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DOE OSTI2026

Faster Randomized Dynamical Decoupling

We present a randomized dynamical decoupling (DD) protocol that can substantially improve the performance of any given deterministic DD scheme for suppressing coherent noise by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system’s Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. Here, we also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.

Quantum algorithms & computation↗
DOE OSTI2026

Fokker-Planck Equation Governing the Distribution of Walkers in Auxiliary-Field Quantum Monte Carlo

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. Here, in this Letter, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wave function actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wave function in constrained path AFQMC, contrary to the common assumption, the wave function sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this Letter.

Monte Carlo methods↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Exploring Memory Hierarchy to Improve Scientific Data Read Performance, In: 2015 IEEE International Conference on Cluster Computing

Improving read performance is one of the major challenges with speeding up scientific data analytic applications. Utilizing the memory hierarchy is one major line of researches to address the read performance bottleneck. Related methods usually combine solide-state-drives(SSDs) with dynamic random-access memory(DRAM) and/or parallel file system(PFS) to mitigate the speed and space gap between DRAM and PFS. However, these methods are unable to handle key performance issues plaguing SSDs, namely read contention that may cause up to 50% performance reduction. In this paper, we propose a framework that exploits the memory hierarchy resource to address the read contention issues involved with SSDs. The framework employs a general purpose online read algorithm that able to detect and utilize memory hierarchy resource to relieve the problem. To maintain a near optimal operating environment for SSDs, the framework is able to orchastrate data chunks across different memory layers to facilitate the read algorithm. Compared to existing tools, our framework achieves up to 50% read performance improvement when tested on datasets from real-world scientific simulations.

Computer Science↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗
DOE OSTI2017

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if—and only if—the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Finally, we use gate set tomography to completely characterize operations on a trapped-Yb + -ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10 -4 ).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A multicomponent matched filter cluster confirmation tool for eROSITA: initial application to the RASS and DES-SV data sets

We describe a multi-component matched filter cluster confirmation tool (MCMF) designed for the study of large X-ray source catalogs produced by the upcoming X-ray all-sky survey mission eROSITA. We apply the method to confirm a sample of 88 clusters with redshifts $0.05<z<0.8$ in the recently published 2RXS catalog from the ROSAT all-sky survey (RASS) over the 208 deg$^2$ region overlapped by the Dark Energy Survey (DES) science verification (DES-SV) dataset. In our pilot study, we examine all X-ray sources, regardless of their extent. Our method employs a multi-color red sequence (RS) algorithm that incorporates the X-ray count rate and peak position in determining the region of interest for followup and extracts the positionally and color weighted optical richness $\lambda_{\mathrm{MCMF}}$ as a function of redshift for each source. Peaks in the $\lambda_{\mathrm{MCMF}}$-redshift distribution are identified and used to extract photometric redshifts, richness and uncertainties. The significances of all optical counterparts are characterized using the distribution of richnesses defined along random lines of sight. These significances are used to extract cluster catalogs and to estimate the contamination by random superpositions of unassociated optical systems. The delivered photometric redshift accuracy is $\delta z / (1+z)=0.010$. We find a well defined X-ray luminosity-$\lambda_{\mathrm{MCMF}}$ relation with an intrinsic scatter of $\delta \ln(\lambda_\mathrm{MCMF}| L_\mathrm{x})=0.21$. Matching our catalog with the DES-SV redMaPPer catalog yields good agreement in redshift and richness estimates; comparing our catalog with the South Pole Telescope (SPT) selected clusters shows no inconsistencies. SPT clusters in our dataset are consistent with the high mass extension of the RASS based $\lambda_{\mathrm{MCMF}}$-mass relation

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Simulated Contrast of Two Dislocations

A three-dimensional Monte Carlo simulation algorithm is used to study the contrast of two dislocations perpendicular to the irradiated surface of an n-doped silicon sample in the electron beam induced current mode. The dislocations are positioned in the irradiation trajectory, and each of both is considered as a cylinder where the minority carrier diffusion length varies abruptly from a low inside dislocations up to a high value outside dislocations. The EBIC contrast was obtained by simulating the random diffusion of carriers generated at point-like sources randomly distributed within the generation volume. Results are analyzed on the basis of change in the generation volume in the bulk of the sample and of carrier trapping process inside dislocations. The EBIC contrast increases with the increase of the electron beam energy. It also increases when the minority diffusion length inside dislocations, or their separating distance decreases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A spatially regularized detector for emergent/re-emergent disease outbreaks

