M. Penwarden, A.D. Jagtap, S. Zhe, G.E. Karniadakis, R.M. Kirby. A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions, Subtitled arXiv:2302.14227v1, 2023.
Physics-informed neural networks (PINNs) as a means of solving partial differential equations (PDE) have garnered much attention in the Computational Science and Engineering (CS&E) world. However, a recent topic of interest is exploring various training (i.e., optimization) challenges – in particular, arriving at poor local minima in the optimization landscape results in a PINN approximation giving an inferior, and sometimes trivial, solution when solving forward time-dependent PDEs with no data. This problem is also found in, and in some sense more difficult, with domain decomposition strategies such as temporal decomposition using XPINNs. To address this problem, we first enable a general categorization for previous causality methods, from which we identify a gap (e.g., opportunity) in the previous approaches. We then furnish examples and explanations for different training challenges, their cause, and how they relate to information propagation and temporal decomposition. We propose a solution to fill this gap by reframing these causality concepts into a generalized information propagation framework in which any prior method or combination of methods can be described. This framework is easily modifiable via user parameters in the open-source code accompanying this paper. Our unified framework moves toward reducing the number of PINN methods to consider and the reimplementation and retuning cost for thorough comparisons rather than increasing it. Using the idea of information propagation, we propose a new stacked-decomposition method that bridges the gap between time-marching PINNs and XPINNs. We also introduce significant computational speed-ups by using transfer learning concepts to initialize subnetworks in the domain and loss tolerance-based propagation for the subdomains. Finally, we formulate a new time-sweeping collocation point algorithm inspired by the previous PINNs causality literature, which our framework can still describe, and provides a significant computational speed-up via reduced-cost collocation point segmentation. The proposed methods overcome training challenges in PINNs and XPINNs for time-dependent PDEs by respecting the causality in multiple forms and improving scalability by limiting the computation required per optimization iteration. Finally, we provide numerical results for these methods on baseline PDE problems for which unmodified PINNs and XPINNs struggle to train.
C. Peters, T. Patel, W. Usher, C R. Johnson.
Ray Tracing Spherical Harmonics Glyphs, In Vision, Modeling, and Visualization, The Eurographics Association, 2023.
Spherical harmonics glyphs are an established way to visualize high angular resolution diffusion imaging data. Starting from a unit sphere, each point on the surface is scaled according to the value of a linear combination of spherical harmonics basis functions. The resulting glyph visualizes an orientation distribution function. We present an efficient method to render these glyphs using ray tracing. Our method constructs a polynomial whose roots correspond to ray-glyph intersections. This polynomial has degree 2k + 2 for spherical harmonics bands 0, 2, . . . , k. We then find all intersections in an efficient and numerically stable fashion through polynomial root finding. Our formulation also gives rise to a simple formula for normal vectors of the glyph. Additionally, we compute a nearly exact axis-aligned bounding box to make ray tracing of these glyphs even more efficient. Since our method finds all intersections for arbitrary rays, it lets us perform sophisticated shading and uncertainty visualization. Compared to prior work, it is faster, more flexible and more accurate.
M. Shao, T. Tasdizen, S. Joshi. Analyzing the Domain Shift Immunity of Deep Homography Estimation, Subtitled arXiv:2304.09976v1, 2023.
Homography estimation is a basic image-alignment method in many applications. Recently, with the development of convolutional neural networks (CNNs), some learning based approaches have shown great success in this task. However, the performance across different domains has never been researched. Unlike other common tasks (e.g., classification, detection, segmentation), CNN based homography estimation models show a domain shift immunity, which means a model can be trained on one dataset and tested on another without any transfer learning. To explain this unusual performance, we need to determine how CNNs estimate homography. In this study, we first show the domain shift immunity of different deep homography estimation models. We then use a shallow network with a specially designed dataset to analyze the features used for estimation. The results show that networks use low-level texture information to estimate homography. We also design some experiments to compare the performance between different texture densities and image features distorted on some common datasets to demonstrate our findings. Based on these findings, we provide an explanation of the domain shift immunity of deep homography estimation.
N. Shingde, M. Berzins, T. Blattner, W. Keyrouz, A. Bardakoff. Extending Hedgehog’s dataflow graphs to multi-node GPU architectures, In Workshop on Asynchronous Many-Task Systems and Applications (WAMTA23), 2023.
Asynchronous task-based systems offer the possibility of making it easier to take advantage of scalable heterogeneous architectures.
