Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Vectorization”

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 901 records · Page 50
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Simplified Two-Stage Model Predictive Control for a Hybrid Multilevel Converter With Floating H-Bridge

This paper proposes a simplified two-stage model predictive control (ST-MPC) for a hybrid multilevel converter, which is an active-neutral-point-clamped converter with floating H-bridge (ANPC-H). The objective of the first stage is to select the voltage vector that has the optimal current tracking performance by using a novel geometrical positioning approach in the complex plane. The second stage selects the best switching state among all the available switching states that belong to the same voltage vector obtained in the first stage, to balance dc capacitor voltages and reduce the common mode voltage. The proposed ST-MPC can dramatically reduce the computational burden and ensure the best current tracking by the two-stage structure, such that the execution time is much shorter compared with the conventional MPC. In addition, the geometrical positioning approach in the first stage is generic and can be applicable for any multilevel converters with N-level output; thus, this ST-MPC can be applied for both sevenand nine-level operation of the hybrid ANPC-H converter under different dc voltage ratios. Both simulation results and experimental results obtained on a silicon carbide hybrid ANPC-H converter prototype validate the feasibility and effectiveness of the proposed ST-MPC strategy.

42 ENGINEERING↗
DOE OSTI2025

Characterization of Impedance and Stability for Doubly-Fed Induction Generator Based on Voltage-Modulated Direct Power Control

Voltage-modulated direct power control (VM-DPC) applied to the doubly-fed induction generator (DFIG) offers superior steady-state and transient performance but remains underexplored for suppressing wideband oscillations. Here, this article proposes a comprehensive impedance for the VM-DPC-based DFIG, analyzing its impedance characteristics and stability mechanisms compared with the DFIG based on vector-oriented control (VOC). The unified power transfer function is defined for DFIGs employing VM-DPC or VOC to ensure consistent comparison benchmarks. The comprehensive impedance of VM-DPC-based DFIG, incorporating mechanical and grid-side converter (GSC) dynamics, is derived using complex vector modeling in the αβ -frame. Furthermore, the influence of VM-DPC parameters and grid strength on the stability of grid-connected DFIG systems is assessed through eigenvalue trajectory analysis. Impedance analysis reveals the significant contributions of mechanical and GSC dynamics to DFIG impedance, as well as the narrower frequency range of negative resistance in the VM-DPC-based DFIG compared to the VOC-based DFIG. Stability analysis identifies the VM-DPC parameters of the rotor-side converter as dominant factors affecting system stability and confirms that the VM-DPC-based DFIG achieves better stability under weak grid conditions than its VOC-based counterpart. These findings are validated through simulations and experiments.

42 ENGINEERING↗
DOE OSTI2024

Scalable Risk Assessment of Rare Events in Power Systems With Uncertain Wind Generation and Loads

Risk assessment of rare events has become increasingly important in power system planning and operation with the increasing integration of renewable energy and the presence of system uncertainties. However, quantifying the risk posed by rare events via the traditional method, i.e., Monte Carlo sampling (MCS), incurs substantial computational expense stemming from the vast ensemble of power flow simulations. To accelerate the assessment, this paper proposes a Deep Neural Network (DNN)-kernelized vector-valued Gaussian Process (VVGP) approach with excellent computational efficiency while maintaining high accuracy. Consequently, serving as a surrogate model for the power flow solver, the DNN-kernelized VVGP enables significantly faster but accurate risk assessment compared to the power flow solver. The developed surrogate model evaluates low-order N - k events that contain more than 90% instances by adeptly capturing the topological features while the high-order N - k events are assessed via a power flow solver, thereby striking a balance between computational efficiency and uncertainty quantification accuracy. Moreover, the model incorporates a Support Vector Machine (SVM) classifier to resample concerning low-probability tail events to counteract the biases potentially introduced during the DNN-kernelized VVGP evaluations. Simulations conducted on the modified IEEE 24-bus, 118-bus, and European 1354-bus systems demonstrate that the proposed method maintains the accuracy benchmark set by MCS while significantly reducing computational demands in large-scale power systems as compared to other state-of-the-art methods.

