DFTpy : An efficient and object-oriented platform for orbital-free DFT simulations
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Chemistry↗
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Results for “Mathematical Computing”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Can machine learning accelerate process understanding and decision‐relevant predictions of river water quality?
Abstract The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub‐daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state‐of‐the art applications of ML for water quality models and discuss opportunities to improve the use of ML with emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model‐data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge‐guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision‐relevant predictions of riverine water quality.
54 ENVIRONMENTAL SCIENCES↗
Optimal PMU design based on sampling model and sensitivity analysis
The precise measurements of the synchrophasor and frequency from phasor measurement units (PMUs) are widely used in power grid applications. With the improvement of the technique, applications always require stable dynamic performance and higher accuracy for the synchrophasor and frequency measurements, which is challenging for PMU development. To evaluate the contribution of PMU hardware to measurement accuracy, this paper proposes a general-purpose sampling model to analyze the measurement error. In the proposed sampling model, a strict mathematical derivation is derived, where its error is purely determined by the parameters of the PMU hardware. The sensitivity analysis is carried out by three methods, including mathematical analysis, computer simulation, and variance-based sensitivity analysis. Through the sensitivity analysis, this paper establishes the systematic formulation and the inclusion of synchrophasor, frequency, and ROCOF. Experimental results based on the real-world testbench involving distribution-level PMUs match the mathematical analysis conclusion, which verifies the correctness of the general-purpose sampling model. Furthermore, a strategy for the optimal PMU design is proposed, which could guide PMU design in the future.
42 ENGINEERING↗
PNNL Strategic Goods Testbed: A Data Library for Illicit Nuclear Trafficking
Pacific Northwest National Laboratory (PNNL) has put significant effort into nonproliferation activities as an institution, both in terms of the classical nuclear material focused approach and in the examination of other strategic goods necessary to implement a nuclear program. To assist in these efforts, several projects in the Analysis in Motion (AIM) and Signature Discovery (SDI) Initiatives at PNNL are developing machine learning methodology for human-computer interaction in real time environments to assist analysts in this domain. All of these technical projects require access to data – whether it is in terms of detector data, shipping records, financial information, company relations, or other communications. The first question that mathematical and computational researchers come up with when asked to build analyst assist or automated tools is “What does the data look like? ” They become frustrated when basic questions like this can not be easily answered and this can have the effect of pushing researchers away from the nuclear trafficking domain, especially in strategic commodity and export control areas where data sets can not easily be generated through standard experimental techniques. For small projects that are building a proof of concept for their methodology, obtaining this data can be arduous and expensive. To relieve the burden of data collection from these projects and grow a lab-wide capability, the Strategic Goods Testbed Team has taken over data collection and placed subscriptions and access to flat data files in a centralized location so that all projects can benefit from these items. We have collected shipping data in the form of PIERS records, judicial information about export control cases, NAC data on the nuclear fuel industry, and financial data from Dun and Bradstreet and our data sets are continuing to expand. With a single access agreement, researchers in data-mining and other fields can utilize all of the records that have been downloaded, make requests through subscription services, and interact with other researchers through our interface. Our testbed team provides more than a simply static repository by working with researchers to refine their data needs and insure data quality as well as quantity. We are currently working with laboratory and initiative specific management to examine effective ways for continuing data growth and sustainability.
data capability↗
Explainable and trustworthy artificial intelligence for correctable modeling in chemical sciences
Data science has primarily focused on big data, but for many physics, chemistry, and engineering applications, data are often small, correlated and, thus, low dimensional, and sourced from both computations and experiments with various levels of noise. Typical statistics and machine learning methods do not work for these cases. Expert knowledge is essential, but a systematic framework for incorporating it into physics-based models under uncertainty is lacking. Here, we develop a mathematical and computational framework for probabilistic artificial intelligence (AI)–based predictive modeling combining data, expert knowledge, multiscale models, and information theory through uncertainty quantification and probabilistic graphical models (PGMs). We apply PGMs to chemistry specifically and develop predictive guarantees for PGMs generally. Our proposed framework, combining AI and uncertainty quantification, provides explainable results leading to correctable and, eventually, trustworthy models. The proposed framework is demonstrated on a microkinetic model of the oxygen reduction reaction.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Stable vacua with realistic phenomenology and cosmology in heterotic M-theory satisfying Swampland conjectures
We recently described a protocol for computing the potential energy in heterotic M-theory for the dilaton, complex structure and Kähler moduli. This included the leading order non-perturbative contributions to the complex structure, gaugino condensation and worldsheet instantons assuming a hidden sector that contains an anomalous U(1) structure group embedded in E8. In this paper, we elucidate, in detail, the mathematical and computational methods required to utilize this protocol. These methods are then applied to a realistic heterotic M-theory model, the B – L MSSM, whose observable sector is consistent with all particle physics requirements. Within this context, it is shown that the dilaton and universal moduli can be completely stabilized at values compatible with every phenomenological and mathematical constraint — as well as with ΛCDM cosmology. We also show that the heterotic M-theory vacua are consistent with all well-supported Swampland conjectures based on considerations of string theory and quantum gravity, and we discuss the implications of dark energy theorems for compactified theories.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Residuals-based distributionally robust optimization with covariate information
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.
