Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Algorithmic differentiation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Towards a Quantum Algorithm for the Incompressible Nonlinear Navier-Stokes Equations

In this work, we present novel concepts for quantum algorithms to solve transient, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the incompressible Navier-Stokes equations as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts solving nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. We propose a new framework based on matrix product states (MPSs) and matrix product operators (MPOs), in addition to the Krylov subspace methods. For example, the solution variables of the Navier-Stokes equations are represented by MPSs, and the linear and nonlinear terms are processed by MPOs. The time evolution of the operators is attained by a fast-forwarding algorithm using Krylov subspace methods. Furthermore, we discuss various techniques for efficient encoding of MPSs, measurement reduction for MPOs, and use of tensor operations to treat multi-variate, multi-physics characteristics of Navier-Stokes.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2023

Using machine learning to predict the correlation of spectra using SDSS magnitudes as an improvement to the Locus Algorithm

The Locus Algorithm is a new technique to improve the quality of differential photometry by optimising the choices of reference stars. At the heart of this algorithm is a routine to assess how good each potential reference star is by comparing its SDSS magnitude values to those of the target star. In this way, the difference in wavelength-dependent effects of the Earth’s atmospheric scattering between target and reference can be minimised. This paper sets out a new way to estimate the quality of each reference star using machine learning. A random subset of stars from SDSS with spectra was chosen. For each one, a suitable reference star, also with a spectrum, was chosen. The correlation between the two spectra in the SDSS r band (between 550 nm and 700 nm) was taken to be the gold-standard measure of how well they match up for differential photometry. The five SDSS magnitude values for each of these stars were used as predictors. A number of supervised machine learning models were constructed on a training set of the stars and were each evaluated on a testing set. The model using Support Vector Regression had the best performance of these models. It was then tested on a final, hold-out, validation set of stars to get an unbiased measure of its performance. With an R 2 of 0.62, the SVR model presents enhanced performance for the Locus Algorithm technique.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Performance and Feature Improvements in Parareal-based Power System Dynamic Simulation

In recent years, a novel Parareal-based approach has been developed for fast transient simulations of large power system interconnections. Parareal belongs to the class of Parallel-in-time algorithms for solution of systems of differential-algebraic equations in parallel over an interval of time. The selection of a reasonably fast and accurate coarse solution is crucial to improve the performance of Parareal algorithm. Semi-analytical solution methods are one promising approach to achieve this goal. They have been investigated, and some preliminary results are presented here. In addition, Parareal-based simulator has been expanded to enable co-simulation with OpenDSS, a widely used open-source distribution system simulator. Preserving the parallel nature of the Parareal approach and taking advantage of the parallel capabilities of the latest versions of OpenDSS, each distribution system can be solved in their entirety on different processors in parallel within the main Parareal simulator. This paper also presents the structure of the transmission and distribution co-simulation and some results with different dynamic models of inverter-based resources in the distribution systems.

Park, Byungkwon↗
DOE OSTI2020

The Locus Algorithm IV: Performance metrics of a grid computing system used to create catalogues of optimised pointings

This paper discusses the requirements for and performance metrics of the the Grid Computing system used to implement the Locus Algorithm to identify optimum pointings for differential photometry of 61,662,376 stars and 23,779 quasars. Initial operational tests indicated a need for a software system to analyse the data and a High Performance Computing system to run that software in a scalable manner. Practical assessments of the performance of the software in a serial computing environment were used to provide a benchmark against which the performance metrics of the HPC solution could be compared, as well as to indicate any bottlenecks in performance. These performance metrics indicated a distinct split in the performance dictated more by differences in the input data than by differences in the design of the systems used. This indicates a need for experimental analysis of system performance, and suggests that algorithmic complexity analyses may lead to incorrect or naive conclusions, especially in systems with high data I/O overhead such as grid computing. Further, it implies that systems which reduce or eliminate this bottleneck such as in-memory processing could lead to a substantial increase in performance.