17 WIND ENERGY↗
DOE OSTI2020

Anomaly Detection and Mitigation for Wide-Area Damping Control using Machine Learning

In an interconnected multi-area power system, wide-area measurement based damping controllers are used to damp out inter-area oscillations, which jeopardize grid stability and constrain the power flows below to their transmission capacity. The effect of wide-area damping control (WADC) significantly depends on both power and cyber systems. At the cyber system layer, an adversary can inflict the WADC process by compromising either measurement signals, control signals or both. Stealthy and coordinated cyber-attacks may bypass the conventional cybersecurity measures to disrupt the seamless operation of WADC. This paper proposes an anomaly detection (AD) algorithm using supervised Machine Learning and a model-based logic for mitigation. The proposed AD algorithm considers measurement signals (input of WADC) and control signals (output of WADC) as input to evaluate the type of activity such as normal, perturbation (small or large signal faults), attack and perturbation-and-attack. Upon anomaly detection, the mitigation module tunes the WADC signal and sets the control status mode as either wide-area mode or local mode. The proposed anomaly detection and mitigation (ADM) module works inline with the WADC at the control center for attack detection on both measurement and control signals and eliminates the need for ADMs at the geographically distributed actuators. Here, we consider coordinated and primitive data-integrity attack vectors such as pulse, ramp, relay-trip and replay attacks. The performance of the proposed ADM algorithms was evaluated under these attack vector scenarios on a testbed environment for 2-area 4-machine power system. The ADM module shows effective performance with 96:5% accuracy to detect anomalies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

PWM for Simultaneous Minimization of Switching Losses and CM Voltage in Current Source Inverters

This article proposes a new pulsewidth modulation (PWM) scheme that reduces common-mode (CM) voltage and switching losses simultaneously in CSI. The proposed PWM [i.e., reduced voltages PWM (RVM)] reduces CM voltages and switching losses by selecting the optimal zero current vector and PWM sequence based on the CSI output voltage conditions. This article also proves the proposed RVM achieves both objectives (i.e., reduced CM voltage and switching losses) simultaneously for all CSI operating conditions without compromising the other objective. The proposed RVM inherently achieves zero-voltage switching (ZVS) conditions during the zero current vector transitions, further reducing the switching losses. Experimental results demonstrate significant reductions in CM voltage, reaching up to approximately 95%, accompanied by an increase of up to about 5.5% in CSI efficiency across a wide operating range compared to alternative PWM methods, confirming the predicted advantages of the proposed RVM.

42 ENGINEERING↗
DOE OSTI2023

TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclones

Tropical cyclones (TCs) are among the most destructive weather systems. Realistically and efficiently detecting and tracking TCs are critical for assessing their impacts and risks. In particular, the eye is a signature feature of a mature TC. Therefore, knowing the eyes’ locations and movements is crucial for both operational weather forecasts and climate risk assessments. Recently, a multilevel robustness framework has been introduced to study the critical points of time-varying vector fields. The framework quantifies the robustness (i.e., structural stability) of critical points across varying neighborhoods. By relating the multilevel robustness with critical point tracking, the framework has demonstrated its potential in cyclone tracking. An advantage is that it identifies cyclonic features using only 2D wind vector fields, which is encouraging as most tracking algorithms require multiple dynamic and thermodynamic variables at different altitudes. A disadvantage is that the framework does not scale well computationally for datasets containing a large number of cyclones. Herein this paper introduces a topologically robust physics-informed tracking framework (TROPHY) for TC tracking. The main idea is to integrate physical knowledge of TC to drastically improve the computational efficiency of multilevel robustness framework for large-scale climate datasets. First, during preprocessing, we propose a physics-informed feature selection strategy to filter 90% of critical points that are short-lived and have low stability, thus preserving good candidates for TC tracking. Second, during in-processing, we impose constraints during the multilevel robustness computation to focus only on physics-informed neighborhoods of TCs. We apply TROPHY to 30 years of 2D wind fields from reanalysis data in ERA5 and generate a number of TC tracks. In comparison with the observed tracks, we demonstrate that TROPHY can capture TC characteristics (e.g., frequency, intensity, duration, latitudes with maximum intensity, and genesis) that are comparable to and sometimes even better than a well-validated TC tracking algorithm that requires multiple dynamic and thermodynamic scalar fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Predicting nepheline precipitation in waste glasses using ternary submixture model and machine learning

