2021

J. D. Tate, W. W. Good, N. Zemzemi, M. Boonstra, P. van Dam, D. H. Brooks, A. Narayan, R. S. MacLeod.
**“Uncertainty Quantification of the Effects of Segmentation Variability in ECGI,”** In *Functional Imaging and Modeling of the Heart*, Springer International Publishing, pp. 515--522. 2021.

DOI: 10.1007/978-3-030-78710-3_49

Despite advances in many of the techniques used in Electrocardiographic Imaging (ECGI), uncertainty remains insufficiently quantified for many aspects of the pipeline. The effect of geometric uncertainty, particularly due to segmentation variability, may be the least explored to date. We use statistical shape modeling and uncertainty quantification (UQ) to compute the effect of segmentation variability on ECGI solutions. The shape model was made with Shapeworks from nine segmentations of the same patient and incorporated into an ECGI pipeline. We computed uncertainty of the pericardial potentials and local activation times (LATs) using polynomial chaos expansion (PCE) implemented in UncertainSCI. Uncertainty in pericardial potentials from segmentation variation mirrored areas of high variability in the shape model, near the base of the heart and the right ventricular outflow tract, and that ECGI was less sensitive to uncertainty in the posterior region of the heart. Subsequently LAT calculations could vary dramatically due to segmentation variability, with a standard deviation as high as 126ms, yet mainly in regions with low conduction velocity. Our shape modeling and UQ pipeline presented possible uncertainty in ECGI due to segmentation variability and can be used by researchers to reduce said uncertainty or mitigate its effects. The demonstrated use of statistical shape modeling and UQ can also be extended to other types of modeling pipelines.

J. Tate, S. Rampersad, C. Charlebois, Z. Liu, J. Bergquist, D. White, L. Rupp, D. Brooks, A. Narayan, R. MacLeod.
**“Uncertainty Quantification in Brain Stimulation using UncertainSCI,”** In *Brain Stimulation: Basic, Translational, and Clinical Research in Neuromodulation*, Vol. 14, No. 6, Elsevier, pp. 1659-1660. 2021.

Predicting the effects of brain stimulation with computer models presents many challenges, including estimating the possible error from the propagation of uncertain input parameters through the model. Quantification and control of these errors through uncertainty quantification (UQ) provide statistics on the likely impact of parameter variation on solution accuracy, including total variance and sensitivity associated to each parameter. While the need and importance of UQ in clinical modeling is generally accepted, tools for implementing UQ techniques remain limited or inaccessible for many researchers.

M. Thorpe, B. Wang.
**“Robust Certification for Laplace Learning on Geometric Graphs,”** Subtitled **“arXiv preprint arXiv:2104.10837,”** 2021.

Graph Laplacian (GL)-based semi-supervised learning is one of the most used approaches for classifying nodes in a graph. Understanding and certifying the adversarial robustness of machine learning (ML) algorithms has attracted large amounts of attention from different research communities due to its crucial importance in many security-critical applied domains. There is great interest in the theoretical certification of adversarial robustness for popular ML algorithms. In this paper, we provide the first adversarial robust certification for the GL classifier. More precisely we quantitatively bound the difference in the classification accuracy of the GL classifier before and after an adversarial attack. Numerically, we validate our theoretical certification results and show that leveraging existing adversarial defenses for the -nearest neighbor classifier can remarkably improve the robustness of the GL classifier.

J. P. Torres, Z. Lin, M. Watkins, P. F. Salcedo, R. P. Baskin, S. Elhabian, H. Safavi-Hemami, D. Taylor, J. Tun, G. P. Concepcion, N. Saguil, A. A. Yanagihara, Y. Fang, J. R. McArthur, H. Tae, R. K. Finol-Urdaneta, B. D. Özpolat, B. M. Olivera, E. W. Schmidt.
**“Small-molecule mimicry hunting strategy in the imperial cone snail, Conus imperialis,”** In *Science Advances*, Vol. 7, No. 11, American Association for the Advancement of Science, 2021.

