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Multiresolution convolutional autoencoders

Herein we propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer learning. The method provides an adaptive, hierarchical architecture that capitalizes on a progressive training approach for multiscale spatio-temporal data. This framework allows for inputs across multiple scales: starting from a compact (small number of weights) network architecture and low-resolution data, our network progressively deepens and widens itself in a principled manner to encode new information in the higher resolution data based on its current performance of reconstruction. Basic transfer learning techniques are applied to ensure information learned from previous training steps can be rapidly transferred to the larger network. As a result, the network can dynamically capture different scaled features at different depths of the network. The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.

97 MATHEMATICS AND COMPUTING↗

Multiresolution edge detection using enhanced fuzzy c-means clustering for ultrasound image speckle reduction

Purpose: Speckle suppression in ultrasound (US) images of various anatomic structures via a novel speckle noise reduction algorithm. Methods: The proposed algorithm employs an enhanced fuzzy c-means (EFCM) clustering and multiresolution wavelet analysis to distinguish edges from speckle noise in US images. The edge detection procedure involves a coarse-to-fine strategy with spatial and interscale constraints so as to classify wavelet local maxima distribution at different frequency bands. As an outcome, an edge map across scales is derived whereas the wavelet coefficients that correspond to speckle are suppressed in the inverse wavelet transform acquiring the denoised US image. Results: A total of 34 thyroid, liver, and breast US examinations were performed on a Logiq 9 US system. Each of these images was subjected to the proposed EFCM algorithm and, for comparison, to commercial speckle reduction imaging (SRI) software and another well-known denoising approach, Pizurica's method. The quantification of the speckle suppression performance in the selected set of US images was carried out via Speckle Suppression Index (SSI) with results of 0.61, 0.71, and 0.73 for EFCM, SRI, and Pizurica's methods, respectively. Peak signal-to-noise ratios of 35.12, 33.95, and 29.78 and edge preservation indices of 0.94, 0.93, and 0.86 were found for the EFCM, SIR, and Pizurica's method, respectively, demonstrating that the proposed method achieves superior speckle reduction performance and edge preservation properties. Based on two independent radiologists’ qualitative evaluation the proposed method significantly improved image characteristics over standard baseline B mode images, and those processed with the Pizurica's method. Furthermore, it yielded results similar to those for SRI for breast and thyroid images significantly better results than SRI for liver imaging, thus improving diagnostic accuracy in both superficial and in-depth structures. Conclusions: A new wavelet-based EFCM clustering model was introduced toward noise reduction and detail preservation. The proposed method improves the overall US image quality, which in turn could affect the decision-making on whether additional imaging and/or intervention is needed.

60 APPLIED LIFE SCIENCES↗

A multiresolution adaptive wavelet method for nonlinear partial differential equations

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

97 MATHEMATICS AND COMPUTING↗

MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.

00A72↗

DynaM: Dynamic Multiresolution Data Representation for Large-Scale Scientific Analysis

Fast growing large-scale systems enable scientific applications to run at a much larger scale and accordingly produce gigantic volumes of simulation output. Such data imposes a grand challenge to post-processing tasks such as visualization and data analysis, because these tasks are often performed at a host machine that is remotely located and equipped with much less memory and storage resources. During the simulation runs, it is also desirable for scientists to be able to interactively monitor and steer the progress of simulation. This requires scientific data to be represented in an efficient form for initial exploration and computation steering. In this paper, we propose DynaM a software framework that can represent scientific data in a multiresolution form, and dynamically organize data blocks into an optimized layout for efficient scientific analysis. DynaM supports a convolution-based multiresolution data representation for abstracting scientific data for visualization at a wide spectrum of resolution. To support the efficient generation and retrieval of different data granularities from such representation, a dynamic data organization in DynaM is enabled to cater distinct peculiarities of different size data blocks for efficient and balanced I/O performance. Our experimental results demonstrate that DynaM can efficiently represent large scientific dataset and speed up the visualization of multidimensional scientific data. An up to 29 times speedup is achieved on Jaguar supercomputer at Oak Ridge National Laboratory.

Tian, Yuan↗

Multiscale geometric modeling of macromolecules I: Cartesian representation

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the polarized curvature, for the prediction of protein binding sites.

