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At least 811 records · Page 45

Nonlinear Ensemble Filtering with Diffusion Models: Application to the Surface Quasigeostrophic Dynamics

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here, we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed ensemble score filter (EnSF) is completely training free and can efficiently generate a set of analysis ensemble members. Here, in this study, we apply the EnSF to a surface quasigeostrophic model and compare its performance against the popular local ensemble transform Kalman filter (LETKF), which makes Gaussian assumptions in the analysis step. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that while LETKF maintains optimal performance in the case of linear observations of the entire state and a perfect model, EnSF shows improvements over LETKF when nonlinear observations are assimilated and the system is subject to unexpected model errors. A spectral decomposition of the analysis results in this nonlinear observation regime shows that the largest improvements over LETKF occur at large scales (small wavenumbers), where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity motivates further development of the algorithm for more realistic problems.

Artificial intelligence↗

A Data Type for Efficient Representation of Other Data Types

A self-organizing, monomorphic data type denoted a sequence has been conceived to address certain concerns that arise in programming parallel computers. A sequence in the present sense can be regarded abstractly as a vector, set, bag, queue, or other construct. Heretofore, in programming a parallel computer, it has been necessary for the programmer to state explicitly, at the outset, what parts of the program and the underlying data structures must be represented in parallel form. Not only is this requirement not optimal from the perspective of implementation; it entails an additional requirement that the programmer have intimate understanding of the underlying parallel structure. The present sequence data type overcomes both the implementation and parallel structure obstacles. In so doing, the sequence data type provides unified means by which the programmer can represent a data structure for natural and automatic decomposition to a parallel computing architecture. Sequences exhibit the behavioral and structural characteristics of vectors, but the underlying representations are automatically synthesized from combinations of programmers advice and execution use metrics. Sequences can vary bidirectionally between sparseness and density, making them excellent choices for many kinds of algorithms. The novelty and benefit of this behavior lies in the fact that it can relieve programmers of the details of implementations. The creation of a sequence enables decoupling of a conceptual representation from an implementation. The underlying representation of a sequence is a hybrid of representations composed of vectors, linked lists, connected blocks, and hash tables. The internal structure of a sequence can automatically change from time to time on the basis of how it is being used. Those portions of a sequence where elements have not been added or removed can be as efficient as vectors. As elements are inserted and removed in a given portion, then different methods are utilized to provide both an access and memory strategy that is optimized for that portion and the use to which it is put.

James, Mark↗

A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems

We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share “nonlocal” interfaces of the size of the nonlocal horizon. This system of nonlocal equations is first rewritten in terms of minimization of a nonlocal energy, then discretized with a meshfree approximation and finally solved via a Lagrange multiplier approach in a way that resembles the finite element tearing and interconnect method. Specifically, we propose a distributed projected gradient algorithm for the solution of the Lagrange multiplier system, whose unknowns determine the nonlocal interface conditions between subdomains. Several two-dimensional numerical tests on problems as large as 191 million unknowns illustrate the strong and the weak scalability of our algorithm, which outperforms the standard approach to the distributed numerical solution of the problem. Finally, this work is the first rigorous numerical study in a two-dimensional multi-domain setting for nonlocal operators with finite horizon and, as such, it is a fundamental step towards increasing the use of nonlocal models in large scale simulations.

42 ENGINEERING↗

Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes

In this work, we develop a quartic-scaling implementation of coupled-cluster singles and doubles (CCSD) based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced (RR) coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Furthermore, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

GRIZZLY Model of Multi-Reactive Species Diffusion, Moisture/Heat Transfer and Alkali-Silica Reaction for Simulating Concrete Aging and Degradation