Venomous animals hunt using bioactive peptides, but relatively little is known about venom small molecules and the resulting complex hunting behaviors. Here, we explored the specialized metabolites from the venom of the worm-hunting cone snail, *Conus imperialis*. Using the model polychaete worm *Platynereis dumerilii*, we demonstrate that *C. imperialis* venom contains small molecules that mimic natural polychaete mating pheromones, evoking the mating phenotype in worms. The specialized metabolites from different cone snails are species-specific and structurally diverse, suggesting that the cones may adopt many different prey-hunting strategies enabled by small molecules. Predators sometimes attract prey using the prey’s own pheromones, in a strategy known as aggressive mimicry. Instead, *C. imperialis* uses metabolically stable mimics of those pheromones, indicating that, in biological mimicry, even the molecules themselves may be disguised, providing a twist on fake news in chemical ecology.

N. Truong, C. Yuksel, C. Watcharopas, J. A. Levine, R. M. Kirby.
**“Particle Merging-and-Splitting,”** In *IEEE Transactions on Visualization and Computer Graphics*, IEEE, 2021.

Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. We introduce particle merging-and-splitting, a simple scheme for robustly handling collisions between particles that prevents inter-penetrations of separate objects without introducing numerical instabilities. This scheme merges colliding particles at the beginning of the time-step and then splits them at the end of the time-step. Thus, collisions last for the duration of a time-step, allowing neighboring particles of the colliding particles to influence each other. We show that our merging-and-splitting method is effective in robustly handling collisions and avoiding penetrations in particle-based simulations. We also show how our merging-and-splitting approach can be used for coupling different simulation systems using different and otherwise incompatible integrators. We present simulation tests …

W. Usher, X. Huang, S. Petruzza, S. Kumar, S. R. Slattery, S. T. Reeve, F. Wang, C. R. Johnson,, V. Pascucci.
**“Adaptive Spatially Aware I/O for Multiresolution Particle Data Layouts,”** In *IPDPS*, 2021.

V. Vedam-Mai, K. Deisseroth, J. Giordano, G. Lazaro-Munoz, W. Chiong, N. Suthana, J. Langevin, J. Gill, W. Goodman, N. R. Provenza, C. H. Halpern, R. S. Shivacharan, T. N. Cunningham, S. A. Sheth, N. Pouratian, K. W. Scangos, H. S. Mayberg, A. Horn, K. A. Johnson, C. R. Butson, R. Gilron, C. de Hemptinne, R. Wilt, M. Yaroshinsky, S. Little, P. Starr, G. Worrell, P. Shirvalkar, E. Chang, J. Volkmann, M. Muthuraman, S. Groppa, A. A. Kühn, L. Li, M. Johnson, K. J. Otto, R. Raike, S. Goetz, C. Wu, P. Silburn, B. Cheeran, Y. J. Pathak, M. Malekmohammadi, A. Gunduz, J. K. Wong, S. Cernera, A. W. Shukla, A. Ramirez-Zamora, W. Deeb, A. Patterson, K. D. Foote, M. S. Okun.
**“Proceedings of the Eighth Annual Deep Brain Stimulation Think Tank: Advances in Optogenetics, Ethical Issues Affecting DBS Research, Neuromodulatory Approaches for Depression, Adaptive Neurostimulation, and Emerging DBS Technologies,”** In *Frontiers in Human Neuroscience*, Vol. 15, pp. 169. 2021.