This paper extends the National Institute of Standards and Technology’s Hedgehog dataflow graph models, which target a single high-end
compute node, to run on a cluster by borrowing aspects of Uintah’s cluster-scale task graphs and applying them to a sample implementation
of matrix multiplication. These results are compared to implementations using the leading libraries, SLATE and DPLASMA, for illustrative purposes only. The motivation behind this work is to demonstrate that using general purpose high-level abstractions, such as Hedgehog’s dataflow graphs, does not negatively impact performance.
K. Shukla, V. Oommen, A. Peyvan, M. Penwarden, L. Bravo, A. Ghoshal, R.M. Kirby, G. Karniadakis. Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils, Subtitled arXiv:2302.00807v1, 2023.
Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications. Here, we investigate the use of DeepONets to infer flow fields around unseen airfoils with the aim of shape optimization, an important design problem in aerodynamics that typically taxes computational resources heavily. We present results which display little to no degradation in prediction accuracy, while reducing the online optimization cost by orders of magnitude. We consider NACA airfoils as a test case for our proposed approach, as their shape can be easily defined by the four-digit parametrization. We successfully optimize the constrained NACA four-digit problem with respect to maximizing the lift-to-drag ratio and validate all results by comparing them to a high-order CFD solver. We find that DeepONets have low generalization error, making them ideal for generating solutions of unseen shapes. Specifically, pressure, density, and velocity fields are accurately inferred at a fraction of a second, hence enabling the use of general objective functions beyond the maximization of the lift-to-drag ratio considered in the current work.
K. Shukla, V. Oommen, A. Peyvan, M. Penwarden, N. Plewacki, L. Bravo, A. Ghoshal, R.M. Kirby, G. Karniadakis.
Deep neural operators as accurate surrogates for shape optimization, In Engineering Applications of Artificial Intelligence, Vol. 129, pp. 107615. 2023.
Deep neural operators, such as DeepONet, have changed the paradigm in high-dimensional nonlinear regression, paving the way for significant generalization and speed-up in computational engineering applications. Here, we investigate the use of DeepONet to infer flow fields around unseen airfoils with the aim of shape constrained optimization, an important design problem in aerodynamics that typically taxes computational resources heavily. We present results that display little to no degradation in prediction accuracy while reducing the online optimization cost by orders of magnitude. We consider NACA airfoils as a test case for our proposed approach, as the four-digit parameterization can easily define their shape. We successfully optimize the constrained NACA four-digit problem with respect to maximizing the lift-to-drag ratio and validate all results by comparing them to a high-order CFD solver. We find that DeepONets have a low generalization error, making them ideal for generating solutions of unseen shapes. Specifically, pressure, density, and velocity fields are accurately inferred at a fraction of a second, hence enabling the use of general objective functions beyond the maximization of the lift-to-drag ratio considered in the current work. Finally, we validate the ability of DeepONet to handle a complex 3D waverider geometry at hypersonic flight by inferring shear stress and heat flux distributions on its surface at unseen angles of attack. The main contribution of this paper is a modular integrated design framework that uses an over-parametrized neural operator as a surrogate model with good generalizability coupled seamlessly with multiple optimization solvers in a plug-and-play mode.
TEMA project is a Horizon Europe funded project that aims at addressing Natural Disaster Management by the use of sophisticated Cloud-Edge Continuum infrastructures by means of data analysis algorithms wrapped in Serverless functions deployed on a distributed infrastructure according to a Federated Learning scheduler that constantly monitors the infrastructure in search of the best way to satisfy required QoS constraints. In this paper, we discuss the advantages of Serverless workflow and how they can be used and monitored to natively trigger complex algorithm pipelines in the continuum, dynamically placing and relocating them taking into account incoming IoT data, QoS constraints, and the current status of the continuum infrastructure. Therefore we presented the Urgent Function Enabler (UFE) platform, a fully distributed architecture able to define, spread, and manage FaaS functions, using local IOT data managed using the Fiware ecosystem and a computing infrastructure composed of mobile and stable nodes.
K.M.A. Sultan, B. Orkild, A. Morris, E. Kholmovski, E. Bieging, E. Kwan, R. Ranjan, E. DiBella, s. Elhabian. Two-Stage Deep Learning Framework for Quality Assessment of Left Atrial Late Gadolinium Enhanced MRI Images, Subtitled arXiv:2310.08805v1, 2023.