Concrete is widely used in the construction of nuclear facilities because of its structural strength and its ability to shield radiation. The use of concrete in nuclear power plants for containment and shielding of radiation and radioactive materials has made its performance crucial for the safe operation of the facility. As such, when life extension is considered for nuclear power plants, it is critical to have accurate and reliable predictive tools to address concerns related to various aging processes of concrete structures and the capacity of structures subjected to age-related degradation. The goal of this report is to document the progress of the development and implementation of a fully coupled thermo-hydro-mechanical-chemical model in GRIZZLY code with the ultimate goal to reliably simulate and predict long-term performance and response of aged NPP concrete structures subjected to a number of aging mechanisms including external chemical attacks and volume-changing chemical reactions within concrete structures induced by alkali-silica reactions and long-term exposure to irradiation. Based on a number of survey reports of concrete aging mechanisms relevant to nuclear power plants and recommendations from researchers in concrete community, we’ve implemented three modules during FY15 in GRIZZLY code, (1) multi-species reactive diffusion model within cement materials; (2) coupled moisture and heat transfer model in concrete; and (3) anisotropic, stress-dependent, alkali-silica reaction induced swelling model. The multi-species reactive diffusion model was implemented with the objective to model aging of concrete structures subjected to aggressive external chemical attacks (e.g., chloride attack, sulfate attack, etc.). It considers multiple processes relevant to external chemical attacks such as diffusion of ions in aqueous phase within pore spaces, equilibrium chemical speciation reactions and kinetic mineral dissolution/precipitation. The moisture/heat transfer module was implemented to simulate long-term spatial and temporal evolutions of the moisture and temperature fields within concrete structures at both room and elevated temperatures. The ASR swelling model implemented in GRIZZLY code can simulate anisotropic expansions of ASR gel under either uniaxial, biaxial and triaxial stress states, and can be run simultaneously with the moisture/heat transfer model and coupled with various elastic/inelastic solid mechanics models that were implemented in GRIZZLY code previously. This report provides detailed descriptions of the governing equations, constitutive equations and numerical algorithms of the three modules implemented in GRIZZLY during FY15, simulation results of example problems and model validation results by comparing simulations with available experimental data reported in the literature. The close match between the experiments and simulations clearly demonstrate the potential of GRIZZLY code for reliable evaluation and prediction of long-term performance and response of aged concrete structures in nuclear power plants.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Electronic Structure Theories of Singlet Fission and Multiple Exciton Generation (Final Report)

This DOE grant supported the development of electronic structure theory, algorithms, and computer programs for simulating singlet fission and multiple excision generation processes from Sept. 2013 to Aug. 2018 (which was terminated due to the PI’s departure from Northwestern University to industry). One of the main achievements is the development of the so-called active space decomposition (ASD) method hat describes exciton dynamics in organic semiconductors and spin dynamics in strongly correlated materials. The resulting software was interfaced with the Brilliantly Advanced General Electronic-structure Library (BAGEL) package and widely disseminated to the research community.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A real-time robot arm collision avoidance system

A data structure and update algorithm are presented for a prototype real-time collision avoidance safety system simulating a multirobot workspace. The data structure is a variant of the octree, which serves as a spatial index. An octree recursively decomposes 3D space into eight equal cubic octants until each octant meets some decomposition criteria. The N-objects octree, which indexes a collection of 3D primitive solids is used. These primitives make up the two (seven-degrees-of-freedom) robot arms and workspace modeled by the system. As robot arms move, the octree is updated to reflect their changed positions. During most update cycles, any given primitive does not change which octree nodes it is in. Thus, modification to the octree is rarely required. Cycle time for interpreting current arm joint angles, updating the octree to reflect new positions, and detecting/reporting imminent collisions averages 30 ms on an Intel 80386 processor running at 20 MHz.

Shaffer, Clifford A.↗

Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators

Electron transport in realistic physical and chemical systems often involves the nontrivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a nonunitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here, we present a general algorithm for implementing the action of any nonunitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. Furthermore, the results are in agreement with classical calculations, showing promise in simulating nonunitary operations on intermediate-term and future quantum devices.

74 ATOMIC AND MOLECULAR PHYSICS↗

A Flexible Forwarding Scheme to Improve Latency-Bound Irregular P2P Communication in MPI

We propose an algorithm to efficiently perform latency-bound communication scenarios that consist of many small messages. In these parallel scenarios, processes typically pass around a lot of small-sized messages of a few KBs of size. Performing communication operations with P2P MPI routines or collective MPI routines (including neighborhood collectives) in such scenarios may not always yield the optimal results and may not resolve the latency bottleneck. To this end, we develop a regular structure called virtual process topology (VPT) on which the messages can be communicated in a structured and controlled manner. Using parameters of this topology, one can tune the rate of aggression in tackling the latency costs. We demonstrate that our communication algorithm is preferable to MPI P2P and collective routines for latency-bound communication and it can easily be adapted only by replacing calls to MPI routines in a parallel application. We show how to adapt existing topology-aware mapping heuristics to address the volume overhead due to communicating messages on the VPT. Moreover, we propose a novel swap-based mapping heuristic to address this overhead by optimizing the maximum volume handled by a process. Experiments on synthetic communication graphs as well as real-world applications such as parallel Canonical Polyadic sparse tensor decomposition and parallel sparse matrix-dense matrix multiplication show that our approach is a powerful way of overcoming the bottlenecks posed by sparse and latency-bound irregular communication.