ISSN: 1662-5161

DOI: 10.3389/fnhum.2021.644593

We estimate that 208,000 deep brain stimulation (DBS) devices have been implanted to address neurological and neuropsychiatric disorders worldwide. DBS Think Tank presenters pooled data and determined that DBS expanded in its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. The DBS Think Tank was founded in 2012 providing a space where clinicians, engineers, researchers from industry and academia discuss current and emerging DBS technologies and logistical and ethical issues facing the field. The emphasis is on cutting edge research and collaboration aimed to advance the DBS field. The Eighth Annual DBS Think Tank was held virtually on September 1 and 2, 2020 (Zoom Video Communications) due to restrictions related to the COVID-19 pandemic. The meeting focused on advances in: (1) optogenetics as a tool for comprehending neurobiology of diseases and on optogenetically-inspired DBS, (2) cutting edge of emerging DBS technologies, (3) ethical issues affecting DBS research and access to care, (4) neuromodulatory approaches for depression, (5) advancing novel hardware, software and imaging methodologies, (6) use of neurophysiological signals in adaptive neurostimulation, and (7) use of more advanced technologies to improve DBS clinical outcomes. There were 178 attendees who participated in a DBS Think Tank survey, which revealed the expansion of DBS into several indications such as obesity, post-traumatic stress disorder, addiction and Alzheimer’s disease. This proceedings summarizes the advances discussed at the Eighth Annual DBS Think Tank.

A. Venkat, A. Gyulassy, G. Kosiba, A. Maiti, H. Reinstein, R. Gee, P.-T. Bremer, V. Pascucci.
**“Towards replacing physical testing of granular materials with a Topology-based Model,”** Subtitled **“arXiv preprint arXiv:2109.08777,”** 2021.

In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The "effective surface area," the surface area accessible to the airflow, is typically measured using a permeametry apparatus that relates the flow conductance to the permeable surface area via the Carman-Kozeny equation. This equation allows calculating the flow rate of a fluid flowing through the granules packed in the sample for a given pressure drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and flow paths that may not accurately hold in situations where the particles possess a wide distribution in shapes, sizes, and aspect ratios, as is true with many powdered systems of technological and commercial interest. To address this challenge, we replicate these measurements virtually on micro-CT images of the powdered material, introducing a new Pore Network Model based on the skeleton of the Morse-Smale complex. Pores are identified as basins of the complex, their incidence encodes adjacency, and the conductivity of the capillary between them is computed from the cross-section at their interface. We build and solve a resistive network to compute an approximate laminar fluid flow through the pore structure. We provide two means of estimating flow-permeable surface area: (i) by direct computation of conductivity, and (ii) by identifying dead-ends in the flow coupled with isosurface extraction and the application of the Carman-Kozeny equation, with the aim of establishing consistency over a range of particle shapes, sizes, porosity levels, and void distribution patterns.

B. Wang, D. Zou, Q. Gu, S. J. Osher.
**“Laplacian smoothing stochastic gradient markov chain monte carlo,”** In *SIAM Journal on Scientific Computing*, Vol. 43, No. 1, SIAM, pp. A26-A53. 2021.

As an important Markov chain Monte Carlo (MCMC) method, the stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, SGLD typically suffers from a slow convergence rate due to its large variance caused by the stochastic gradient. In order to alleviate these drawbacks, we leverage the recently developed Laplacian smoothing technique and propose a Laplacian smoothing stochastic gradient Langevin dynamics (LS-SGLD) algorithm. We prove that for sampling from both log-concave and non-log-concave densities, LS-SGLD achieves strictly smaller discretization error in 2-Wasserstein distance, although its mixing rate can be slightly slower. Experiments on both synthetic and real datasets verify our theoretical results and demonstrate the superior performance of LS-SGLD on different machine learning tasks including posterior …

Z. Wang, W. Xing, R. Kirby, S. Zhe.
**“Multi-Fidelity High-Order Gaussian Processes for Physical Simulation,”** In *International Conference on Artificial Intelligence and Statistics*, PMLR, pp. 847-855. 2021.

The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions are much more expensive than low-fidelity ones. To reduce the cost, we consider novel Gaussian process (GP) models that leverage simulation examples of different fidelities to predict high-dimensional PDE solution outputs. Existing GP methods are either not scalable to high-dimensional outputs or lack effective strategies to integrate multi-fidelity examples. To address these issues, we propose Multi-Fidelity High-Order Gaussian Process (MFHoGP) that can capture complex correlations both between the outputs and between the fidelities to enhance solution estimation, and scale to large numbers of outputs. Based on a novel nonlinear coregionalization model, MFHoGP propagates bases throughout fidelities to fuse information, and places a deep matrix GP prior over the basis weights to capture the (nonlinear) relationships across the fidelities. To improve inference efficiency and quality, we use bases decomposition to largely reduce the model parameters, and layer-wise matrix Gaussian posteriors to capture the posterior dependency and to simplify the computation. Our stochastic variational learning algorithm successfully handles millions of outputs without extra sparse approximations. We show the advantages of our method in several typical applications.

