SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

A common feature of many methods in computational mechanics is that there is often a way of estimating the error in the computed solution. The situation for computational mechanics codes based upon the Material Point Method is very different in that there has been comparatively little work on computable error estimates for these methods. This work is concerned with introducing such an approach for the Material Point Method. Although it has been observed that spatial errors may dominate temporal ones at stable time steps, recent work has made more precise the sources and forms of the different MPM errors. There is then a need to estimate these errors computationally through computable estimates of the different errors in the material point method. Estimates of the different spatial errors in the Material Point Method are constructed based upon nodal derivatives of the different physical variables in MPM. These derivatives are then estimated using standard difference approximations calculated on the background mesh. The use of these estimates of the spatial error makes it possible to measure the growth of errors over time. A number of computational experiments are used to illustrate the performance of the computed error estimates. As the key feature of the approach is the calculation of derivatives on the regularly spaced background mesh, the extension to calculating derivatives and hence to error estimates for higher dimensional problems is clearly possible.

Electrocardiographic imaging (ECGI) is a clinical and research tool for noninvasive diagnosis of cardiac electrical dysfunction. The position of the heart within the torso is both an input and common source of error in ECGI. Many studies have sought to improve cardiac localization accuracy, however, few have examined quantitatively the effects of uncertainty in the position of the heart within the torso. Recently developed uncertainty quantification (UQ) tools enable the robust application of UQ to ECGI reconstructions. In this study, we developed an ECGI formulation, which for the first time, directly incorporated uncertainty in the heart position. The result is an ECGI solution that is robust to variation in heart position. Using data from two Langendorff experimental preparations, each with 120 heartbeats distributed across three activation sequences, we found that as heart position uncertainty increased above ±10 mm, the solution quality of the ECGI degraded. However, even at large heart position uncertainty (±40 mm) our novel UQ-ECGI formulation produced reasonable solutions (root mean squared error < 1 mV, spatial correlation >0.6, temporal correlation >0.75).

Purpose:

A subset of patients with metopic craniosynostosis are noted to have elevated intracranial pressure (ICP). However, it is not known if the propensity for elevated ICP is influenced by the severity of metopic cranial dysmorphology.

Children with nonsyndromic single-suture metopic synostosis were prospectively enrolled and underwent optical coherence tomography to measure optic nerve head morphology. Preoperative head computed tomography scans were assessed for endocranial bifrontal angle as well as scaled metopic synostosis severity score (MSS) and cranial morphology deviation score determined by CranioRate, an automated severity classifier.

Forty-seven subjects were enrolled between 2014 and 2019, at an average age of 8.5 months at preoperative computed tomography and 11.8 months at index procedure. Fourteen patients (29.7%) had elevated optical coherence tomography parameters suggestive of elevated ICP at the time of surgery. Ten patients (21.3%) had been diagnosed with developmental delay, eight of whom demonstrated elevated ICP. There were no significant associations between measures of metopic severity and ICP. Metopic synostosis severity score and endocranial bifrontal angle were inversely correlated, as expected (r=−0.545, P<0.001). A negative correlation was noted between MSS and formally diagnosed developmental delay (r=−0.387, P=0.008). Likewise, negative correlations between age at procedure and both MSS and cranial morphology deviation was observed (r=−0.573, P<0.001 and r=−0.312, P=0.025, respectively).

Increased metopic severity was not associated with elevated ICP at the time of surgery. Patients who underwent later surgical correction showed milder phenotypic dysmorphology with an increased incidence of developmental delay.

Objective

This study aims to determine the utility of 3D photography for evaluating the severity of metopic craniosynostosis (MCS) using a validated, supervised machine learning (ML) algorithm.

This single-center retrospective cohort study included patients who were evaluated at our tertiary care center for MCS from 2016 to 2020 and underwent both head CT and 3D photography within a 2-month period.

The analysis method builds on our previously established ML algorithm for evaluating MCS severity using skull shape from CT scans. In this study, we regress the model to analyze 3D photographs and correlate the severity scores from both imaging modalities.

