Designed especially for neurobiologists, FluoRender is an interactive tool for multi-channel fluorescence microscopy data visualization and analysis.
Deep brain stimulation
BrainStimulator is a set of networks that are used in SCIRun to perform simulations of brain stimulation such as transcranial direct current stimulation (tDCS) and magnetic transcranial stimulation (TMS).
Developing software tools for science has always been a central vision of the SCI Institute.

Scientific Computing

Numerical simulation of real-world phenomena provides fertile ground for building interdisciplinary relationships. The SCI Institute has a long tradition of building these relationships in a win-win fashion – a win for the theoretical and algorithmic development of numerical modeling and simulation techniques and a win for the discipline-specific science of interest. High-order and adaptive methods, uncertainty quantification, complexity analysis, and parallelization are just some of the topics being investigated by SCI faculty. These areas of computing are being applied to a wide variety of engineering applications ranging from fluid mechanics and solid mechanics to bioelectricity.


martin

Martin Berzins

Parallel Computing
GPUs
mike

Mike Kirby

Finite Element Methods
Uncertainty Quantification
GPUs
pascucci

Valerio Pascucci

Scientific Data Management
chris

Chris Johnson

Problem Solving Environments
amir

Amir Arzani

Scientific machine learning
Data-driven fluid flow modeling

Funded Research Projects:


Publications in Scientific Computing:


Quadrature Sampling of Parametric Models with Bi-fidelity Boosting
Subtitled “arXiv:2209.05705v1,” N. Cheng, O.A. Malik, Y. Xu, S. Becker, A. Doostan, A. Narayan. 2022.

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.



Fast Algorithms for Monotone Lower Subsets of Kronecker Least Squares Problems
Subtitled “arXiv:2209.05662v1,” O.A. Malik, Y. Xu, N. Cheng, S. Becker, A. Doostan, A. Narayan. 2022.

Approximate solutions to large least squares problems can be computed efficiently using leverage score-based row-sketches, but directly computing the leverage scores, or sampling according to them with naive methods, still requires an expensive manipulation and processing of the design matrix. In this paper we develop efficient leverage score-based sampling methods for matrices with certain Kronecker product-type structure; in particular we consider matrices that are monotone lower column subsets of Kronecker product matrices. Our discussion is general, encompassing least squares problems on infinite domains, in which case matrices formally have infinitely many rows. We briefly survey leverage score-based sampling guarantees from the numerical linear algebra and approximation theory communities, and follow this with efficient algorithms for sampling when the design matrix has Kronecker-type structure. Our numerical examples confirm that sketches based on exact leverage score sampling for our class of structured matrices achieve superior residual compared to approximate leverage score sampling methods.



Uncertainty quantification for ecological models with random parameters
J.R. Reimer, F.R. Adler, K.M. Golden, A. Narayan. In Ecology Letters, Wiley, pp. 1--13. 2022.

There is often considerable uncertainty in parameters in ecological models. This uncertainty can be incorporated into models by treating parameters as random variables with distributions, rather than fixed quantities. Recent advances in uncertainty quantification methods, such as polynomial chaos approaches, allow for the analysis of models with random parameters. We introduce these methods with a motivating case study of sea ice algal blooms in heterogeneous environments. We compare Monte Carlo methods with polynomial chaos techniques to help understand the dynamics of an algal bloom model with random parameters. Modelling key parameters in the algal bloom model as random variables changes the timing, intensity and overall productivity of the modelled bloom. The computational efficiency of polynomial chaos methods provides a promising avenue for the broader inclusion of parametric uncertainty in ecological models, leading to improved model predictions and synthesis between models and data.



Democratizing Science Through Advanced Cyberinfrastructure
M. Parashar. In Computer, IEEE, 2022.

Democratizing access to cyberinfrastructure is essential to democratizing science. This article explores knowledge, technical, and social barriers to accessing and using cyberinfrastructure and explores approaches to addresses them. It also highlights recent activities and investments at the National Science Foundation that implement some of these approaches.



Adaptive and Implicit Regularization for Matrix Completion
Subtitled “arXiv preprint arXiv:2208.05640,” Z. Li, T. Sun, H. Wang, B. Wang. 2022.