Creaner, Oisín↗
DOE OSTI2024

Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models that includes the Navier–Stokes, Kuramoto–Sivashinsky and Sine–Gordon equations. We thus provide a mathematically rigorous explanation for the observed robustness to noise of weak-form equation learning. Conversely, we also show that, in general, the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level exceeds a critical threshold σ c . We provide explicit bounds on σ c in the case of Gaussian white noise and we explicitly characterize the spurious terms that arise in the case of trigonometric and/or polynomial libraries. Furthermore, we show that, if the data is suitably denoised (a simple moving average filter is sufficient), then asymptotic consistency is recovered for models with locally-Lipschitz, polynomial-growth nonlinearities. Our results reveal important aspects of weak-form equation learning, which may be used to improve future algorithms. We demonstrate our findings numerically using the Lorenz system, the cubic oscillator, a viscous Burgers-growth model and a Kuramoto–Sivashinsky-type high-order PDE.

asymptotic consistency↗
DOE OSTI2023

Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions

Abstract The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms, including those for solving partial differential equations and Monte Carlo estimation. In this work, we introduce the Fourier series loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. Specifically, the FSL method prepares a (Dn)-qubit state encoding the 2 Dn -point uniform discretization of aD-dimensional function specified by aD-dimensional Fourier series. A free parameter,m, which must be less thann, determines the number of Fourier coefficients, 2 D ( m + 1 ) , used to represent the function. The FSL method uses a quantum circuit of depth at most 2 ( n − 2 ) + ⌈ log 2 ( n − m ) ⌉ + 2 D ( m + 1 ) + 2 − 2 D ( m + 1 ) , which is linear in the number of Fourier coefficients, and linear in the number of qubits (Dn) despite the fact that the loaded function’s discretization is over exponentially many (2 Dn ) points. The FSL circuit consists of at most D n + 2 D ( m + 1 ) + 1 − 1 single-qubit and D n ( n + 1 ) / 2 + 2 D ( m + 1 ) + 1 − 3 D ( m + 1 ) − 2 two-qubit gates; we present a classical compilation algorithm with runtime O ( 2 3 D ( m + 1 ) ) to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than 10 −6 and 10 −3 , respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H1-1 and H1-2 trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over 95 % , as well as various 1D real-valued functions on up to 6 qubits with classical fidelities ≈99%, and a 2D function on 10 qubits with a classical fidelity ≈94%.

Physics↗
DOE OSTI2021

Progress on the National Solar Radiation Data Base (NSRDB): A New DNI Computation

This study introduces a new technique to compute direct normal irradiance (DNI) for improving the National Solar Radiation Data Base (NSRDB). A finite-surface integration algorithm is developed to compute solar radiation in differential solid angles and efficiently infer its contribution to a surface perpendicular to the solar direction. A lookup table of cloud bi-directional transmittance distribution function (BTDF) is developed by use of the discrete ordinates radiative transfer (DISORT) model for possible solar and observing directions and various cloud optical and microphysical properties. In each solar incident direction, DNI is given by the cloud BTDFs from approximately 200 differential solid angles. The simulated DNI is calibrated and evaluated using surface observations at the National Renewable Energy Laboratory's (NREL's) Solar Energy Research Laboratory (SRRL) and the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) facility.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2023