97 MATHEMATICS AND COMPUTING↗

Multiresolution persistent homology for excessively large biomolecular datasets

Although persistent homology has emerged as a promising tool for the topological simplification of complex data, it is computationally intractable for large datasets. We introduce multiresolution persistent homology to handle excessively large datasets. We match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. We utilize flexibility-rigidity index to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution of the rigidity density, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA molecules. In particular, the topological persistence of a virus capsid with 273 780 atoms is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks, and graphs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Selecting registration schemes in case of interstitial lung disease follow-up in CT

Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information), four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the range of 1.985–2.156 mm and 1.966–2.234 mm, for NLP and ILD affected regions, respectively, excluding schemes with statistically significant lower performance (Wilcoxon signed-ranks test, p < 0.05), resulting in 13 finally selected registration schemes. Conclusions: Selected registration schemes in case of ILD CT follow-up analysis indicate the significance of adaptive stochastic gradient descent optimizer, as well as the importance of combined rigid and nonrigid schemes providing high accuracy and time efficiency. The selected optimal deformable registration schemes are equivalent in terms of their accuracy and thus compatible in terms of their clinical outcome.

60 APPLIED LIFE SCIENCES↗

Multiresolution molecular mechanics: Implementation and efficiency

Atomistic/continuum coupling methods combine accurate atomistic methods and efficient continuum methods to simulate the behavior of highly ordered crystalline systems. Coupled methods utilize the advantages of both approaches to simulate systems at a lower computational cost, while retaining the accuracy associated with atomistic methods. Many concurrent atomistic/continuum coupling methods have been proposed in the past; however, their true computational efficiency has not been demonstrated. The present work presents an efficient implementation of a concurrent coupling method called the Multiresolution Molecular Mechanics (MMM) for serial, parallel, and adaptive analysis. First, we present the features of the software implemented along with the associated technologies. The scalability of the software implementation is demonstrated, and the competing effects of multiscale modeling and parallelization are discussed. Then, the algorithms contributing to the efficiency of the software are presented. These include algorithms for eliminating latent ghost atoms from calculations and measurement-based dynamic balancing of parallel workload. The efficiency improvements made by these algorithms are demonstrated by benchmark tests. The efficiency of the software is found to be on par with LAMMPS, a state-of-the-art Molecular Dynamics (MD) simulation code, when performing full atomistic simulations. Speed-up of the MMM method is shown to be directly proportional to the reduction of the number of the atoms visited in force computation. Finally, an adaptive MMM analysis on a nanoindentation problem, containing over a million atoms, is performed, yielding an improvement of 6.3–8.5 times in efficiency, over the full atomistic MD method. For the first time, the efficiency of a concurrent atomistic/continuum coupling method is comprehensively investigated and demonstrated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fast Multiresolution Reads of Massive Simulation Datasets

Today’s massively parallel simulation codes can produce output ranging up to many terabytes of data. Utilizing this data to support scientific inquiry requires analysis and visualization, yet the sheer size of the data makes it cumbersome or impossible to read without computational resources similar to the original simulation. We identify two broad classes of problems for reading data and present effective solutions for both. The first class of data reads depends on user requirements and available resources. Tasks such as visualization and user-guided analysis may be accomplished using only a subset of variables with a restricted spatial extent at a reduced resolution. The other class of reads requires full resolution multivariate data to be loaded, for example to restart a simulation. We show that utilizing the hierarchical multiresolution IDX data format enables scalable and efficient serial and parallel read access on a variety of hardware from supercomputers down to portable devices. Here, we demonstrate interactive view-dependent visualization and analysis of massive scientific datasets using low-power commodity hardware, and we compare read performance with other parallel file formats for both full and partial resolution data.