Y. Wan, H.A. Holman, C. Hansen.
**“Interactive Analysis for Large Volume Data from Fluorescence Microscopy at Cellular Precision,”** In *Computers & Graphics*, Vol. 98, Pergamon, pp. 138-149. 2021.

DOI: https://doi.org/10.1016/j.cag.2021.05.006

The main objective for understanding fluorescence microscopy data is to investigate and evaluate the fluorescent signal intensity distributions as well as their spatial relationships across multiple channels. The quantitative analysis of 3D fluorescence microscopy data needs interactive tools for researchers to select and focus on relevant biological structures. We developed an interactive tool based on volume visualization techniques and GPU computing for streamlining rapid data analysis. Our main contribution is the implementation of common data quantification functions on streamed volumes, providing interactive analyses on large data without lengthy preprocessing. Data segmentation and quantification are coupled with brushing and executed at an interactive speed. A large volume is partitioned into data bricks, and only user-selected structures are analyzed to constrain the computational load. We designed a framework to assemble a sequence of GPU programs to handle brick borders and stitch analysis results. Our tool was developed in collaboration with domain experts and has been used to identify cell types. We demonstrate a workflow to analyze cells in vestibular epithelia of transgenic mice.

Z. Wang, P. Subedi, M. Dorier, P.E. Davis, M. Parashar.
**“Facilitating Staging-based Unstructured Mesh Processing to Support Hybrid In-Situ Workflows,”** In *2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)*, pp. 960-964. 2021.

DOI: 10.1109/IPDPSW52791.2021.00152

In-situ and in-transit processing alleviate the gap between the computing and I/O capabilities by scheduling data analytics close to the data source. Hybrid in-situ processing splits data analytics into two stages: the data processing that runs in-situ aims to extract regions of interest, which are then transferred to staging services for further in-transit analytics. To facilitate this type of hybrid in-situ processing, the data staging service needs to support complex intermediate data representations generated/consumed by the in-situ tasks. Unstructured (or irregular) mesh is one such derived data representation that is typically used and bridges simulation data and analytics. However, how staging services efficiently support unstructured mesh transfer and processing remains to be explored. This paper investigates design options for transferring and processing unstructured mesh data using staging services. Using polygonal mesh data as an example, we show that hybrid in-situ workflows with staging-based unstructured mesh processing can effectively support hybrid in-situ workflows, and can significantly decrease data movement overheads.

Z. Wang, M. Dorier, P. Subedi, P..E Davis, M. Parashar.
**“An Adaptive Elasticity Policy For Staging Based In-Situ Processing,”** In *IEEE Workshop on Workflows in Support of Large-Scale Science (WORKS)*, pp. 33-41. 2021.

DOI: 10.1109/WORKS54523.2021.00010

In-situ processing alleviates the gap between computation and I/O capabilities by performing data analysis close to the data source. With simulation data varying in size and content during workflow execution, it becomes necessary for insitu processing to support resource elasticity, i.e., the ability to change resource configurations such as the number of computing nodes/processes during workflow execution. An elastic job may dynamically adjust resource configurations; it may use a few resources at the beginning and more resources towards the end of the job when interesting data appears. However, it is hard to predict a priori how many computing nodes/processes need to be added/removed during the workflow execution to adapt to changing workflow needs. How to efficiently guide elasticity operations, such as growing or shrinking the number of processes used for in-situ analysis during workflow execution, is an open-ended research question. In this paper, we present an adaptive elasticity policy that adopts workflow runtime information collected online to predict how to trigger the addition and removal of processes in order to minimize in-situ processing overheads. We integrate the presented elasticity policy into a staging-based elastic workflow and evaluate its efficiency in multiple elasticity scenarios. The results indicate that an adaptive elasticity policy can save overhead in finding a proper resource configuration, when compared with a static policy that uses a fixed number of processes for each rescaling operation. Finally, we discuss multiple existing research opportunities of elastic insitu processing from different aspects.