communication algorithm↗

Interregional Transmission Operational Coordination (IRTOC)

This report presents a modeling and evaluation framework developed through the Inter-Regional Transmission Operational Coordination (IRTOC) project to study market-to-market (M2M) congestion management across day-ahead and real-time markets. The framework extends the Sienna platform through Sienna Decomposition, a multi-stage evaluation architecture that enables flexible representation of multiple regions and systematic assessment of alternative market coordination designs. Additional modeling capabilities include reserve deliverability constraints, High-Voltage Direct Current (HVDC) optimization for Alternating Current (AC) congestion management, and several real-time distributed coordination algorithms. Case studies using the RTS-GMLC test system and a large-scale Eastern Interconnection model demonstrate that the framework can evaluate alternative coordination structures and quantify their economic and operational impacts. The proposed framework provides a scalable platform for analyzing inter-regional coordination strategies in large-scale electricity markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Strong scaling of general-purpose molecular dynamics simulations on GPUs

We describe a highly optimized implementation of MPI domain decomposition in a GPU-enabled, general-purpose molecular dynamics code, HOOMD-blue (Anderson and Glotzer, 2013). Here, our approach is inspired by a traditional CPU-based code, LAMMPS (Plimpton, 1995), but is implemented within a code that was designed for execution on GPUs from the start (Anderson et al., 2008). The software supports short-ranged pair force and bond force fields and achieves optimal GPU performance using an autotuning algorithm. We are able to demonstrate equivalent or superior scaling on up to 3375 GPUs in Lennard-Jones and dissipative particle dynamics (DPD) simulations of up to 108 million particles. GPUDirect RDMA capabilities in recent GPU generations provide better performance in full double precision calculations. For a representative polymer physics application, HOOMD-blue 1.0 provides an effective GPU vs. CPU node speed-up of 12.5x.

97 MATHEMATICS AND COMPUTING↗

First-principles calculated decomposition pathways for LiBH 4 nanoclusters

Here, we analyze thermodynamic stability and decomposition pathways of LiBH 4 nanoclusters using grand-canonical free-energy minimization based on total energies and vibrational frequencies obtained from density-functional theory (DFT) calculations. We consider (LiBH 4 ) n nanoclusters with n = 2 to 12 as reactants, while the possible products include (Li) n , (B) n , (LiB) n , (LiH) n , and Li 2 B n H n ; off-stoichiometric LinBnHm (m ≤ 4n) clusters were considered for n = 2, 3, and 6. Cluster ground-state configurations have been predicted using prototype electrostatic ground-state (PEGS) and genetic algorithm (GA) based structural optimizations. Free-energy calculations show hydrogen release pathways markedly differ from those in bulk LiBH 4 . While experiments have found that the bulk material decomposes into LiH and B, with Li 2 B 12 H 12 as a kinetically inhibited intermediate phase, (LiBH 4 ) n nanoclusters with n ≤ 12 are predicted to decompose into mixed Li n B n clusters via a series of intermediate clusters of Li n B n H m (m ≤ 4n). The calculated pressure-composition isotherms and temperature-pressure isobars exhibit sloping plateaus due to finite size effects on reaction thermodynamics. Generally, decomposition temperatures of free-standing clusters are found to increase with decreasing cluster size due to thermodynamic destabilization of reaction products.

36 MATERIALS SCIENCE↗

Parallel Implicit Algorithms for CFD

The main goal of this project was efficient distributed parallel and workstation cluster implementations of Newton-Krylov-Schwarz (NKS) solvers for implicit Computational Fluid Dynamics (CFD.) "Newton" refers to a quadratically convergent nonlinear iteration using gradient information based on the true residual, "Krylov" to an inner linear iteration that accesses the Jacobian matrix only through highly parallelizable sparse matrix-vector products, and "Schwarz" to a domain decomposition form of preconditioning the inner Krylov iterations with primarily neighbor-only exchange of data between the processors. Prior experience has established that Newton-Krylov methods are competitive solvers in the CFD context and that Krylov-Schwarz methods port well to distributed memory computers. The combination of the techniques into Newton-Krylov-Schwarz was implemented on 2D and 3D unstructured Euler codes on the parallel testbeds that used to be at LaRC and on several other parallel computers operated by other agencies or made available by the vendors. Early implementations were made directly in Massively Parallel Integration (MPI) with parallel solvers we adapted from legacy NASA codes and enhanced for full NKS functionality. Later implementations were made in the framework of the PETSC library from Argonne National Laboratory, which now includes pseudo-transient continuation Newton-Krylov-Schwarz solver capability (as a result of demands we made upon PETSC during our early porting experiences). A secondary project pursued with funding from this contract was parallel implicit solvers in acoustics, specifically in the Helmholtz formulation. A 2D acoustic inverse problem has been solved in parallel within the PETSC framework.