Transcriptome architecture of the three main lineages of agrobacteria

ABSTRACT Agrobacteria are a diverse, polyphyletic group of prokaryotes with multipartite genomes capable of transferring DNA into the genomes of host plants, making them an essential tool in plant biotechnology. Despite their utility in plant transformation, genome-wide transcriptional regulation is not well understood across the three main lineages of agrobacteria. Transcription start sites (TSSs) are a necessary component of gene expression and regulation. In this study, we used differential RNA-seq and a TSS identification algorithm optimized on manually annotated TSS, then validated with existing TSS to identify thousands of TSS with nucleotide resolution for representatives of each lineage. We extend upon the 356 TSSs previously reported in Agrobacterium fabrum C58 by identifying 1,916 TSSs. In addition, we completed genomes and phenotyping of Rhizobium rhizogenes C16/80 and Allorhizobium vitis T60/94, identifying 2,650 and 2,432 TSSs, respectively. Parameter optimization was crucial for an accurate, high-resolution view of genome and transcriptional dynamics, highlighting the importance of algorithm optimization in genome-wide TSS identification and genomics at large. The optimized algorithm reduced the number of TSSs identified internal and antisense to the coding sequence on average by 90.5% and 91.9%, respectively. Comparison of TSS conservation between orthologs of the three lineages revealed differences in cell cycle regulation of ctrA as well as divergence of transcriptional regulation of chemotaxis-related genes when grown in conditions that simulate the plant environment. These results provide a framework to elucidate the mechanistic basis and evolution of pathology across the three main lineages of agrobacteria. IMPORTANCE Transcription start sites (TSSs) are fundamental for understanding gene expression and regulation. Agrobacteria, a group of prokaryotes with the ability to transfer DNA into the genomes of host plants, are widely used in plant biotechnology. However, the genome-wide transcriptional regulation of agrobacteria is not well understood, especially in less-studied lineages. Differential RNA-seq and an optimized algorithm enabled identification of thousands of TSSs with nucleotide resolution for representatives of each lineage. The results of this study provide a framework for elucidating the mechanistic basis and evolution of pathology across the three main lineages of agrobacteria. The optimized algorithm also highlights the importance of parameter optimization in genome-wide TSS identification and genomics at large.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Discovering hidden geothermal signatures using non-negative matrix factorization with customized k-means clustering

Discovery of hidden geothermal resources is challenging. It requires the mining of large datasets with diverse data attributes representing subsurface hydrogeological and geothermal conditions. The commonly used play fairway analysis approach typically incorporates subject-matter expertise to analyze regional data to estimate geothermal characteristics and favorability. We demonstrate an alternative approach based on machine learning (ML) to process a geothermal dataset from southwest New Mexico (SWNM). The study region includes low- and medium-temperature hydrothermal systems. Several of these systems are not well characterized because of insufficient existing data and limited past explorative work. This study discovers hidden patterns and relations in the SWNM geothermal dataset to improve our understanding of the regional hydrothermal conditions and energy-production favorability. This understanding is obtained by applying an unsupervised ML algorithm based on non-negative matrix factorization coupled with customized k-means clustering (NMFk). NMFk can automatically identify (1) hidden signatures characterizing analyzed datasets, (2) the optimal number of these signatures, (3) the dominant data attributes associated with each signature, and (4) the spatial distribution of the extracted signatures. Here, in this study, NMFk is applied to analyze 18 geological, geophysical, hydrogeological, and geothermal attributes at 44 locations in SWNM. Using NMFk, we find data patterns and identify the spatial associations of hydrothermal signatures within two physiographic provinces (Colorado Plateau and Basin and Range) and two sub-regions of these provinces (the Mogollon-Datil volcanic field and the Rio Grande rift) in SWNM. The ML algorithm extracted five hydrothermal signatures in the SWNM datasets that differentiate between low (<90°C) and medium (90-150°C)-temperature hydrothermal systems. The algorithm also suggests that the Rio Grande rift and northern Mogollon-Datil volcanic field are the most favorable regions for future geothermal resource discovery. NMFk also identified critical attributes to identify medium-temperature hydrothermal systems in the study area. The resulting NMFk model can be applied to predict geothermal conditions and their uncertainties at new SWNM locations based on limited data from unexplored regions. The code to execute the performed analyses as well as the corresponding data can be found at https://github.com/SmartTensors/GeoThermalCloud.jl.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Solving the Hele–Shaw flow using the Harrow–Hassidim–Lloyd algorithm on superconducting devices: A study of efficiency and challenges

The development of quantum processors for practical fluid flow problems is a promising yet distant goal. Recent advances in quantum linear solvers have highlighted their potential for classical fluid dynamics. In this study, we evaluate the Harrow–Hassidim–Lloyd (HHL) quantum linear systems algorithm (QLSA) for solving the idealized Hele–Shaw flow. Our focus is on the accuracy and computational cost of the HHL solver, which we find to be sensitive to the condition number, scaling exponentially with problem size. This emphasizes the need for preconditioning to enhance the practical use of QLSAs in fluid flow applications. Moreover, we perform shots-based simulations on quantum simulators and test the HHL solver on superconducting quantum devices, where noise, large circuit depths, and gate errors limit performance. Error suppression and mitigation techniques improve accuracy, suggesting that such fluid flow problems can benchmark noise mitigation efforts. Finally, our findings provide a foundation for future, more complex application of QLSAs in fluid flow simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