97 MATHEMATICS AND COMPUTING↗

Dynamics and lipid membrane coupling of the RAS-RAF complex revealed via multiscale simulations

To gain molecular and mechanistic insights into initiation of the RAS-RAF signaling cascade, we developed and used a combination of multiscale simulation and experimental approaches. The influence and impact of the membrane on RAS and RAF proteins is a factor we are just beginning to understand and appreciate in more detail. Molecular simulation is an ideal methodology to further study this complicated relationship between the membrane and associated proteins. Our previous work using Multiscale Machine-learned Modeling Infrastructure investigated different lipid compositions solely around the KRAS4b protein and the interplay between protein behavior and these membrane environments. Multiscale Machine-learned Modeling Infrastructure uses machine learning to couple adjacent simulation scales and has been efficiently scaled across some of the world’s largest high-performance computers. Recently, we have expanded this multiresolution framework to include the all-atom simulation scale and to incorporate the RAF RBDCRD domains. Here, we present the overall analysis results from this new simulation campaign comprising a mixture of RAS and RAF RBDCRD proteins. Approximately 35,000 coarse-grained and 10,000 all-atom molecular dynamics simulations were completed, sampled from a variety of protein/lipid composition configurations that were generated from a micron-scale continuum simulation containing hundreds of copies of the proteins. Our studies suggest that orientations of the RAS-RBDCRD complex on the membrane occupy distinct configurational states, and the spatial patterns of lipid arrangements around these different protein states are unique to each state. The extent and size of lipid “fingerprints” imposed on the membrane by the RAS-RBDCRD protein complex are significantly larger than observed for just the RAS protein on its own. These protein complexes strongly associate, but we do not observe statistically significant preferred protein-protein orientations. These observations indicate that spatial colocalization of RAS-RBDCRD proteins in the same vicinity may be assisted by specific membrane environments, acting to increase the probability of signaling complex formation.

Carpenter, Timothy S. [Lawrence Livermore National↗

Impact of Model Resolution on Tropical Cyclone Simulation Using the HighResMIP–PRIMAVERA Multimodel Ensemble

A multimodel, multiresolution set of simulations over the period 1950–2014 using a common forcing protocol from CMIP6 HighResMIP have been completed by six modeling groups. Analysis of tropical cyclone performance using two different tracking algorithms suggests that enhanced resolution toward 25 km typically leads to more frequent and stronger tropical cyclones, together with improvements in spatial distribution and storm structure. Both of these factors reduce typical GCM biases seen at lower resolution. Using single ensemble members of each model, there is little evidence of systematic improvement in interannual variability in either storm frequency or accumulated cyclone energy as compared with observations when resolution is increased. Changes in the relationships between large-scale drivers of climate variability and tropical cyclone variability in the Atlantic Ocean are also not robust to model resolution. However, using a larger ensemble of simulations (of up to 14 members) with one model at different resolutions does show evidence of increased skill at higher resolution. The ensemble mean correlation of Atlantic interannual tropical cyclone variability increases from ~0.5 to ~0.65 when resolution increases from 250 to 100 km. In the northwestern Pacific Ocean the skill keeps increasing with 50-km resolution to 0.7. These calculations also suggest that more than six members are required to adequately distinguish the impact of resolution within the forced signal from the weather noise.

54 ENVIRONMENTAL SCIENCES↗

Group‐sparsity regularization for ill‐posed subsurface flow inverse problems

Abstract Sparse representations provide a flexible and parsimonious description of high‐dimensional model parameters for reconstructing subsurface flow property distributions from limited data. To further constrain ill‐posed inverse problems, group‐sparsity regularization can take advantage of possible relations among the entries of unknown sparse parameters when: (i) groups of sparse elements are either collectively active or inactive and (ii) only a small subset of the groups is needed to approximate the parameters of interest. Since subsurface properties exhibit strong spatial connectivity patterns they may lead to sparse descriptions that satisfy the above conditions. When these conditions are established, a group‐sparsity regularization can be invoked to facilitate the solution of the resulting inverse problem by promoting sparsity across the groups. The proposed regularization penalizes the number of groups that are active without promoting sparsity within each group. Two implementations are presented in this paper: one based on the multiresolution tree structure of Wavelet decomposition, without a need for explicit prior models, and another learned from explicit prior model realizations using sparse principal component analysis (SPCA). In each case, the approach first classifies the parameters of the inverse problem into groups with specific connectivity features, and then takes advantage of the grouped structure to recover the relevant patterns in the solution from the flow data. Several numerical experiments are presented to demonstrate the advantages of additional constraining power of group‐sparsity in solving ill‐posed subsurface model calibration problems.

