drawn increasing attention recently owing to their balanced mechanical properties, including excellent creep resistance, ductility, and oxidation resistance. The mechanical and thermal properties of RCCAs are directly linked with the elastic constants. However, it is time consuming and expensive to obtain the elastic constants of RCCAs with conventional trial-and-error experiments. The elastic constants of RCCAs are predicted using a combination of density functional theory simulation data and machine learning (ML) algorithms in this study. The elastic constants of several RCCAs are predicted using the random forest regressor, gradient boosting regressor (GBR), and XGBoost regression models. Based on performance metrics R-squared, mean average error and root mean square error, the GBR model was found to be most promising in predicting the elastic constant of RCCAs among the three ML models. Additionally, GBR model accuracy was verified using the other four RHEAs dataset which was never seen by the GBR model, and reasonable agreements between ML prediction and available results were found. The present findings show that the GBR model can be used to predict the elastic constant of new RHEAs more accurately without performing any expensive computational and experimental work.
36 MATERIALS SCIENCE↗
Initial position optimization in molecular dynamics simulations for a Coulomb system
A new algorithm for molecular dynamics (MD) simulations is developed to optimize plasma particle distributions at given initial temperatures. By combining velocity scaling and reassignment, the method effectively eliminates the initial rise and oscillation in temperatures observed with randomly distributed positions. These rises and oscillations are undesired numerical artifacts observed in conventional plasma MD simulations, arising from unoptimized particle positions. The algorithm demonstrates temperature relaxation without initial rises or oscillations, as well as precise flow velocity relaxation, enabling accurate measurement of relaxation times. The code is accelerated using graphics processing units for parallel processing, enhancing the study of plasma dynamics. The proposed method for distributing physically valid particles in MD simulations enables accurate studies of intrinsic collision processes in plasmas, including the dynamics of strongly coupled plasmas, plasma–wave interactions, and transport phenomena in magnetized plasmas. The paper concludes with a discussion of potential applications and future enhancements to the algorithm.
Jo, Jawon (ORCID:0009000924193285)↗
Statistics of base polytopes in F-theory
We propose a new statistical ensemble of toric bases for elliptic Calabi-Yaus used in F-theory models, by focusing on only the convex hull of the base, i.e., the base polytope. This physically motivated coarse-graining greatly simplifies the combinatorial complexity of the part of the 4d F-theory landscape with toric bases. We develop a Monte Carlo approach that randomly samples the base polytopes within fixed boxes, with proper statistical weights. We first apply the algorithm to the set of 2d base polytopes, generating an enlarged set of toric 2d bases that include certain types of codimension-two (4,6) points, and we validate our approach against exact numbers. We then explore the set of 3d base polytopes which fit in a set of “maximal” 3d boxes, and estimate the total number of inequivalent 3d base polytopes to be 10 85 –10 90 . We provide statistical data such as the distribution of non-Higgsable gauge groups on these bases. Amusingly, a similar method can also be applied to generate reflexive polytopes in various dimensions. In both the reflexive and base polytope cases, the number of relevant polytopes obeys a Gaussian distribution as a function of the number of vertices, which can be understood in terms of other results on random polytopes in the math literature.
Differential and algebraic geometry↗
Mapping Stochastic Devices to Probabilistic Algorithms
Probabilistic and Bayesian neural networks have long been proposed as a method to incorporate uncertainty about the world (both in training data and operation) into artificial intelligence applications. One approach to making a neural network probabilistic is to leverage a Monte Carlo sampling approach that samples a trained network while incorporating noise. Such sampling approaches for neural networks have not been extensively studied due to the prohibitive requirement of many computationally expensive samples. While the development of future microelectronics platforms that make this sampling more efficient is an attractive option, it has not been immediately clear how to sample a neural network and what the quality of random number generation should be. This research aimed to start addressing these two fundamental questions by examining basic “off the shelf” neural networks can be sampled through a few different mechanisms (including synapse “dropout” and neuron “dropout”) and examine how these sampling approaches can be evaluated both in terms of evaluating algorithm effectiveness and the required quality of random numbers.
97 MATHEMATICS AND COMPUTING↗
Spoofing Cross-Entropy Measure in Boson Sampling
Cross-entropy (XE) measure is a widely used benchmark to demonstrate quantum computational advantage from sampling problems, such as random circuit sampling using superconducting qubits and boson sampling (BS). We present a heuristic classical algorithm that attains a better XE than the current BS experiments in a verifiable regime and is likely to attain a better XE score than the near-future BS experiments in a reasonable running time. The key idea behind the algorithm is that there exist distributions that correlate with the ideal BS probability distribution and that can be efficiently computed. The correlation and the computability of the distribution enable us to postselect heavy outcomes of the ideal probability distribution without computing the ideal probability, which essentially leads to a large XE. Our method scores a better XE than the recent Gaussian BS experiments when implemented at intermediate, verifiable system sizes. Much like current state-of-the-art experiments, we cannot verify that our spoofer works for quantum-advantage-size systems. However, we demonstrate that our approach works for much larger system sizes in fermion sampling, where we can efficiently compute output probabilities. Finally, we provide analytic evidence that the classical algorithm is likely to spoof noisy BS efficiently.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