Early detection of outbreaks caused by emergent pathogens, using epidemiological surveillance data i.e., daily case counts, is difficult. This is because the data tend to be noisy during the early epoch of the outbreak. In contrast, the spread-rate of the disease tends to be well-behaved, as it depends only on the mixing patterns of the population and the characteristics of the pathogen, neither of which behave erratically in space-time. In this report, we explore whether the spread-rate can be used for epidemiological surveillance, conditional on case count data. Estimating the spread-rate from case count data allows us to exploit exogenous information, e.g., incubation period distributions etc., which can considerably smooth out any erratic temporal behavior. Further, epidemiological dynamics are spatially correlated, and if case counts are available for multiple areal units e.g., counties, these correlations could potentially be used to suppress noise in the early epoch data. These exogenous information and structure are not exploited by conventional syndromic surveillance detectors to extract a well-behaved latent variable for monitoring purposes. The technical challenge lies in the estimation of the spread-rate field jointly over a collection of areal units; further, the spread-rate varies over time. We develop a method based on mean-field variational inference to approximately estimate the spread-rate field, using a Gaussian Random Field Model for spatial regularization. The method is tested on the estimation of spread-rate in the thirty-three counties of New Mexico and detect the arrival of the Fall 2020 COVID-19 wave in September 2020. We find that the method is scalable, but underestimates the uncertainty in the estimated spread-rate field. We detect the arrival of the Fall 2020 wave a week ahead of conventional syndromic surveillance algorithms, but our simplistic detection algorithm, based on simple anomaly detection, suffers from a high false positive rate, similar to conventional detectors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Robust Online Sequential RVFLNs for Data Modeling of Dynamic Time-Varying Systems with Application of an Ironmaking Blast Furnace

In a world where the increasing complexity of modern industrial processes brings difficulties for accurate mathematical modeling, taking advantage of data has become an efficient solution to complex dynamic process modeling issue. In this paper, we develop a novel robust online sequential version of random vector functional-link networks (RVFLNs) for data-driven modeling of dynamic time-varying system and applied it in a blast furnace (BF) ironmaking process. First, to overcome the time-varying dynamics of process and to enable the RVFLNs to learn online with avoiding data saturation, an improved online sequential version of RVFLNs (OS-RFVLNs) is first presented by online sequential learning with forgetting factor. This improved OS-RVFLNs algorithm is not only suitable for the real-time and large data transfer situation, but also can adjust the sensitivity of the algorithm to different samples with the help of the introduced forgetting factor. Second, since the output weights of the improved OS-RVFLNs as well as other RVFLNs algorithms are obtained by the least squares approach, a robustness problem may occur when the training dataset is contaminated with various outliers. To solve this problem, a Cauchy distribution weighted M-estimator is introduced to improve the robustness of the improved OS- RVFLNs. For this proposed robust OS-RVFLNs (R-OS- RVFLNs), since the weights of different outlier data are properly determined by the Cauchy distribution function, their corresponding contribution on modeling can be properly distinguished. Thus robust and better modeling results can be achieved. Experiments using actual industrial data of BF ironmaking process and comparative studies have demonstrated that the proposed method produces a better estimation accuracy and stronger robustness than other methods.

Blast furnace (BF), Modelling, Dynamic systems↗
DOE OSTI2014

Rare-event Simulation for Stochastic Korteweg-de Vries Equation

An asymptotic analysis of the tail probabilities for the dynamics of a soliton wave $U(x,t)$ under a stochastic time-dependent force is developed. The dynamics of the soliton wave $U(x,t)$ is described by the Korteweg-de Vries Equation with homogeneous Dirichlet boundary conditions under a stochastic time-dependent force, which is modeled as a time-dependent Gaussian noise with amplitude $\epsilon$. The tail probability we considered is $w(b) :=P(\sup_{t\in [0,T]} U(x,t) > b ),$ as $b\rightarrow \infty,$ for some constant $T>0$ and a fixed $x$, which can be interpreted as tail probability of the amplitude of water wave on shallow surface of a fluid or long internal wave in a density-stratified ocean. Our goal is to characterize the asymptotic behaviors of $w(b)$ and to evaluate the tail probability of the event that the soliton wave exceeds a certain threshold value under a random force term. Such rare-event calculation of $w(b)$ is very useful for fast estimation of the risk of the potential damage that could caused by the water wave in a density-stratified ocean modeled by the stochastic KdV equation. In this work, the asymptotic approximation of the probability that the soliton wave exceeds a high-level $b$ is derived. In addition, we develop a provably efficient rare-event simulation algorithm to compute $w(b)$. The efficiency of the algorithm only requires mild conditions and therefore it is applicable to a general class of Gaussian processes and many diverse applications.