The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another issue is that the fixed explicit regularization limits the applicability to broad images since different images favor different features captured by different explicit regularizations. As such, this paper proposes a new adaptive and implicit low-rank regularization that captures the low-rank prior dynamically from the training data. The core of our new adaptive and implicit low-rank regularization is parameterizing the Laplacian matrix in the Dirichlet energy-based regularization, which we call the regularization AIR. Theoretically, we show that the adaptive regularization of AIR enhances the implicit regularization and vanishes at the end of training. We validate AIR’s effectiveness on various benchmark tasks, indicating that the AIR is particularly favorable for the scenarios when the missing entries are non-uniform. The code can be found at https://github.com/lizhemin15/AIR-Net.



Research Reproducibility
M. Parashar, M.A. Heroux, V. Stodde. In Computer, Vol. 55, No. 8, IEEE, pp. 16--18. August, 2022.

Reproducibility has a foundational role in ensuring robust and trustworthy research, but achieving reproducibility can be challenging. This theme issue explores these challenges along with research and implementations across communities addressing them, with the goal of understanding the impact of existing solutions and synthesizing lessons learned and emerging best practices.



Momentum Transformer: Closing the Performance Gap Between Self-attention and Its Linearization
Subtitled “arXiv preprint arXiv:2208.00579,” T. Nguyen, R.G. Baraniuk, R.M. Kirby, S.J. Osher, B. Wang. 2022.

Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence. Leveraging techniques include sparse and linear attention and hashing tricks; efficient transformers have been proposed to reduce the quadratic complexity of transformers but significantly degrade the accuracy. In response, we first interpret the linear attention and residual connections in computing the attention map as gradient descent steps. We then introduce momentum into these components and propose the \emphmomentum transformer, which utilizes momentum to improve the accuracy of linear transformers while maintaining linear memory and computational complexities. Furthermore, we develop an adaptive strategy to compute the momentum value for our model based on the optimal momentum for quadratic optimization. This adaptive momentum eliminates the need to search for the optimal momentum value and further enhances the performance of the momentum transformer. A range of experiments on both autoregressive and non-autoregressive tasks, including image generation and machine translation, demonstrate that the momentum transformer outperforms popular linear transformers in training efficiency and accuracy.



Assembling Portable In-Situ Workflow from Heterogeneous Components using Data Reorganization
B. Zhang, P. Subedi, P. E. Davis, F. Rizzi, K. Teranishi, M. Parashar. In 22nd IEEE International Symposium on Cluster, Cloud and Internet Computing (CCGrid), pp. 41-50. 2022.
DOI: 10.1109/CCGrid54584.2022.00013

Heterogeneous computing is becoming common in the HPC world. The fast-changing hardware landscape is pushing programmers and developers to rely on performance-portable programming models to rewrite old and legacy applications and develop new ones. While this approach is suitable for individual applications, outstanding challenges still remain when multiple applications are combined into complex workflows. One critical difficulty is the exchange of data between communicating applications where performance constraints imposed by heterogeneous hardware advantage different data layouts. We attempt to solve this problem by exploring asynchronous data layout conversions for applications requiring different memory access patterns for shared data. We implement the proposed solution within the DataSpaces data staging service, extending it to support heterogeneous application workflows across a broad spectrum of programming models. In addition, we integrate heterogeneous DataSpaces with the Kokkos programming model and propose the Kokkos Staging Space as an extension of the Kokkos data abstraction. This new abstraction enables us to express data on a virtual shared space for multiple Kokkos applications, thus guaranteeing the portability of each application when assembling them into an efficient heterogeneous workflow. We present performance results for the Kokkos Staging Space using a synthetic workflow emulator and three different scenarios representing access frequency and use patterns in shared data. The results show that the Kokkos Staging Space is a superior solution in terms of time-to-solution and scalability compared to existing file-based Kokkos data abstractions for inter-application data exchange.



Transforming science through cyberinfrastructure
M. Parashar, A. Friedlander, E. Gianchandani,, M. Martonosi. In Communications of the ACM, Vol. 65, No. 8, pp. 30–32. 2022.

NSF's vision for the U.S. cyberinfrastructure ecosystem for science and engineering in the 21st century.



Adaptive Self-supervision Algorithms for Physics-informed Neural Networks
Subtitled “arXiv:2207.04084,” S. Subramanian, R.M. Kirby, M.W. Mahoney, A. Gholami. 2022.