Nepheline precipitation in nuclear waste glasses during vitrification can be detrimental due to its negative effect on chemical durability. Developing models to accurately predict nepheline precipitation from compositions is important to increase waste loading since existing models can be overly conservative. In this study, an expanded dataset containing 955 glasses was compiled from literature data, where 355 glasses are for high-level waste (HLW). Previously developed submixture models were refitted using the new dataset, where a misclassification rate of 7.8% was achieved. Nine machine learning (ML) algorithms (e.g., k-nearest neighbor, Gaussian process regression, artificial neural network, support vector machine, decision tree, etc.) were applied to evaluate their ability of predicting nepheline precipitation from compositions. Model accuracy, precision, recall/sensitivity, and F1 score were systemically compared between different ML algorithms and modeling protocols. Good model prediction with an accuracy ~0.9 (misclassification rate of ~10%) was observed with different algorithms under certain protocol. This study evaluated various ML models to predict nepheline precipitations in waste glasses, highlighting the importance of data preparation, modeling protocol, and their effect on model stability and reproducibility. The results provide insights into applying ML to predict glass properties and suggest areas for future research on modeling nepheline precipitations.

Lu, Xiaonan↗
DOE OSTI2022

Dislocation loop evolution in Kr-irradiated ThO 2

Here, the early stage of microstructural evolution of ThO 2 , under krypton irradiation at 600, 800, and 1000°C, was investigated using in situ transmission electron microscopy (TEM). Dislocation loops grew faster, whereas their number density decreased with increasing irradiation temperature. Loop density was found to decrease with ion dose. Interstitial dislocation loops, including Frank loops with Burgers vector of $\textit{a}/3\langle111\rangle$ and perfect loops with Burgers vector of $\textit{a}/2\langle110\rangle$, were determined by traditional TEM and atomic resolution–scanning TEM techniques. Atomistic and mesoscale level modeling are performed to interpret experimental observations. The migration energy barriers of defects in ThO 2 were calculated using density-functional theory. The energetics of different dislocation loop types were studied using molecular dynamics simulations. Loop density and diameter were analyzed using a kinetic rate theory model that considers stoichiometric loop evolution. This analysis reveals that loop growth is governed by the mobility of cation interstitials, whereas loop nucleation is determined by the mobility of anion defects. Lastly, a rate theory model was used to extract the diffusion coefficients of thorium interstitials, oxygen interstitials, and vacancies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Rapid and efficient in planta genome editing in sorghum using foxtail mosaic virus‐mediated sgRNA delivery

SUMMARY The requirement of in vitro tissue culture for the delivery of gene editing reagents limits the application of gene editing to commercially relevant varieties of many crop species. To overcome this bottleneck, plant RNA viruses have been deployed as versatile tools for in planta delivery of recombinant RNA. Viral delivery of single‐guide RNAs (sgRNAs) to transgenic plants that stably express CRISPR‐associated (Cas) endonuclease has been successfully used for targeted mutagenesis in several dicotyledonous and few monocotyledonous plants. Progress with this approach in monocotyledonous plants is limited so far by the availability of effective viral vectors. We engineered a set of foxtail mosaic virus (FoMV) and barley stripe mosaic virus (BSMV) vectors to deliver the fluorescent protein AmCyan to track viral infection and movement in Sorghum bicolor . We further used these viruses to deliver and express sgRNAs to Cas9 and Green Fluorescent Protein (GFP) expressing transgenic sorghum lines, targeting Phytoene desaturase ( PDS ), Magnesium‐chelatase subunit I ( MgCh ), 4‐hydroxy‐3‐methylbut‐2‐enyl diphosphate reductase , orthologs of maize Lemon white1 ( Lw1 ) or GFP . The recombinant BSMV did neither infect sorghum nor deliver or express AmCyan and sgRNAs. In contrast, the recombinant FoMV systemically spread throughout sorghum plants and induced somatic mutations with frequencies reaching up to 60%. This mutagenesis led to visible phenotypic changes, demonstrating the potential of FoMV for in planta gene editing and functional genomics studies in sorghum.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Machine-learning-enabled on-the-fly analysis of RHEED patterns during thin film deposition by molecular beam epitaxy