14 patients met inclusion criteria, 64.3% male (n = 9). The mean age in years at 3D photography and CT imaging was 0.97 and 0.94, respectively. Ten patient images were obtained preoperatively, and 4 patients did not require surgery. The severity prediction of the ML algorithm correlates closely when comparing the 3D photographs to CT bone data (Spearman correlation coefficient [SCC] r = 0.75; Pearson correlation coefficient [PCC] r = 0.82).

Conclusion

The results of this study show that 3D photography is a valid alternative to CT for evaluation of head shape in MCS. Its use will provide an objective, quantifiable means of assessing outcomes in a rigorous manner while decreasing radiation exposure in this patient population.

Previous studies have compared recorded torso potentials with electrocardiographic forward solutions from a pericardial cage. In this study, we introduce new comparisons of the forward solutions from the sock and cage with each other and with respect to the measured potentials on the torso. The forward problem of electrocardiographic imaging is expected to achieve high levels of accuracy since it is mathematically well posed. However, unexpectedly high residual errors remain between the computed and measured torso signals in experiments. A possible source of these errors is the limited spatial coverage of the cardiac sources in most experiments; most capture potentials only from the ventricles. To resolve the relationship between spatial coverage and the accuracy of the forward simulations, we combined two methods of capturing cardiac potentials using a 240-electrode sock and a 256-electrode cage, both surrounding a heart suspended in a 192-electrode torso tank. We analyzed beats from three pacing sites and calculated the RMSE, spatial correlation, and temporal correlation. We found that the forward solutions using the sock as the cardiac source were poorer compared to those obtained from the cage. In this study, we explore the differences in forward solution accuracy using the sock and the cage and suggest some possible explanations for these differences.

Least squares regression is a ubiquitous tool for building emulators (a.k.a. surrogate models) of problems across science and engineering for purposes such as design space exploration and uncertainty quantification. When the regression data are generated using an experimental design process (e.g., a quadrature grid) involving computationally expensive models, or when the data size is large, sketching techniques have shown promise to reduce the cost of the construction of the regression model while ensuring accuracy comparable to that of the full data. However, random sketching strategies, such as those based on leverage scores, lead to regression errors that are random and may exhibit large variability. To mitigate this issue, we present a novel boosting approach that leverages cheaper, lower-fidelity data of the problem at hand to identify the best sketch among a set of candidate sketches. This in turn specifies the sketch of the intended high-fidelity model and the associated data. We provide theoretical analyses of this bi-fidelity boosting (BFB) approach and discuss the conditions the low- and high-fidelity data must satisfy for a successful boosting. In doing so, we derive a bound on the residual norm of the BFB sketched solution relating it to its ideal, but computationally expensive, high-fidelity boosted counterpart. Empirical results on both manufactured and PDE data corroborate the theoretical analyses and illustrate the efficacy of the BFB solution in reducing the regression error, as compared to the non-boosted solution.

Computational fluid dynamics (CFD) is known for producing high-dimensional spatiotemporal data. Recent advances in machine learning (ML) have introduced a myriad of techniques for extracting physical information from CFD. Identifying an optimal set of coordinates for representing the data in a low-dimensional embedding is a crucial first step toward data-driven reduced-order modeling and other ML tasks. This is usually done via principal component analysis (PCA), which gives an optimal linear approximation. However, fluid flows are often complex and have nonlinear structures, which cannot be discovered or efficiently represented by PCA. Several unsupervised ML algorithms have been developed in other branches of science for nonlinear dimensionality reduction (NDR), but have not been extensively used for fluid flows. Here, four manifold learning and two deep learning (autoencoder)-based NDR methods are investigated and compared to PCA. These are tested on two canonical fluid flow problems (laminar and turbulent) and two biomedical flows in brain aneurysms. The data reconstruction capabilities of these methods are compared, and the challenges are discussed. The temporal vs spatial arrangement of data and its influence on NDR mode extraction is investigated. Finally, the modes are qualitatively compared. The results suggest that using NDR methods would be beneficial for building more efficient reduced-order models of fluid flows. All NDR techniques resulted in smaller reconstruction errors for spatial reduction. Temporal reduction was a harder task; nevertheless, it resulted in physically interpretable modes. Our work is one of the first comprehensive comparisons of various NDR methods in unsteady flows.