Z. Wang, P. Subedi, M. Dorier, P.E. Davis, M. Parashar.
**“Adaptive Placement of Data Analysis Tasks For Staging Based In-Situ Processing,”** In *2021 IEEE 28th International Conference on High Performance Computing, Data, and Analytics (HiPC)*, pp. 242-251. 2021.

DOI: 10.1109/HiPC53243.2021.00038

In-situ processing addresses the gap between speeds of computing and I/O capabilities by processing data close to the data source, i.e., on the same system as the data source (e.g., a simulation). However, the effective implementation of in-situ processing workflows requires the optimization of several design parameters such as where on the system workflow data analysis/visualization (ana/vis) as placed and how execution as well as the interaction and data exchanges between ana/vis are coordinated. For example, in the case of hybrid in-situ processing, interacting ana/vis may be tightly or loosely coupled depending on their placement, and this can lead to very different performance and scalability. A key challenge is deciding the most appropriate ana/vis placement, which depends on dynamic applications, workflow, and system characteristics that might change at runtime. In this paper, we present a framework to support online adaptive data analysis placement during the execution of an in-situ workflow. Specifically, the paper presents a model and architecture, and explores several data analysis placement strategies. Evaluation results show that dynamically choosing appropriate data analysis placement strategies can balance the benefits and overhead of different data analysis placement patterns to reduce in-situ processing time.

W. W. Xing, A. A. Shah, P. Wang, S. Zhe, Q. Fu, R. M. Kirby.
**“Residual Gaussian process: A tractable nonparametric Bayesian emulator for multi-fidelity simulations,”** In *Applied Mathematical Modelling*, Vol. 97, Elsevier, pp. 36-56. 2021.

Challenges in multi-fidelity modelling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity solution is written as a sum of the lowest fidelity solution and residuals between the solutions at successive fidelity levels, with Gaussian process priors placed over the low fidelity solution and each of the residuals. The resulting model is equipped with a closed-form solution for the predictive posterior, making it applicable to advanced, high-dimensional tasks that require uncertainty estimation. Its advantages are demonstrated on univariate benchmarks and on three challenging multivariate problems. It is shown how active learning can be used to enhance the model, especially with a limited computational budget. Furthermore, error bounds are derived for the mean prediction in the univariate case.

W. W. Xing, R. M. Kirby, S. Zhe.
**“Deep coregionalization for the emulation of simulation-based spatial-temporal fields,”** In *Journal of Computational Physics*, Academic Press, pp. 109984. 2021.

Data-driven surrogate models are widely used for applications such as design optimization and uncertainty quantification, where repeated evaluations of an expensive simulator are required. For most partial differential equation (PDE) simulations, the outputs of interest are often spatial or spatial-temporal fields, leading to very high-dimensional outputs. Despite the success of existing data-driven surrogates for high-dimensional outputs, most methods require a significant number of samples to cover the response surface in order to achieve a reasonable degree of accuracy. This demand makes the idea of surrogate models less attractive considering the high-computational cost to generate the data. To address this issue, we exploit the multifidelity nature of a PDE simulation and introduce deep coregionalization, a Bayesian nonparametric autoregressive framework for efficient emulation of spatial-temporal fields. To effectively extract the output correlations in the context of multifidelity data, we develop a novel dimension reduction technique, residual principal component analysis. Our model can simultaneously capture the rich output correlations and the fidelity correlations and make high-fidelity predictions with only a small number of expensive, high-fidelity simulation samples. We show the advantages of our model in three canonical PDE models and a fluid dynamics problem. The results show that the proposed method can not only approximate simulation results with significantly less cost (by bout 10%-25%) but also further improve model accuracy.

Y. Xu, V. Keshavarzzadeh, R. M. Kirby, A. Narayan.
**“A bandit-learning approach to multifidelity approximation,”** Subtitled **“arXiv preprint arXiv:2103.15342,”** 2021.