Thin film deposition is a fundamental technology for the discovery, optimization, and manufacturing of functional materials. Deposition by molecular beam epitaxy (MBE) typically employs reflection high-energy electron diffraction (RHEED) as a real-time in situ probe of the growing film. However, the state-of-the-art for RHEED analysis during deposition requires human observation. Here, we present an approach using machine learning (ML) methods to monitor, analyze, and interpret RHEED images on-the-fly during thin film deposition. In the analysis workflow, RHEED pattern images are collected at one frame per second and featurized using a pretrained deep convolutional neural network. The feature vectors are then statistically analyzed to identify changepoints; these changepoints can be related to changes in the deposition mode from initial film nucleation to a transition regime, smooth film deposition, and in some cases, an additional transition to a rough, islanded deposition regime. The feature vectors are additionally analyzed via graph analysis and community classification. The graph is quantified as a stabilization plot, and we show that inflection points in the stabilization plot correspond to changes in the growth regime. The full RHEED analysis workflow is termed RHAAPsody and includes data transfer and output to a visual dashboard. We demonstrate the functionality of RHAAPsody by analyzing the precaptured RHEED images from epitaxial depositions of anatase TiO2 on SrTiO3(001) and show that the analysis workflow can be executed in less than 1 s. Our approach shows promise as one component of ML-enabled real-time feedback control of the MBE deposition process.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Physics-informed neural networks for identification of material properties using standing waves

A metallic structure in its initial stage of failure involves plastic deformation or environmental degradation that changes the elastic modulus and density. This work presents the detection of change in wave velocity (a function of elastic modulus and density) as a system identification problem. A physics-informed neural network (PINN) is proposed to solve the system identification problem. The PINN takes the spatial coordinates of scanning locations and time as inputs and provides the displacement and wave velocity as outputs. The governing partial differential equation of standing waves in a rod is incorporated into the neural network as physics in the form of a loss function. The wave velocity vector is randomly initiated. During the training of the network, physics is used to determine and update the wave velocity target vector from the network’s displacement predictions. The measured data, comprising sparse displacement response on the rod structure, are used to train the PINN. The wave velocity at the sparse locations on the rod is learned from the predicted displacements during the training. Using the predictions of the trained network, the response of free vibration or material property variation can be reconstructed at unscanned locations on the structure to obtain high-resolution maps for full-field imaging to detect and localize the changes caused by plastic deformation. The PINN’s sparse scanning and simultaneous prediction capability during training can lead to high scanning and data-processing speeds. This capability yields a nondestructive evaluation system that can predict the presence of degraded material locations as the structural vibrations are scanned and processed in real time.

Rathod, Vivek↗
DOE OSTI2021

ChAdOx1 interacts with CAR and PF4 with implications for thrombosis with thrombocytopenia syndrome

Vaccines derived from chimpanzee adenovirus Y25 (ChAdOx1), human adenovirus type 26 (HAdV-D26), and human adenovirus type 5 (HAdV-C5) are critical in combatting the severe acute respiratory coronavirus 2 (SARS-CoV-2) pandemic. As part of the largest vaccination campaign in history, ultrarare side effects not seen in phase 3 trials, including thrombosis with thrombocytopenia syndrome (TTS), a rare condition resembling heparin-induced thrombocytopenia (HIT), have been observed. This study demonstrates that all three adenoviruses deployed as vaccination vectors versus SARS-CoV-2 bind to platelet factor 4 (PF4), a protein implicated in the pathogenesis of HIT. We have determined the structure of the ChAdOx1 viral vector and used it in state-of-the-art computational simulations to demonstrate an electrostatic interaction mechanism with PF4, which was confirmed experimentally by surface plasmon resonance. These data confirm that PF4 is capable of forming stable complexes with clinically relevant adenoviruses, an important step in unraveling the mechanisms underlying TTS.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Evaluation of Immunocompetent Mouse Models for Borrelia miyamotoi Infection