To statistically study the variability and differences between normal and abnormal brain connectomes, a mathematical model of the neural connections is required. In this paper, we represent the brain connectome as a Riemannian manifold, which allows us to model neural connections as geodesics. We show for the first time how one can leverage deep neural networks to estimate a Riemannian metric of the brain that can accommodate fiber crossings and is a natural modeling tool to infer the shape of the brain from DWMRI. Our method achieves excellent performance in geodesic-white-matter-pathway alignment and tackles the long-standing issue in previous methods: the inability to recover the crossing fibers with high fidelity.

In situ analysis and visualization have grown increasingly popular for enabling direct access to data from high-performance computing (HPC) simulations. As a simulation progresses and interesting physical phenomena emerge, however, the data produced may become increasingly complex, and users may need to dynamically change the type and scale of in situ analysis tasks being carried out and consequently adapt the amount of resources allocated to such tasks. To date, none of the production in situ analysis frameworks offer such an elasticity feature, and for good reason: the assumption that the number of processes could vary during run time would force developers to rethink software and algorithms at every level of the in situ analysis stack. In this paper we present Colza, a data staging service with elastic in situ visualization capabilities. Colza relies on the widely used ParaView Catalyst in situ visualization framework and enables elasticity by replacing MPI with a custom collective communication library based on the Mochi suite of libraries. To the best of our knowledge, this work is the first to enable elastic in situ visualization capabilities for HPC applications on top of existing production analysis tools.

Tensor decomposition is a dominant framework for multiway data analysis and prediction. Although practical data often contains timestamps for the observed entries, existing tensor decomposition approaches overlook or under-use this valuable time information. They either drop the timestamps or bin them into crude steps and hence ignore the temporal dynamics within each step or use simple parametric time coefficients. To overcome these limitations, we propose Bayesian Continuous-Time Tucker Decomposition (BCTT). We model the tensor-core of the classical Tucker decomposition as a time-varying function, and place a Gaussian process prior to flexibly estimate all kinds of temporal dynamics. In this way, our model maintains the interpretability while is flexible enough to capture various complex temporal relationships between the tensor nodes. For efficient and high-quality posterior inference, we use the stochastic differential equation (SDE) representation of temporal GPs to build an equivalent state-space prior, which avoids huge kernel matrix computation and sparse/low-rank approximations. We then use Kalman filtering, RTS smoothing, and conditional moment matching to develop a scalable message-passing inference algorithm. We show the advantage of our method in simulation and several real-world applications.

As the field of data science continues to grow, so does the need for adequate tools to understand and debug data science scripts. Current debugging practices fall short when applied to a data science setting, due to the exploratory and iterative nature of analysis scripts. Additionally, computational notebooks, the preferred scripting environment of many data scientists, present additional challenges to understanding and debugging workflows, including the non-linear execution of code snippets. This paper presents Anteater, a trace-based visual debugging method for data science scripts. Anteater automatically traces and visualizes execution data with minimal analyst input. The visualizations illustrate execution and value behaviors that aid in understanding the results of analysis scripts. To maximize the number of workflows supported, we present prototype implementations in both Python and Jupyter. Last, to demonstrate Anteater’s support for analysis understanding tasks, we provide two usage scenarios on real world analysis scripts.

Pathologists diagnose and grade prostate cancer by examining tissue from needle biopsies on glass slides. The cancer's severity and risk of metastasis are determined by the Gleason grade, a score based on the organization and morphology of prostate cancer glands. For diagnostic work-up, pathologists first locate glands in the whole biopsy core, and---if they detect cancer---they assign a Gleason grade. This time-consuming process is subject to errors and significant inter-observer variability, despite strict diagnostic criteria. This paper proposes an automated workflow that follows pathologists' modus operandi, isolating and classifying multi-scale patches of individual glands in whole slide images (WSI) of biopsy tissues using distinct steps: (1) two fully convolutional networks segment epithelium versus stroma and gland boundaries, respectively; (2) a classifier network separates benign from cancer glands at high magnification; and (3) an additional classifier predicts the grade of each cancer gland at low magnification. Altogether, this process provides a gland-specific approach for prostate cancer grading that we compare against other machine-learning-based grading methods.