Keyes, David E.↗

Problematic projection to the in-sample subspace for a kernelized anomaly detector

We examine the properties and performance of kernelized anomaly detectors, with an emphasis on the Mahalanobis-distance-based kernel RX (KRX) algorithm. Although the detector generally performs well for high-bandwidth Gaussian kernels, it exhibits problematic (in some cases, catastrophic) performance for distances that are large compared to the bandwidth. By comparing KRX to two other anomaly detectors, we can trace the problem to a projection in feature space, which arises when a pseudoinverse is used on the covariance matrix in that feature space. Here, we show that a regularized variant of KRX overcomes this difficulty and achieves superior performance over a wide range of bandwidths.

58 GEOSCIENCES↗

A real-time robot arm collision detection system

A data structure and update algorithm are presented for a prototype real time collision detection safety system for a multi-robot environment. The data structure is a variant of the octree, which serves as a spatial index. An octree recursively decomposes 3-D space into eight equal cubic octants until each octant meets some decomposition criteria. The octree stores cylspheres (cylinders with spheres on each end) and rectangular solids as primitives (other primitives can easily be added as required). These primitives make up the two seven degrees-of-freedom robot arms and environment modeled by the system. Octree nodes containing more than a predetermined number N of primitives are decomposed. This rule keeps the octree small, as the entire environment for the application can be modeled using a few dozen primitives. As robot arms move, the octree is updated to reflect their changed positions. During most update cycles, any given primitive does not change which octree nodes it is in. Thus, modification to the octree is rarely required. Incidents in which one robot arm comes too close to another arm or an object are reported. Cycle time for interpreting current joint angles, updating the octree, and detecting/reporting imminent collisions averages 30 milliseconds on an Intel 80386 processor running at 20 MHz.

Shaffer, Clifford A.↗

Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. In this work, we consider a class of polyhedral functions that arise particularly as convex lower envelopes of multibang regularizers and show that they have beneficial properties with respect to regularization of relaxations of integer optimal control problems. We extend the algorithmic framework of the combinatorial integral approximation such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control problem.

97 MATHEMATICS AND COMPUTING↗

Optimal message log reclamation for uncoordinated checkpointing

Uncoordinated checkpointing for message-passing systems allows maximum process autonomy and general nondeterministic execution, but suffers from potential domino effect and the large space overhead for maintaining checkpoints and message logs. Traditionally, it has been assumed that only obsolete checkpoints and message logs before the global recovery line can be garbage-collected. Recently, an approach to identifying all garbage checkpoints based on recovery line transformation and decomposition has been developed. We show in this paper that the same approach can be applied to the problem of identifying all garbage message logs for systems requiring message logging to record in-transit messages. Communication trace-driven simulation for several parallel programs is used to evaluate the proposed algorithm.

Wang, Yi-Min↗

DeMAID/GA an Enhanced Design Manager's Aid for Intelligent Decomposition

Many companies are looking for new tools and techniques to aid a design manager in making decisions that can reduce the time and cost of a design cycle. One tool is the Design Manager's Aid for Intelligent Decomposition (DeMAID). Since the initial public release of DeMAID in 1989, much research has been done in the areas of decomposition, concurrent engineering, parallel processing, and process management; many new tools and techniques have emerged. Based on these recent research and development efforts, numerous enhancements have been added to DeMAID to further aid the design manager in saving both cost and time in a design cycle. The key enhancement, a genetic algorithm (GA), will be available in the next public release called DeMAID/GA. The GA sequences the design processes to minimize the cost and time in converging a solution. The major enhancements in the upgrade of DeMAID to DeMAID/GA are discussed in this paper. A sample conceptual design project is used to show how these enhancements can be applied to improve the design cycle.

Rogers, J. L.↗