Physics-informed neural networks (PINNs) incorporate physical knowledge from the problem domain as a soft constraint on the loss function, but recent work has shown that this can lead to optimization difficulties. Here, we study the impact of the location of the collocation points on the trainability of these models. We find that the vanilla PINN performance can be significantly boosted by adapting the location of the collocation points as training proceeds. Specifically, we propose a novel adaptive collocation scheme which progressively allocates more collocation points (without increasing their number) to areas where the model is making higher errors (based on the gradient of the loss function in the domain). This, coupled with a judicious restarting of the training during any optimization stalls (by simply resampling the collocation points in order to adjust the loss landscape) leads to better estimates for the prediction error. We present results for several problems, including a 2D Poisson and diffusion-advection system with different forcing functions. We find that training vanilla PINNs for these problems can result in up to 70% prediction error in the solution, especially in the regime of low collocation points. In contrast, our adaptive schemes can achieve up to an order of magnitude smaller error, with similar computational complexity as the baseline. Furthermore, we find that the adaptive methods consistently perform on-par or slightly better than vanilla PINN method, even for large collocation point regimes. The code for all the experiments has been open sourced.



A scalable adaptive-matrix SPMV for heterogeneous architectures
H. D. Tran, M. Fernando, K. Saurabh, B. Ganapathysubramanian, R. M. Kirby, H. Sundar. In 2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS), IEEE, pp. 13--24. 2022.
DOI: 10.1109/IPDPS53621.2022.00011

In most computational codes, the core computational kernel is the Sparse Matrix-Vector product (SpMV) that enables specialized linear algebra libraries like PETSc to be used, especially in the distributed memory setting. However, optimizing SpMvperformance and scalability at all levels of a modern heterogeneous architecture can be challenging as it is characterized by irregular memory access. This work presents a hybrid approach (HyMV) for evaluating SpMV for matrices arising from PDE discretization schemes such as the finite element method (FEM). The approach enables localized structured memory access that provides improved performance and scalability. Additionally, it simplifies the programmability and portability on different architectures. The developed HyMV approach enables efficient parallelization using MPI, SIMD, OpenMP, and CUDA with minimum programming effort. We present a detailed comparison of HyMV with the two traditional approaches in computational code, matrix-assembled and matrix-free approaches, for structured and unstructured meshes. Our results demonstrate that the HyMV approach achieves excellent scalability and outperforms both approaches, e.g., achieving average speedups of 11x for matrix setup, 1.7x for SpMV with structured meshes, 3.6x for SpMV with unstructured meshes, and 7.5x for GPU SpMV.



Colza: Enabling Elastic In Situ Visualization for High-performance Computing Simulations
M. Dorier, Z. Wang, U. Ayachit, S. Snyder, R. Ross, M. Parashar. In 2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS), IEEE, pp. 538-548. 2022.
DOI: 10.1109/IPDPS53621.2022.00059

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.



Nonparametric Embeddings of Sparse High-Order Interaction Events
Z. Wang, Y. Xu, C. Tillinghast, S. Li, A. Narayan, S. Zhe. In Proceedings of the 39 th International Conference on Machine Learning, PLMR, pp. 23237-23253. 2022.

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, eg Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound) of the sparse ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.



Infinite-Fidelity Coregionalization for Physical Simulation
Subtitled “arXiv:2207.00678,” S. Li, Z Wang, R.M. Kirby, S. Zhe. 2022.

Multi-fidelity modeling and learning are important in physical simulation-related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation while still achieving good performance. While existing approaches only model finite, discrete fidelities, in practice, the fidelity choice is often continuous and infinite, which can correspond to a continuous mesh spacing or finite element length. In this paper, we propose Infinite Fidelity Coregionalization (IFC). Given the data, our method can extract and exploit rich information within continuous, infinite fidelities to bolster the prediction accuracy. Our model can interpolate and/or extrapolate the predictions to novel fidelities, which can be even higher than the fidelities of training data. Specifically, we introduce a low-dimensional latent output as a continuous function of the fidelity and input, and multiple it with a basis matrix to predict high-dimensional solution outputs. We model the latent output as a neural Ordinary Differential Equation (ODE) to capture the complex relationships within and integrate information throughout the continuous fidelities. We then use Gaussian processes or another ODE to estimate the fidelity-varying bases. For efficient inference, we reorganize the bases as a tensor, and use a tensor-Gaussian variational posterior to develop a scalable inference algorithm for massive outputs. We show the advantage of our method in several benchmark tasks in computational physics.



Adaptive Random Walk Gradient Descent for Decentralized Optimization
T. Sun, D. Li, B. Wang. In Proceedings of the 39th International Conference on Machine Learning, 2022.