Multi-principal element, high entropy alloys (HEAs) are an emerging class of materials that have found applications across the board. Owing to the multitude of possible candidate alloys, exploration and compositional design of HEAs for targeted applications is challenging since it necessitates a rational approach to identify compositions exhibiting enriched performance. Here, we report an innovative framework that integrates molecular dynamics and machine learning to explore a large chemical-configurational space for evaluating elastic modulus of equiatomic and non-equiatomic HEAs along primary crystallographic directions. Vital thermodynamic properties and machine learning features have been incorporated to establish fundamental relationships correlating Young’s modulus with Gibbs free energy, valence electron concentration, and atomic size difference. In HEAs, as the number of elements increases …

Upcoming exascale applications could introduce significant data management challenges due to their large sizes, dynamic work distribution, and involvement of accelerators such as graphical processing units, GPUs. In this work, we explore the performance of reading and writing operations involving one such scientific application on two different supercomputers. Our tests showed that the Adaptable Input and Output System, ADIOS, was able to achieve speeds over 1TB/s, a significant fraction of the peak I/O performance on Summit. We also demonstrated the querying functionality in ADIOS could effectively support common selective data analysis operations, such as conditional histograms. In tests, this query mechanism was able to reduce the execution time by a factor of five. More importantly, ADIOS data management framework allows us to achieve these performance improvements with only a minimal amount …

Time-varying vector fields produced by computational fluid dynamics simulations are often prohibitively large and pose challenges for accurate interactive analysis and exploration. To address these challenges, reduced Lagrangian representations have been increasingly researched as a means to improve scientific time-varying vector field exploration capabilities. This paper presents a novel deep neural network-based particle tracing method to explore time-varying vector fields represented by Lagrangian flow maps. In our workflow, in situ processing is first utilized to extract Lagrangian flow maps, and deep neural networks then use the extracted data to learn flow field behavior. Using a trained model to predict new particle trajectories offers a fixed small memory footprint and fast inference. To demonstrate and evaluate the proposed method, we perform an in-depth study of performance using a well-known analytical data set, the Double Gyre. Our study considers two flow map extraction strategies, the impact of the number of training samples and integration durations on efficacy, evaluates multiple sampling options for training and testing, and informs hyperparameter settings. Overall, we find our method requires a fixed memory footprint of 10.5 MB to encode a Lagrangian representation of a time-varying vector field while maintaining accuracy. For post hoc analysis, loading the trained model costs only two seconds, significantly reducing the burden of I/O when reading data for visualization. Moreover, our parallel implementation can infer one hundred locations for each of two thousand new pathlines in 1.3 seconds using one NVIDIA Titan RTX GPU.

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of en-semble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.

Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes. For training in such a computationally prohibitive regime, dimensionality reduction techniques ease the computational burden, and allow implementations of more robust networks. We propose a novel type of such dimensionality reduction via a new deep learning architecture based on fast matrix multiplication of a Kronecker product decomposition; in particular our network construction can be viewed as a Kronecker product-induced sparsification of an "extended" fully connected network. Analysis and practical examples show that this architecture allows a neural network to be trained and implemented with a significant reduction in computational time and resources, while achieving a similar error level compared to a traditional feedforward neural network.

This research addresses node-level scalability, portability, and heterogeneous computing challenges facing asynchronous many-task (AMT) runtime systems. These challenges have arisen due to increasing socket/core/thread counts and diversity among supported architectures on current and emerging high-performance computing (HPC) systems. This places greater emphasis on thread scalability and simultaneous use of diverse architectures to maximize node use and is complicated by architecture-specific programming models.

The Uintah Computational Framework is being prepared to make portable use of forthcoming exascale systems, initially the DOE Aurora system through the Aurora Early Science Program. This paper describes the evolution of Uintah to be ready for such architectures. A key part of this preparation has been the adoption of the Kokkos performance portability layer in Uintah. The sheer size of the Uintah codebase has made it imperative to have a representative benchmark. The design of this benchmark and the use of Kokkos within it is discussed. This paper complements recent work with additional details and new scaling studies run 24x further than earlier studies. Results are shown for two benchmarks executing workloads representative of typical Uintah applications. These results demonstrate single-source portability across the DOE Summit and NSF Frontera systems with good strong-scaling characteristics. The challenge of extending this approach to anticipated exascale systems is also considered.