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DOE OSTI2010

A truncated Levenberg-Marquardt algorithm for the calibration of highly parameterized nonlinear models

We propose a modification to the Levenberg-Marquardt minimization algorithm for a more robust and more efficient calibration of highly parameterized, strongly nonlinear models of multiphase flow through porous media. The new method combines the advantages of truncated singular value decomposition with those of the classical Levenberg-Marquardt algorithm, thus enabling a more robust solution of underdetermined inverse problems with complex relations between the parameters to be estimated and the observable state variables used for calibration. The truncation limit separating the solution space from the calibration null space is re-evaluated during the iterative calibration process. In between these re-evaluations, fewer forward simulations are required, compared to the standard approach, to calculate the approximate sensitivity matrix. Truncated singular values are used to calculate the Levenberg-Marquardt parameter updates, ensuring that safe small steps along the steepest-descent direction are taken for highly correlated parameters of low sensitivity, whereas efficient quasi-Gauss-Newton steps are taken for independent parameters with high impact. The performance of the proposed scheme is demonstrated for a synthetic data set representing infiltration into a partially saturated, heterogeneous soil, where hydrogeological, petrophysical, and geostatistical parameters are estimated based on the joint inversion of hydrological and geophysical data.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Data processing pipeline for Tianlai experiment

The Tianlai project is a 21cm intensity mapping experiment for detecting dark energy by measuring the baryon acoustic oscillation (BAO) features in the large scale structure power spectrum. This experiment provides an opportunity to test the data processing methods for cosmological 21cm signal extraction, which is still a great challenge in current radio astronomy research. The 21cm signal is much weaker than the foregrounds and easily aected by the imperfections in the instrumental responses. Furthermore, processing the large volumes of interferometer data poses a practical challenge. We have developed a data processing pipeline called tlpipe to process the drift scan survey data from the Tianlai experiment. It performs oine data processing tasks such as radio frequency interference (RFI) agging, array calibration, binning, and map-making, etc. It also includes utility functions needed for the data analysis, such as data selection, transformation, visualization and others. A number of new algorithms are implemented, for example the eigenvector decomposition method for array calibration and the Tikhnov regularization for m-mode analysis. In this paper we describe the design and implementation of the pipeline and illustrate its functions with some analysis of real data. Finally, we outline directions for future development of this publicly code.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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 OSTI2023

Fermionic quantum processing with programmable neutral atom arrays

Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2012

Domain decomposition for the SPN solver MINOS

In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3 (R) code. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Artificial intelligence-empowered cellular morphometric risk score improves prognostic stratification of cutaneous squamous cell carcinoma

Abstract Background Risk stratification of cutaneous squamous cell carcinoma (cSCC) is essential for managing patients. Objectives To determine if artificial intelligence and machine learning might help to stratify patients with cSCC by risk using more than solely clinical and histopathological factors. Methods We retrieved a retrospective cohort of 104 patients whose cSCCs had been excised with clear margins. Clinical and histopathological risk factors were evaluated. Haematoxylin and eosin-stained slides were scanned and analysed by an algorithm based on the stacked predictive sparse decomposition technique. Cellular morphometric biomarkers (CMBs) were identified via machine learning and used to derive a cellular morphometric risk score (CMRS) that classified cSCCs into clusters of differential prognoses. Concordance analysis, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and accuracy were calculated and compared with results obtained with the Brigham and Women’s Hospital (BWH) staging system. The performance of the combination of the BWH staging system and the CMBs was also analysed. Results There were no differences among the CMRS groups in terms of clinical and histopathological risk factors and T-stage assignment, but there were significant differences in prognosis. Combining the CMRS with BWH staging systems increased distinctiveness and improved prognostic performance. C-indices were 0.91 local recurrence and 0.91 for nodal metastasis when combining the two approaches. The NPV was 94.41% and 96.00%, the PPV was 36.36% and 41.67%, and accuracy reached 86.75% and 89.16%, respectively, with the combined approach. Conclusions CMRS is helpful for cSCC risk stratification beyond classic clinical and histopathological risk features. Combining the information from the CMRS and the BWH staging system offers outstanding prognostic performance for patients with high-risk cSCC.

Pérez-Baena, Manuel J.↗

DOE OSTI2020

Extending the Frontier of Quantum Computers with Qutrits

Here, we advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log 2 (3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla - an exponential improvement over the best qubit-only equivalent. Our approach features a 70× improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Optimizing Service Restoration in Distribution Systems With Uncertain Repair Time and Demand

This paper proposes a novel method to co-optimize the distribution system operation and repair crew routing for outage restoration after extreme weather events. A two-stage stochastic mixed integer linear program is developed. The first stage is to dispatch the repair crews to the damaged components. The second stage is distribution system restoration using distributed generators, and reconfiguration. We consider demand uncertainty in terms of a truncated normal forecast error distribution, and model the uncertainty of the repair time using a lognormal distribution. A new decomposition approach, combined with the progressive hedging algorithm, is developed for solving large-scale outage management problems in an effective and timely manner. Furthermore, the proposed method is validated on modified IEEE 34- and 8500-bus distribution test systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Real-Time Bayesian Inference at Extreme Scale: A Digital Twin for Tsunami Early Warning Applied to the Cascadia Subduction Zone

We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic–gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline–online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Final Technical Report for "Cloud-based Low-Scaling Quantum Chemistry Simulations for Materials"

The objective of phase I was to develop the basic infrastructure for performing efficient hybrid DFT calculations on solid materials with a turnaround time amenable to the use in large-scale data-driven approaches. To fulfill the goal we have developed a novel algorithm that significantly reduces the cost of exchange matrix formation. The algorithm does so by making use of three ingredients (a) interpolative decomposition of the electron integrals (b) robust pseudospectral method and (c) occ-RI approach. Our published work demonstrates that the algorithm is orders of magnitude faster than any other hybrid-DFT method and is on the order of only 3-4 times slower than pure DFT. All steps of the algorithm developed during phase I can be accelerated to the point that, for large enough systems, the diagonalization of the Fock matrix will become the most expensive step. To treat such large systems we have created an interface to the ASCR-funded PEXSI library. The PEXSI method is used to compute the density matrix directly from the Fock matrix in a manner that preserves the sparsity of the local representation.