Accurate assessment of left atrial fibrosis in patients with atrial fibrillation relies on high-quality 3D late gadolinium enhancement (LGE) MRI images. However, obtaining such images is challenging due to patient motion, changing breathing patterns, or sub-optimal choice of pulse sequence parameters. Automated assessment of LGE-MRI image diagnostic quality is clinically significant as it would enhance diagnostic accuracy, improve efficiency, ensure standardization, and contributes to better patient outcomes by providing reliable and high-quality LGE-MRI scans for fibrosis quantification and treatment planning. To address this, we propose a two-stage deep-learning approach for automated LGE-MRI image diagnostic quality assessment. The method includes a left atrium detector to focus on relevant regions and a deep network to evaluate diagnostic quality. We explore two training strategies, multi-task learning, and pretraining using contrastive learning, to overcome limited annotated data in medical imaging. Contrastive Learning result shows about 4%, and 9% improvement in F1-Score and Specificity compared to Multi-Task learning when there’s limited data.
T. Sun, D. Li, B. Wang. On the Decentralized Stochastic Gradient Descent with Markov Chain Sampling, In IEEE Transactions on Signal Processing, IEEE, July, 2023.
The decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD), a variant of the decentralized stochastic gradient method, which draws random samples along the trajectory of a Markov chain. DMGD arises when obtaining independent samples is costly or impossible, excluding the use of the traditional stochastic gradient algorithms. Specifically, we consider the DMGD over a connected graph, where each node only communicates with its neighbors by sending and receiving the intermediate results. We establish both ergodic and nonergodic convergence rates of DMGD, which elucidate the critical dependencies on the topology of the graph that connects all nodes and the mixing time of the Markov chain. We further numerically verify the sample efficiency of DMGD.
J. Tate, Z. Liu, J.A. Bergquist, S. Rampersad, D. White, C. Charlebois, L. Rupp, D. Brooks, R. MacLeod, A. Narayan. UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines, In Journal of Open Source Software, Vol. 8, No. 90, 2023.
We have developed UncertainSCI (UncertainSCI, 2020) as an open-source tool designed to make modern uncertainty quantification (UQ) techniques more accessible in biomedical simulation applications. UncertainSCI is implemented in Python with a noninvasive interface to meet our software design goals of 1) numerical accuracy, 2) simple application programming interface (API), 3) adaptability to many applications and methods, and 4) interfacing with diverse simulation software. Using a Python implementation in UncertainSCI allowed us to utilize the popularity and low barrier-to-entry of Python and its common packages and to leverage the built-in integration and support for Python in common simulation software packages and languages. Additionally, we used noninvasive UQ techniques and created a similarly noninvasive interface to external modeling software that can be called in diverse ways, depending on the complexity and level of Python integration in the external simulation pipeline. We have developed and included examples applying UncertainSCI to relatively simple 1D simulations implemented in Python, and to bioelectric field simulations implemented in external software packages, which demonstrate the use of UncertainSCI and the effectiveness of the architecture and implementation in achieving our design goals. UnceratainSCI differs from similar software, notably UQLab, Uncertainpy, and Simnibs, in that it can be efficiently and non-invasively used with external simulation software, specifically with high resolution 3D simulations often used in Bioelectric field simulations. Figure 1 illustrates the use of UncertainSCI in computing UQ with modeling pipelines for bioelectricity simulations
Separating algorithms from their computation schedule has become a de facto solution to tackle the challenges of developing high performance code on modern heterogeneous architectures. Common approaches include Domain-specific languages (DSLs) which provide familiar APIs to domain experts, code generation frameworks that automate the generation of fast and portable code, and runtime systems that manage threads for concurrency and parallelism. In this paper, we present the Halide code generation framework for Phylanx distributed array processing platform. This extension enables compile-time optimization of Phylanx primitives for target architectures. To accomplish this, (1) we implemented new Phylanx primitives using Halide, and (2) partially exported Halide's thread pool API to carry out parallelism on HPX (Phylanx's runtime) threads. (3) showcased HPX performance analysis tools made available to Halide applications. The evaluation of the work has been done in two steps. First, we compare the performance of Halide applications running on its native runtime with that of the new HPX backend to verify there is no cost associated with using HPX threads. Next, we compare performances of a number of original implementations of Phylanx primitives against the new ones in Halide to verify performance and portability benefits of Halide in the context of Phylanx.
Z. Wang, T. M. Athawale, K. Moreland, J. Chen, C. R. Johnson, D. Pugmire.
FunMC2: A Filter for Uncertainty Visualization of Marching Cubes on Multi-Core Devices, In Eurographics Symposium on Parallel Graphics and Visualization, 2023.