A multiresolution adaptive wavelet method for nonlinear partial differential equations

We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

AMReX: Block-structured adaptive mesh refinement for multiphysics applications

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

Zhang, Weiqun↗
DOE OSTI2021

A clustering-based approach to ocean model–data comparison around Antarctica

The Antarctic Continental Shelf seas (ACSS) are a critical, rapidly changing element of the Earth system. Analyses of global-scale general circulation model (GCM) simulations, including those available through the Coupled Model Intercomparison Project, Phase 6 (CMIP6), can help reveal the origins of observed changes and predict the future evolution of the ACSS. However, an evaluation of ACSS hydrography in GCMs is vital: previous CMIP ensembles exhibit substantial mean-state biases (reflecting, for example, misplaced water masses) with a wide inter-model spread. Because the ACSS are also a sparely sampled region, grid-point-based model assessments are of limited value. Our goal is to demonstrate the utility of clustering tools for identifying hydrographic regimes that are common to different source fields (model or data), while allowing for biases in other metrics (e.g., water mass core properties) and shifts in region boundaries. We apply K-means clustering to hydrographic metrics based on the stratification from one GCM (Community Earth System Model version 2; CESM2) and one observation-based product (World Ocean Atlas 2018; WOA), focusing on the Amundsen, Bellingshausen and Ross seas. When applied to WOA temperature and salinity profiles, clustering identifies “primary” and “mixed” regimes that have physically interpretable bases. For example, meltwater-freshened coastal currents in the Amundsen Sea and a region of high-salinity shelf water formation in the southwestern Ross Sea emerge naturally from the algorithm. Both regions also exhibit clearly differentiated inner- and outer-shelf regimes. The same analysis applied to CESM2 demonstrates that, although mean-state model biases in water mass T–S characteristics can be substantial, using a clustering approach highlights that the relative differences between regimes and the locations where each regime dominates are well represented in the model. CESM2 is generally fresher and warmer than WOA and has a limited fresh-water-enriched coastal regimes. Given the sparsity of observations of the ACSS, this technique is a promising tool for the evaluation of a larger model ensemble (e.g., CMIP6) on a circum-Antarctic basis.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum algorithm for the linear Vlasov equation with collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this paper, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional electrostatic limit. Rather than solving this equation in its native spatial and velocity phase space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. For a given simulation time, the Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. Further, this representation results in a system of linear ordinary differential equations (ODEs) which can be solved with well-developed quantum algorithms: a Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Hardware acceleration for HPS algorithms in two and three dimensions

We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU; in three dimensions, we modify and extend the adaptive discretization technique of Geldermans and Gillman [1] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems.

Fast direct solvers↗
DOE OSTI2020

Parallel Time Integration for Constrained Optimization

The number of transistors in an average processor continues to increase, but individual clock speeds have plateaued. Those transistors are instead going into additional cores, increasing the number of different things that a processor can do at once and placing an emphasis on parallel computation. Many problems in scientific computing follow a time-evolution model, and it can be difficult to solve such problems in parallel across the temporal domain. The Multi-Grid Reduction In Time (MGRIT) algorithm, developed at Lawrence Livermore National Laboratory (LLNL), solves differential equations with a method designed specifically to take advantage of extreme numbers of processors by parallelizing across time. The Tri-diagonal MGRIT (TriMGRIT) algorithm, also developed at LLNL, is a generalization of MGRIT which enables parallel-in-time solving of a greater number of problems. Constrained optimization problems, in particular, may be solved in parallel using TriMGRIT. These consist of choosing a control function such that an objective functional is minimized, constrained by a differential-equation. We consider two such problems: applying torque to a pendulum to bring it to a gentle stop and moving a crowd of people from one distribution into another. We also perform some miscellaneous theoretical and practical research, including investigating the use of a line-search subroutine to refine intermediate TriMGRIT results and preliminary work on strategies for choosing operators for TriMGRIT to use.

97 MATHEMATICS AND COMPUTING↗