Xu, Gongjun↗
DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Influence of source batch S{sub K} dispersion on dosimetry for prostate cancer treatment with permanent implants

Purpose: In clinical practice, specific air kerma strength (S{sub K}) value is used in treatment planning system (TPS) permanent brachytherapy implant calculations with {sup 125}I and {sup 103}Pd sources; in fact, commercial TPS provide only one S{sub K} input value for all implanted sources and the certified shipment average is typically used. However, the value for S{sub K} is dispersed: this dispersion is not only due to the manufacturing process and variation between different source batches but also due to the classification of sources into different classes according to their S{sub K} values. The purpose of this work is to examine the impact of S{sub K} dispersion on typical implant parameters that are used to evaluate the dose volume histogram (DVH) for both planning target volume (PTV) and organs at risk (OARs). Methods: The authors have developed a new algorithm to compute dose distributions with different S{sub K} values for each source. Three different prostate volumes (20, 30, and 40 cm{sup 3}) were considered and two typical commercial sources of different radionuclides were used. Using a conventional TPS, clinically accepted calculations were made for {sup 125}I sources; for the palladium, typical implants were simulated. To assess the many different possible S{sub K} values for each source belonging to a class, the authors assigned an S{sub K} value to each source in a randomized process 1000 times for each source and volume. All the dose distributions generated for each set of simulations were assessed through the DVH distributions comparing with dose distributions obtained using a uniform S{sub K} value for all the implanted sources. The authors analyzed several dose coverage (V{sub 100} and D{sub 90}) and overdosage parameters for prostate and PTV and also the limiting and overdosage parameters for OARs, urethra and rectum. Results: The parameters analyzed followed a Gaussian distribution for the entire set of computed dosimetries. PTV and prostate V{sub 100} and D{sub 90} variations ranged between 0.2% and 1.78% for both sources. Variations for the overdosage parameters V{sub 150} and V{sub 200} compared to dose coverage parameters were observed and, in general, variations were larger for parameters related to {sup 125}I sources than {sup 103}Pd sources. For OAR dosimetry, variations with respect to the reference D{sub 0.1cm{sup 3}} were observed for rectum values, ranging from 2% to 3%, compared with urethra values, which ranged from 1% to 2%. Conclusions: Dose coverage for prostate and PTV was practically unaffected by S{sub K} dispersion, as was the maximum dose deposited in the urethra due to the implant technique geometry. However, the authors observed larger variations for the PTV V{sub 150}, rectum V{sub 100}, and rectum D{sub 0.1cm{sup 3}} values. The variations in rectum parameters were caused by the specific location of sources with S{sub K} value that differed from the average in the vicinity. Finally, on comparing the two sources, variations were larger for {sup 125}I than for {sup 103}Pd. This is because for {sup 103}Pd, a greater number of sources were used to obtain a valid dose distribution than for {sup 125}I, resulting in a lower variation for each S{sub K} value for each source (because the variations become averaged out statistically speaking)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Accelerating and Parallelizing Lagrangian Simulations of Mixing-Limited Reactive Transport

Recent advances in random walk particle tracking have enabled direct simulation of mixing and reactions by allowing the particles to interact with each other using a multipoint mass transfer scheme. The mass transfer scheme allows separation of mixing and spreading processes, among other advantages, but it is computationally expensive because its speed depends on the number of interacting particle pairs. This note explores methods for relieving the computational bottleneck caused by the mass transfer step, and we use these algorithms to develop a new parallel, interacting particle model. The new model is a combination of a sparse search algorithm and a novel domain decomposition scheme, both of which offer significant speedup relative to the reference case—even when they are executed serially. We combine the strengths of these methods to create a parallel particle scheme that is highly accurate and efficient with run times that scale as 1/P for a fixed number of particles, where P is the number of computational cores (equivalently, subdomains, in this work) being used. Here, the new parallel model is a significant advance because it enables efficient simulation of large particle ensembles that are needed for environmental simulations and also because it can naturally pair with parallel geochemical solvers to create a practical Lagrangian tool for simulating mixing and reactions in complex chemical systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Physics-informed machine learning

Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Furthermore, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Polarization-agnostic continuous-variable quantum key distribution

Here, we introduce a polarization-agnostic method for Gaussian-modulated coherent-state (GCMS) continuous-variable quantum key distribution (CVQKD). Due to the random and continuous nature of the GCMS protocol, Alice, the transmitter, can encode two distinct quadratures in each of two orthogonal polarization modes, such that Bob, the receiver, measures valid GCMS quadratures in a single polarization mode even when polarization changes occur during transmission. This method does not require polarization correction in the optical domain, does not require monitoring both polarization modes, reduces loss by eliminating optical components, and avoids the noise injected by polarization correction algorithms.