Visualization is an important tool for scientists to extract understanding from complex scientific data. Scientists need to understand the uncertainty inherent in all scientific data in order to interpret the data correctly. Uncertainty visualization has been an active and growing area of research to address this challenge. Algorithms for uncertainty visualization can be expensive, and research efforts have been focused mainly on structured grid types. Further, support for uncertainty visualization in production tools is limited. In this paper, we adapt an algorithm for computing key metrics for visualizing uncertainty in Marching Cubes (MC) to multi-core devices and present the design, implementation, and evaluation for a Filter for uncertainty visualization of Marching Cubes on Multi-Core devices (FunMC2). FunMC2 accelerates the uncertainty visualization of MC significantly, and it is portable across multi-core CPUs and GPUs. Evaluation results show that FunMC2 based on OpenMP runs around 11× to 41× faster on multi-core CPUs than the corresponding serial version using one CPU core. FunMC2 based on a single GPU is around 5× to 9× faster than FunMC2 running by OpenMP. Moreover, FunMC2 is flexible enough to process ensemble data with both structured and unstructured mesh types. Furthermore, we demonstrate that FunMC2 can be seamlessly integrated as a plugin into ParaView, a production visualization tool for post-processing.
K. Williams, A. Bigelow, K.E. Isaacs. Data Abstraction Elephants: The Initial Diversity of Data Representations and Mental Models, In Proceedings of the 2023 CHI Conference on Human Factors in Computing Systems (CHI ’23), ACM, 2023.
Two people looking at the same dataset will create diferent mental models, prioritize diferent attributes, and connect with diferent visualizations. We seek to understand the space of data abstractions associated with mental models and how well people communicate their mental models when sketching. Data abstractions have a profound infuence on the visualization design, yet it’s unclear how universal they may be when not initially infuenced by a representation. We conducted a study about how people create their mental models from a dataset. Rather than presenting tabular data, we presented each participant with one of three datasets in paragraph form, to avoid biasing the data abstraction and mental model. We observed various mental models, data abstractions, and depictions from the same dataset, and how these concepts are infuenced by communication and purpose-seeking. Our results have implications for visualization design, especially during the discovery and data collection phase.
H. Xu, S. Elhabian. Image2SSM: Reimagining Statistical Shape Models from Images with Radial Basis Functions, Subtitled arXiv:2305.11946, 2023.
Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using lower-dimensional shape features, on which statistical analysis can be performed. Various methods for constructing compact shape representations have been proposed, but they involve laborious and costly steps. We propose Image2SSM, a novel deep-learning-based approach for SSM that leverages image-segmentation pairs to learn a radial-basis-function (RBF)-based representation of shapes directly from images. This RBF-based shape representation offers a rich self-supervised signal for the network to estimate a continuous, yet compact representation of the underlying surface that can adapt to complex geometries in a data-driven manner. Image2SSM can characterize populations of biological structures of interest by constructing statistical landmark-based shape models of ensembles of anatomical shapes while requiring minimal parameter tuning and no user assistance. Once trained, Image2SSM can be used to infer low-dimensional shape representations from new unsegmented images, paving the way toward scalable approaches for SSM, especially when dealing with large cohorts. Experiments on synthetic and real datasets show the efficacy of the proposed method compared to the state-of-art correspondence-based method for SSM.
Particle-Based Shape Modeling for Arbitrary Regions-of-Interest, In Shape in Medical Imaging, Lecture Notes in Computer Science, vol 14350, 2023.H. Xu, A. Morris, S.Y. Elhabian.
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific morphological features. We propose an extension to particle-based shape modeling (PSM), a widely used SSM framework, to allow shape modeling to arbitrary regions of interest. Existing methods to define regions of interest are computationally expensive and have topological limitations. To address these shortcomings, we use mesh fields to define free-form constraints, which allow for delimiting arbitrary regions of interest on shape surfaces. Furthermore, we add a quadratic penalty method to the model optimization to enable computationally efficient enforcement of any combination of cutting-plane and free-form constraints. We demonstrate the effectiveness of this method on a challenging synthetic dataset and two medical datasets.
Optimizing Data Movement for GPU-Based In-Situ Workflow Using GPUDirect RDMA, In Euro-Par 2023: Parallel Processing, Springer Nature Switzerland, pp. 323--338. 2023.