In this paper, we study the adaptive step size random walk gradient descent with momentum for decentralized optimization, in which the training samples are drawn dependently with each other. We establish theoretical convergence rates of the adaptive step size random walk gradient descent with momentum for both convex and nonconvex settings. In particular, we prove that adaptive random walk algorithms perform as well as the nonadaptive method for dependent data in general cases but achieve acceleration when the stochastic gradients are “sparse”. Moreover, we study the zeroth-order version of adaptive random walk gradient descent and provide corresponding convergence results. All assumptions used in this paper are mild and general, making our results applicable to many machine learning problems.



NSDF-FUSE: A Testbed for Studying Object Storage via FUSE File Systems
P. Olaya, J. Luettgau, N. Zhou, J. Lofstead, G. Scorzelli, V. Pascucci, M. Taufer. In Proceedings of the 31st International Symposium on High-Performance Parallel and Distributed Computing, Association for Computing Machinery, pp. 277–278. 2022.
ISBN: 9781450391993
DOI: 10.1145/3502181.3533709

This work presents NSDF-FUSE, a testbed for evaluating settings and performance of FUSE-based file systems on top of S3-compatible object storage; the testbed is part of a suite of services from the National Science Data Fabric (NSDF) project (an NSF-funded project that is delivering cyberinfrastructures for data scientists). We demonstrate how NSDF-FUSE can be deployed to evaluate eight different mapping packages that mount S3-compatible object storage to a file system, as well as six data patterns representing different I/O operations on two cloud platforms. NSDF-FUSE is open-source and can be easily extended to run with other software mapping packages and different cloud platforms.



Decomposing Temporal High-Order Interactions via Latent ODEs
S. Li, R.M. Kirby, S. Zhe. In Proceedings of the 39 th International Conference on Machine Learning, 2022.

High-order interactions between multiple objects are common in real-world applications. Although tensor decomposition is a popular framework for high-order interaction analysis and prediction, most methods cannot well exploit the valuable timestamp information in data. The existent methods either discard the timestamps or convert them into discrete steps or use over-simplistic decomposition models. As a result, these methods might not be capable enough of capturing complex, finegrained temporal dynamics or making accurate predictions for long-term interaction results. To overcome these limitations, we propose a novel Temporal High-order Interaction decompoSition model based on Ordinary Differential Equations (THIS-ODE). We model the time-varying interaction result with a latent ODE. To capture the complex temporal dynamics, we use a neural network (NN) to learn the time derivative of the ODE state. We use the representation of the interaction objects to model the initial value of the ODE and to constitute a part of the NN input to compute the state. In this way, the temporal relationships of the participant objects can be estimated and encoded into their representations. For tractable and scalable inference, we use forward sensitivity analysis to efficiently compute the gradient of ODE state, based on which we use integral transform to develop a stochastic mini-batch learning algorithm. We demonstrate the advantage of our approach in simulation and four real-world applications.



Bayesian Continuous-Time Tucker Decomposition
S. Fang, A. Narayan, R.M. Kirby, S. Zhe. In Proceedings of the 39 th International Conference on Machine Learning, 2022.

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.



Variational Inference for Nonlinear Inverse Problems via Neural Net Kernels: Comparison to Bayesian Neural Networks, Application to Topology Optimization
Subtitled “arXiv:2205.03681,” V. Keshavarzzadeh, R.M. Kirby, A. Narayan. 2022.

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information about the parameters and the information from the observations via likelihood evaluations are incorporated into the inference process. In this paper, we adopt a similar viewpoint with a slightly different numerical procedure from standard inference approaches to provide insight about the localized behavior of unknown underlying parameters. We present a variational inference approach which mainly incorporates the observation data in a point-wise manner, i.e. we invert a limited number of observation data leveraging the gradient information of the forward map with respect to parameters, and find true individual samples of the latent parameters when the forward map is noise-free and one-to-one. For statistical calculations (as the ultimate goal in simulations), a large number of samples are generated from a trained neural network which serves as a transport map from the prior to posterior latent parameters. Our neural network machinery, developed as part of the inference framework and referred to as Neural Net Kernels (NNK), is based on hierarchical (deep) kernels which provide greater flexibility for training compared to standard neural networks. We showcase the effectiveness of our inference procedure in identifying bimodal and irregular distributions compared to a number of approaches including Markov Chain Monte Carlo sampling approaches and a Bayesian neural network approach.



Advancing Reproducibility in Parallel and Distributed Systems Research
M. Parashar. In Computer, Vol. 55, No. 5, pp. 4--5. 2022.
DOI: 10.1109/MC.2022.3158156

This installment of Computer’s series highlighting the work published in IEEE Computer Society journals comes from IEEE Transactions on Parallel and Distributed Systems.