Multifidelity approximation is an important technique in scientific computation and simulation. In this paper, we introduce a bandit-learning approach for leveraging data of varying fidelities to achieve precise estimates of the parameters of interest. Under a linear model assumption, we formulate a multifidelity approximation as a modified stochastic bandit, and analyze the loss for a class of policies that uniformly explore each model before exploiting. Utilizing the estimated conditional mean-squared error, we propose a consistent algorithm, adaptive Explore-Then-Commit (AETC), and establish a corresponding trajectory-wise optimality result. These results are then extended to the case of vector-valued responses, where we demonstrate that the algorithm is efficient without the need to worry about estimating high-dimensional parameters. The main advantage of our approach is that we require neither hierarchical model structure nor\textit a priori knowledge of statistical information (eg, correlations) about or between models. Instead, the AETC algorithm requires only knowledge of which model is a trusted high-fidelity model, along with (relative) computational cost estimates of querying each model. Numerical experiments are provided at the end to support our theoretical findings.

Y. Xu, A. Narayan.
**“Randomized weakly admissible meshes,”** Subtitled **“arXiv preprint arXiv:2101.04043,”** 2021.

A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain. The asymptotic rate of growth of the grid sizes and of the comparability constant must grow in a controlled manner. In this paper we generalize the notion of a WAM to a hierarchical subspaces of not necessarily polynomial functions, and we analyze particular strategies for random sampling as a technique for generating WAMs. Our main results show that WAM's and their stronger variant, admissible meshes, can be generated by random sampling, and our analysis provides concrete estimates for growth of both the meshes and the discrete-continuum comparability constants.

Y. Xu, A. Narayan.
**“Budget-limited distribution learning in multifidelity problems,”** Subtitled **“arXiv preprint arXiv:2105.04599,”** 2021.

Multifidelity methods are widely used for statistical estimation of quantities of interest (QoIs) in uncertainty quantification using simulation codes of differing costs and accuracies. Many methods approximate numerical-valued statistics that represent only limited information of the QoIs. In this paper, we introduce a semi-parametric approach that aims to effectively describe the distribution of a scalar-valued QoI in the multifidelity setup. Under a linear model hypothesis, we propose an exploration-exploitation strategy to reconstruct the full distribution of a scalar-valued QoI using samples from a subset of low-fidelity regressors. We derive an informative asymptotic bound for the mean 1-Wasserstein distance between the estimator and the true distribution, and use it to adaptively allocate computational budget for parametric estimation and non-parametric reconstruction. Assuming the linear model is correct, we prove that such a procedure is consistent, and converges to the optimal policy (and hence optimal computational budget allocation) under an upper bound criterion as the budget goes to infinity. A major advantage of our approach compared to several other multifidelity methods is that it is automatic, and its implementation does not require a hierarchical model setup, cross-model information, or \textita priori known model statistics. Numerical experiments are provided in the end to support our theoretical analysis.

V. Zala, R. M. Kirby, A. Narayan.
**“Structure-preserving Nonlinear Filtering for Continuous and Discontinuous Galerkin Spectral/hp Element Methods,”** Subtitled **“arXiv preprint arXiv:2106.08316,”** 2021.

Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical properties, such as positivity or monotonicity. Such invalid solutions pose both modeling challenges, since the physical interpretation of simulation results is not possible, and computational challenges, since such properties may be required to advance the scheme. We, therefore, consider the problem of computing solutions that preserve these structural solution properties, which we enforce as additional constraints on the solution. We consider in particular the class of convex constraints, which includes positivity and monotonicity. By embedding such constraints as a postprocessing convex optimization procedure, we can compute solutions that satisfy general types of convex constraints. For certain types of constraints (including positivity and monotonicity), the optimization is a filter, i.e., a norm-decreasing operation. We provide a variety of tests on one-dimensional time-dependent PDEs that demonstrate the method's efficacy, and we empirically show that rates of convergence are unaffected by the inclusion of the constraints.