97 MATHEMATICS AND COMPUTING↗
Space-Split Algorithm for Sensitivity Analysis of Discrete Chaotic Systems With Multidimensional Unstable Manifolds
Accurate approximations of the change of a system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing the linear response of chaotic dynamical systems. In this paper, we propose an algorithm for sensitivity analysis of discrete chaos with an arbitrary number of positive Lyapunov exponents. We combine the concept of perturbation space-splitting, which regularizes Ruelle's original expression, together with measure-based parameterization of the expanding subspace. We use these tools to rigorously derive trajectory-following recursive relations that converge exponentially fast, and construct a memory-efficient Monte Carlo scheme for derivatives of the output statistics. Thanks to the regularization and lack of simplifying assumptions on the system's behavior, our method is immune to the common problems of other popular methods such as the exploding tangent solutions and unphysical shadowing directions. Here, we provide a ready-to-use algorithm, analyze its complexity, and demonstrate several numerical examples of sensitivity computation using physically-inspired low-dimensional systems.
97 MATHEMATICS AND COMPUTING↗
Use of comparative genomics approaches to characterize interspecies differences in response to environmental chemicals: Challenges, opportunities, and research needs
A critical challenge for environmental chemical risk assessment is the characterization and reduction of uncertainties introduced when extrapolating inferences from one species to another. The purpose of this article is to explore the challenges, opportunities, and research needs surrounding the issue of how genomics data and computational and systems level approaches can be applied to inform differences in response to environmental chemical exposure across species. We propose that the data, tools, and evolutionary framework of comparative genomics be adapted to inform interspecies differences in chemical mechanisms of action. We compare and contrast existing approaches, from disciplines as varied as evolutionary biology, systems biology, mathematics, and computer science, that can be used, modified, and combined in new ways to discover and characterize interspecies differences in chemical mechanism of action which, in turn, can be explored for application to risk assessment. We consider how genetic, protein, pathway, and network information can be interrogated from an evolutionary biology perspective to effectively characterize variations in biological processes of toxicological relevance among organisms. We conclude that comparative genomics approaches show promise for characterizing interspecies differences in mechanisms of action, and further, for improving our understanding of the uncertainties inherent in extrapolating inferences across species in both ecological and human health risk assessment. To achieve long-term relevance and consistent use in environmental chemical risk assessment, improved bioinformatics tools, computational methods robust to data gaps, and quantitative approaches for conducting extrapolations across species are critically needed. Specific areas ripe for research to address these needs are recommended.
60 APPLIED LIFE SCIENCES↗
Latent Twins
Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical partial differential equations (PDEs), dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With Latent Twins, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ordinary differential equations (ODEs) and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with deep operator network and forecasts with a four-dimensional variational method baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.
Latent Twins↗
Characterization and Optimization of the Fitting of Quantum Correlation Functions
This case study presents a characterization and optimization of an application code for extracting parton distribution functions from high energy electron-proton scattering data. Profiling this application code reveals that the phase-space density computation accounts for 93% of the overall execution time for a single iteration on a single core. When executing multiple iterations in parallel on a multicore system, the application spends 78% of its overall execution time idling due to load imbalance. We address these issues by first transforming the application code from Python to C++ and then tackling the application load imbalance via a hybrid scheduling strategy that combines dynamic and static scheduling. These techniques result in a 62% reduction in CPU idle time and a 2.46x speedup in overall execution time per node. In addition, the typically enabled power-management mechanisms in supercomputers (e.g., AMD Turbo Core, Intel Turbo Boost, and RAPL) can significantly impact intra-node scalability when more than 50% of the CPU cores are used. This finding underscores the importance of understanding system interactions with power management, as they can adversely impact application performance, and highlights the necessity of intra-node scaling tests to identify performance degradation that inter-node scaling tests might otherwise overlook.