Williams, Brian P. [Oak Ridge National Laboratory ↗
DOE OSTI2013

Assessment of cardiac single-photon emission computed tomography performance using a scanning linear observer

Purpose: Single-photon emission computed tomography (SPECT) is widely used to detect myocardial ischemia and myocardial infarction. It is important to assess and compare different SPECT system designs in order to achieve the highest detectability of cardiac defects. Methods: Whitaker et al.'s study ['Estimating random signal parameters from noisy images with nuisance parameters: linear and scanning-linear methods,' Opt. Express 16(11), 8150-8173 (2008)] on the scanning linear observer (SLO) shows that the SLO can be used to estimate the location and size of signals. One major advantage of the SLO is that it can be used with projection data rather than with reconstruction data. Thus, this observer model assesses the overall hardware performance independent of any reconstruction algorithm. In addition, the computation time of image quality studies is significantly reduced. In this study, three systems based on the design of the GE cadmium zinc telluride-based dedicated cardiac SPECT camera Discovery 530c were assessed. This design, which is officially named the Alcyone Technology: Discovery NM 530c, was commercialized in August, 2009. The three systems, GE27, GE19, and GE13, contain 27, 19, and 13 detectors, respectively. Clinically, a human heart can be virtually segmented into three coronary artery territories: the left-anterior descending artery, left-circumflex artery, and right coronary artery. One of the most important functions of a cardiac SPECT system is to produce images from which a radiologist can accurately predict in which territory the defect exists [http://www.asnc.org/media/PDFs/PPReporting081511.pdf, Guideline from American Society of Nuclear Cardiology]. A good estimation of the extent of the defect from the projection images is also very helpful for determining the seriousness of the myocardial ischemia. In this study, both the location and extent of defects were estimated by the SLO, and the system performance was assessed by localization receiver operating characteristic (LROC) [P. Khurd and G. Gindi, 'Decision strategies maximizing the area under the LROC curve,' Proc. SPIE 5749, 150-161 (2005)] or estimation receiver operating characteristic (EROC) [E. Clarkson, 'Estimation receiver operating characteristic curve and ideal observers for combined detection/estimation tasks,' J. Opt. Soc. Am. A 24, B91-B98 (2007)] curves. Results: The area under the LROC/EROC curve (AULC/AUEC) and the true positive fraction (TPF) at a specific false positive fraction (FPF) can be treated as the figures of merit. For radii estimation with a 1 mm tolerance, the AUEC values of the GE27, GE19, and GE13 systems are 0.8545, 0.8488, and 0.8329, and the TPF at FPF = 5% are 77.1%, 76.46%, and 73.55%, respectively. The assessment of all three systems revealed that the GE19 system yields estimated information and cardiac defect detectability very close to those of the GE27 system while using eight fewer detectors. Thus, 30% of the expensive detector units can be removed with confidence. Conclusions: As the results show, a combination of the SLO and LROC/EROC curves can determine the configuration that yields the most relevant estimation/detection information. Thus, this is a useful method for assessing cardiac SPECT systems.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2019

Scalable Extended Dynamic Mode Decomposition Using Random Kernel Approximation

The Koopman operator is a linear, infinite-dimensional operator that governs the dynamics of system observables; extended dynamic mode decomposition (EDMD) is a data-driven method for approximating the Koopman operator using functions (features) of the system state snapshots. This paper investigates an approach to EDMD in which the features used provide random approximations to a particular kernel function. The objective of this is computational economy for large data sets: EDMD is generally ill-suited for problems with large state dimension, and its dual kernel formulation (KDMD) is well-suited for such problems only if the number of data snapshots is relatively small. We discuss two specific methods for generating features: random Fourier features and the Nÿstrom method. The first method is a data-independent method for translation-invariant kernels only and involves random sampling in feature space; the second method is a data-dependent empirical method that may be used for any kernel and involves random sampling of data. We first discuss how these ideas may be applied in an EDMD context, as well as a means for adaptively adding random Fourier features. As a result, we demonstrate these methods on two example problems and conclude with an analysis of the relative benefits and drawbacks of each method.

59 BASIC BIOLOGICAL SCIENCES↗