Shiozaki, Toru↗

DOE OSTI2024

A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method for the Vlasov Dynamics

Abstract In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method for simulating the Vlasov-Poisson (VP) system. The LoMaC property refers to the exact local conservation of macroscopic mass, momentum and energy at the discrete level. This is a follow-up work of our previous development of a conservative low rank tensor approach for Vlasov dynamics ( arXiv:2201.10397 ). In that work, we applied a low rank tensor method with a conservative singular value decomposition to the high dimensional VP system to mitigate the curse of dimensionality, while maintaining the local conservation of mass and momentum. However, energy conservation is not guaranteed, which is a critical property to avoid unphysical plasma self-heating or cooling. The new ingredient in the LoMaC low rank tensor algorithm is that we simultaneously evolve the macroscopic conservation laws of mass, momentum and energy using a flux-difference form with kinetic flux vector splitting; then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables by a conservative orthogonal projection. The algorithm is extended to the high dimensional problems by hierarchical Tuck decomposition of solution tensors and a corresponding conservative projection algorithm. Extensive numerical tests on the VP system are showcased for the algorithm’s efficacy.

Guo, Wei↗

DOE OSTI2011

Simple algorithm for computing the geometric measure of entanglement

We present an easy implementable algorithm for approximating the geometric measure of entanglement from above. The algorithm can be applied to any multipartite mixed state. It involves only the solution of an eigenproblem and finding a singular value decomposition; no further numerical techniques are needed. To provide examples, the algorithm was applied to the isotropic states of three qubits and the three-qubit XX model with external magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Gradient descent algorithm applied to wavefront retrieval from through-focus images by an extreme ultraviolet microscope with partially coherent source

The wavefront retrieval by gradient descent algorithm that is typically applied to coherent or incoherent imaging is extended to retrieve a wavefront from a series of through-focus images by partially coherent illumination. For accurate retrieval, we modeled partial coherence as well as object transmittance into the gradient descent algorithm. However, this modeling increases the computation time due to the complexity of partially coherent imaging simulation that is repeatedly used in the optimization loop. To accelerate the computation, we incorporate not only the Fourier transform but also an eigenfunction decomposition of the image. As a demonstration, the extended algorithm is applied to retrieve a field-dependent wavefront of a microscope operated at extreme ultraviolet wavelength (13.4 nm). The retrieved wavefront qualitatively matches the expected characteristics of the lens design.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Rank-Limiting Strategies for Optimizing Tensor-Train Finite-Difference Time-Domain Simulations

We introduce rank-limiting strategies to optimize tensor-train decompositions for three-dimensional finite-difference time-domain simulations using the relationship between the tensors and their specific dimensionality. These include the use of hard caps on the inner ranks of the tensor train decomposition and the use of a group rounding algorithm taking into account all field components simultaneously. Here, several numerical examples are considered to verify the efficacy of the proposed optimization strategies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Coherency-Based Detection Algorithm for Synchrophasor Cyberattacks

The wide area monitoring system (WAMS) is critical for power system situational awareness, but represents a growing cybersecurity vulnerability. Malicious adversaries may seek to compromise one or more PMUs in order to effect control decisions that unnecessarily disrupt typical grid operations. One example of a particularly pernicious attack vector is the spoofing or replaying of a fault event using one or more compromised PMUs. This work documents the development and validation of a coherency-based cyberattack detection algorithm that integrates a sliding-window singular value decomposition (SVD) with physics-based partitioning analysis to achieve accurate classification of events. Special consideration is given to discerning a sophisticated fault-replay or fault spoofing attack from actual faults. A software-based cybersecurity testbed has been developed for rigorous testing of the algorithm. The algorithm is further validated using simulated synchrophasor datasets obtained from a MinniWECC 63-bus test system. Results show that the algorithm can successfully detect fault-replay attacks even when over half of the PMUs are compromised.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2017

Information criteria for quantifying loss of reversibility in parallelized KMC

Parallel Kinetic Monte Carlo (KMC) is a potent tool to simulate stochastic particle systems efficiently. However, despite literature on quantifying domain decomposition errors of the particle system for this class of algorithms in the short and in the long time regime, no study yet explores and quantifies the loss of time-reversibility in Parallel KMC. Inspired by concepts from non-equilibrium statistical mechanics, we propose the entropy production per unit time, or entropy production rate, given in terms of an observable and a corresponding estimator, as a metric that quantifies the loss of reversibility. Typically, this is a quantity that cannot be computed explicitly for Parallel KMC, which is why we develop a posteriori estimators that have good scaling properties with respect to the size of the system. Through these estimators, we can connect the different parameters of the scheme, such as the communication time step of the parallelization, the choice of the domain decomposition, and the computational schedule, with its performance in controlling the loss of reversibility. From this point of view, the entropy production rate can be seen both as an information criterion to compare the reversibility of different parallel schemes and as a tool to diagnose reversibility issues with a particular scheme. As a demonstration, we use Sandia Lab's SPPARKS software to compare different parallelization schemes and different domain (lattice) decompositions.

97 MATHEMATICS AND COMPUTING↗