Chuang, Pi-Yueh [Virginia Tech,Dept. of Computer S↗
buhito
buhito is a Python library for graph analysis and machine learning. Graphs can represent networks with objects as nodes and their relationships as edges. buhito focuses on graphlet methods that study graphs through enumerating their component subgraphs to enable interpretable and fast models of complex systems. The package provides tools for different algorithmic designs for computing, analyzing, and applying graphlets to research problems such as machine learning, data compression, and anomaly detection in graph-structured data. A central feature is performing decomposition data analysis on graphs for machine learning models. Implemented in Python and built upon open-source scientific libraries such as NetworkX, NumPy, and SciPy, buhito provides high-performance methods for researchers exploring the mathematical and computational foundations of graphlet analysis applicable to systems of different sizes.
Pimonova, Yulia↗
A Peptide-Based Method for 13C Metabolic Flux Analysis in Microbial Communities
The study of intracellular metabolic fluxes and inter-species metabolite exchange for microbial communities is of crucial importance to understand and predict their behaviour. The most authoritative method of measuring intracellular fluxes, 13C Metabolic Flux Analysis (13C MFA), uses the labeling pattern obtained from metabolites (typically amino acids) during 13C labeling experiments to derive intracellular fluxes. However, these metabolite labeling patterns cannot easily be obtained for each of the members of the community. Here we propose a new type of 13C MFA that infers fluxes based on peptide labeling, instead of amino acid labeling. The advantage of this method resides in the fact that the peptide sequence can be used to identify the microbial species it originates from and, simultaneously, the peptide labeling can be used to infer intracellular metabolic fluxes. Peptide identity and labeling patterns can be obtained in a high-throughput manner from modern proteomics techniques. We show that, using this method, it is theoretically possible to recover intracellular metabolic fluxes in the same way as through the standard amino acid based 13C MFA, and quantify the amount of information lost as a consequence of using peptides instead of amino acids. We show that by using a relatively small number of peptides we can counter this information loss. We computationally tested this method with a well-characterized simple microbial community consisting of two species.
59 BASIC BIOLOGICAL SCIENCES↗
Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification
We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.
Autoencoders↗
A hybrid computational strategy to address WGS variant analysis in >5000 samples
Abstract Background The decreasing costs of sequencing are driving the need for cost effective and real time variant calling of whole genome sequencing data. The scale of these projects are far beyond the capacity of typical computing resources available with most research labs. Other infrastructures like the cloud AWS environment and supercomputers also have limitations due to which large scale joint variant calling becomes infeasible, and infrastructure specific variant calling strategies either fail to scale up to large datasets or abandon joint calling strategies. Results We present a high throughput framework including multiple variant callers for single nucleotide variant (SNV) calling, which leverages hybrid computing infrastructure consisting of cloud AWS, supercomputers and local high performance computing infrastructures. We present a novel binning approach for large scale joint variant calling and imputation which can scale up to over 10,000 samples while producing SNV callsets with high sensitivity and specificity. As a proof of principle, we present results of analysis on Cohorts for Heart And Aging Research in Genomic Epidemiology (CHARGE) WGS freeze 3 dataset in which joint calling, imputation and phasing of over 5300 whole genome samples was produced in under 6 weeks using four state-of-the-art callers. The callers used were SNPTools, GATK-HaplotypeCaller, GATK-UnifiedGenotyper and GotCloud. We used Amazon AWS, a 4000-core in-house cluster at Baylor College of Medicine, IBM power PC Blue BioU at Rice and Rhea at Oak Ridge National Laboratory (ORNL) for the computation. AWS was used for joint calling of 180 TB of BAM files, and ORNL and Rice supercomputers were used for the imputation and phasing step. All other steps were carried out on the local compute cluster. The entire operation used 5.2 million core hours and only transferred a total of 6 TB of data across the platforms. Conclusions Even with increasing sizes of whole genome datasets, ensemble joint calling of SNVs for low coverage data can be accomplished in a scalable, cost effective and fast manner by using heterogeneous computing platforms without compromising on the quality of variants.
59 BASIC BIOLOGICAL SCIENCES↗