Borrelia miyamotoi is a relapsing fever spirochete that is harbored by Ixodes spp. ticks and is virtually uncharacterized, compared to other relapsing fever Borrelia vectored by Ornithodoros spp. ticks. There is not an immunocompetent mouse model for studying B. miyamotoi infection in vivo or for transmission in the vector-host cycle. Our goal was to evaluate B. miyamotoi infections in multiple mouse breeds/strains as a prelude to the ascertainment of the best experimental infection model. Two B. miyamotoi strains, namely, LB-2001 and CT13-2396, as well as three mouse models, namely, CD-1, C3H/HeJ, and BALB/c, were evaluated. We were unable to observe B. miyamotoi LB-2001 spirochetes in the blood via darkfield microscopy or to detect DNA via real-time PCR post needle inoculation in the CD-1 and C3H/HeJ mice. However, LB-2001 DNA was detected via real-time PCR in the blood of the BALB/c mice after needle inoculation, although spirochetes were not observed via microscopy. CD-1, C3H/HeJ, and BALB/c mice generated an antibody response to B. miyamotoi LB-2001 following needle inoculation, but established infections were not detected, and the I. scapularis larvae failed to acquire spirochetes from the exposed CD-1 mice. In contrast, B. miyamotoi CT13-2396 was visualized in the blood of the CD-1 and C3H/HeJ mice via darkfield microscopy and detected by real-time PCR post needle inoculation. Both mouse strains seroconverted. However, no established infection was detected in the mouse organs, and the I. scapularis larvae failed to acquire Borrelia after feeding on CT13-2396 exposed CD-1 or C3H/HeJ mice. Furthermore, these findings underscore the challenges in establishing an experimental B. miyamotoi infection model in immunocompetent laboratory mice.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Iterated Gauss-Seidel GMRES

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vk ). It is well known that this process can be viewed as a QR factorization of the matrix Bk = [r0, AVk] at each iteration. Despite an O (..epsilon..)..kappa.. (Bk ) loss of orthogonality, for unit roundoff ..epsilon..and condition number ..kappa.. , the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal.Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Swirydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (..epsilon..)..kappa.. (Bk ) or O (..epsilon..), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vk remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems.

Arnoldi-QR↗
DOE OSTI2023

An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-Anisotropy-Aligned Meshes

This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Finally, numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An Incremental Tensor Train Decomposition Algorithm

We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the tensor train incremental core expansion (TT-ICE) improves upon the current state-of-the-art algorithms for compressing in tensor train format by developing a new adaptive approach that incurs significantly slower rank growth and guarantees compression accuracy. This capability is achieved by limiting the number of new vectors appended to the TT-cores of an existing accumulation tensor after each data increment. These vectors represent directions orthogonal to the span of existing cores and are limited to those needed to represent a newly arrived tensor to a target accuracy. We provide two versions of the algorithm: TT-ICE and TT-ICE accelerated with heuristics (TT-ICE*). Here, we provide a proof of correctness for TT-ICE and empirically demonstrate the performance of the algorithms in compressing large-scale video and scientific simulation datasets. Compared to existing approaches that also use rank adaptation, TT-ICE* achieves 57× higher compression and up to 95% reduction in computational time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Streaming Compression of Scientific Data via Weak-SINDy

Here, in this paper, a streaming weak-SINDy algorithm is developed specifically for compressing streaming scientific data. The production of scientific data, either via simulation or experiments, is undergoing a stage of exponential growth, which makes data compression important and often necessary for storing and utilizing large scientific data sets. As opposed to classical “offline” compression algorithms that perform compression on a readily available data set, streaming compression algorithms compress data “online” while the data generated from simulation or experiments is still flowing through the system. This feature makes streaming compression algorithms well suited for scientific data compression, where storing the full data set offline is often infeasible. This work proposes a new streaming compression algorithm, streaming weak-SINDy, which takes advantage of the underlying data characteristics during compression. The streaming weak-SINDy algorithm constructs feature matrices and target vectors in the online stage via a streaming integration method in a memory efficient manner. The feature matrices and target vectors are then used in the offline stage to build a model through a regression process that aims to recover equations that govern the evolution of the data. For compressing high-dimensional streaming data, we adopt a streaming proper orthogonal decomposition (POD) process to reduce the data dimension and then use the streaming weak-SINDy algorithm to compress the temporal data of the POD expansion. We propose modifications to the streaming weak-SINDy algorithm to accommodate the dynamically updated POD basis. By combining the built model from the streaming weak-SINDy algorithm and a small amount of data samples, the full data flow could be reconstructed accurately at a low memory cost, as shown in the numerical tests.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