Golmohammadi, Azarang↗

Multiresolution classification of turbulence features in image data through machine learning

During large-scale simulations, intermediate data products such as image databases have become popular due to their low relative storage cost and fast in-situ analysis. Serving as a form of data reduction, these image databases have become more acceptable to perform data analysis on. In this work, we present an image-space detection and classification system for extracting vortices at multiple scales through wavelet-based filtering. A custom image-space descriptor is used to encode a large variety of vortex-types and a machine learning system is trained for fast classification of vortex regions. By combining a radial-based histogram descriptor, a bag of visual words feature descriptor, and a support vector machine, our results show that we are able to detect and classify vortex features at various sizes at multiple scales. Once trained, our framework enables the fast extraction of vortices on new, unknown image datasets for flow analysis.

97 MATHEMATICS AND COMPUTING↗

A domain-specific compiler for a parallel multiresolution adaptive numerical simulation environment

This paper describes the design and implementation of a layered domain-specific compiler to support MADNESS---Multiresolution ADaptive Numerical Environment for Scientific Simulation. MADNESS is a high-level software environment for the solution of integral and differential equations in many dimensions, using adaptive and fast harmonic analysis methods with guaranteed precision. MADNESS uses k-d trees to represent spatial functions and implements operators like addition, multiplication, differentiation, and integration on the numerical representation of functions. The MADNESS runtime system provides global namespace support and a task-based execution model including futures. MADNESS is currently deployed on massively parallel supercomputers and has enabled many science advances. Due to the highly irregular and statically unpredictable structure of the k-d trees representing the spatial functions encountered in MADNESS applications, only purely runtime approaches to optimization have previously been implemented in the MADNESS framework. This paper describes a layered domain-specific compiler developed to address some performance bottlenecks in MADNESS. The newly developed static compile-time optimizations, in conjunction with the MADNESS runtime support, enable significant performance improvement for the MADNESS framework.

Rajbhandari, Samyam↗

Algorithms and data structures to accelerate network analysis

As the sheer amount of computer generated data continues to grow exponentially, new bottlenecks are unveiled that require rethinking our traditional software and hardware architectures. Here in this paper we present five algorithms and data structures (long queue emulation, lockless bimodal queues, tail early dropping, LFN tables, and multiresolution priority queues) designed to optimize the process of analyzing network traffic. We integrated these optimizations on R-Scope, a high performance network appliance that runs the Bro network analyzer, and present benchmarks showcasing performance speed ups of 5X at traffic rates of 10 Gbps.

97 MATHEMATICS AND COMPUTING↗

Resolution dependence of precipitation statistical fidelity in hindcast simulations

This article is a U.S. Government work and is in the public domain in the USA. Numerous studies have shown that atmospheric models with high horizontal resolution better represent the physics and statistics of precipitation in climate models. While it is abundantly clear from these studies that high-resolution increases the rate of extreme precipitation, it is not clear whether these added extreme events are “realistic”; whether they occur in simulations in response to the same forcings that drive similar events in reality. In order to understand whether increasing horizontal resolution results in improved model fidelity, a hindcast-based, multiresolution experimental design has been conceived and implemented: the InitiaLIzed-ensemble, Analyze, and Develop (ILIAD) framework. The ILIAD framework allows direct comparison between observed and simulated weather events across multiple resolutions and assessment of the degree to which increased resolution improves the fidelity of extremes. Analysis of 5 years of daily 5 day hindcasts with the Community Earth System Model at horizontal resolutions of 220, 110, and 28 km shows that: (1) these hindcasts reproduce the resolution-dependent increase of extreme precipitation that has been identified in longer-duration simulations, (2) the correspondence between simulated and observed extreme precipitation improves as resolution increases; and (3) this increase in extremes and precipitation fidelity comes entirely from resolved-scale precipitation. Evidence is presented that this resolution-dependent increase in precipitation intensity can be explained by the theory of Rauscher et al. (), which states that precipitation intensifies at high resolution due to an interaction between the emergent scaling (spectral) properties of the wind field and the constraint of fluid continuity.

54 ENVIRONMENTAL SCIENCES↗