The extreme-scale computing landscape is increasingly dominated by GPU-accelerated systems. At the same time, in-situ workflows that employ memory-to-memory inter-application data exchanges have emerged as an effective approach for leveraging these extreme-scale systems. In the case of GPUs, GPUDirect RDMA enables third-party devices, such as network interface cards, to access GPU memory directly and has been adopted for intra-application communications across GPUs. In this paper, we present an interoperable framework for GPU-based in-situ workflows that optimizes data movement using GPUDirect RDMA. Specifically, we analyze the characteristics of the possible data movement pathways between GPUs from an in-situ workflow perspective, and design a strategy that maximizes throughput. Furthermore, we implement this approach as an extension of the DataSpaces data staging service, and experimentally evaluate its performance and scalability on a current leadership GPU cluster. The performance results show that the proposed design reduces data-movement time by up to 53% and 40% for the sender and receiver, respectively, and maintains excellent scalability for up to 256 GPUs.
Orchestration of materials science workflows for heterogeneous resources at large scale, In The International Journal of High Performance Computing Applications, Sage, 2023.N. Zhou, G. Scorzelli, J. Luettgau, R.R. Kancharla, J. Kane, R. Wheeler, B. Croom, B. Newell, V. Pascucci, M. Taufer.
In the era of big data, materials science workflows need to handle large-scale data distribution, storage, and computation. Any of these areas can become a performance bottleneck. We present a framework for analyzing internal material structures (e.g., cracks) to mitigate these bottlenecks. We demonstrate the effectiveness of our framework for a workflow performing synchrotron X-ray computed tomography reconstruction and segmentation of a silica-based structure. Our framework provides a cloud-based, cutting-edge solution to challenges such as growing intermediate and output data and heavy resource demands during image reconstruction and segmentation. Specifically, our framework efficiently manages data storage, scaling up compute resources on the cloud. The multi-layer software structure of our framework includes three layers. A top layer uses Jupyter notebooks and serves as the user interface. A middle layer uses Ansible for resource deployment and managing the execution environment. A low layer is dedicated to resource management and provides resource management and job scheduling on heterogeneous nodes (i.e., GPU and CPU). At the core of this layer, Kubernetes supports resource management, and Dask enables large-scale job scheduling for heterogeneous resources. The broader impact of our work is four-fold: through our framework, we hide the complexity of the cloud’s software stack to the user who otherwise is required to have expertise in cloud technologies; we manage job scheduling efficiently and in a scalable manner; we enable resource elasticity and workflow orchestration at a large scale; and we facilitate moving the study of nonporous structures, which has wide applications in engineering and scientific fields, to the cloud. While we demonstrate the capability of our framework for a specific materials science application, it can be adapted for other applications and domains because of its modular, multi-layer architecture.
J. Adams, N. Khan, A. Morris, S. Elhabian. Spatiotemporal Cardiac Statistical Shape Modeling: A Data-Driven Approach, Subtitled arXiv preprint arXiv:2209.02736, 2022.
Clinical investigations of anatomy’s structural changes over time could greatly benefit from population-level quantification of shape, or spatiotemporal statistic shape modeling (SSM). Such a tool enables characterizing patient organ cycles or disease progression in relation to a cohort of interest. Constructing shape models requires establishing a quantitative shape representation (e.g., corresponding landmarks). Particle-based shape modeling (PSM) is a data-driven SSM approach that captures population-level shape variations by optimizing landmark placement. However, it assumes cross-sectional study designs and hence has limited statistical power in representing shape changes over time. Existing methods for modeling spatiotemporal or longitudinal shape changes require predefined shape atlases and pre-built shape models that are typically constructed cross-sectionally. This paper proposes a data-driven approach inspired by the PSM method to learn population-level spatiotemporal shape changes directly from shape data. We introduce a novel SSM optimization scheme that produces landmarks that are in correspondence both across the population (inter-subject) and across time-series (intra-subject). We apply the proposed method to 4D cardiac data from atrial-fibrillation patients and demonstrate its efficacy in representing the dynamic change of the left atrium. Furthermore, we show that our method outperforms an image-based approach for spatiotemporal SSM with respect to a generative time-series model, the Linear Dynamical System (LDS). LDS fit using a spatiotemporal shape model optimized via our approach provides better generalization and specificity, indicating it accurately captures the underlying time-dependency.
M. Alirezaei, T. Tasdizen. Adversarially Robust Classification by Conditional Generative Model Inversion, Subtitled arXiv preprint arXiv:2201.04733, 2022.
Most adversarial attack defense methods rely on obfuscating gradients. These methods are successful in defending against gradient-based attacks; however, they are easily circumvented by attacks which either do not use the gradient or by attacks which approximate and use the corrected gradient. Defenses that do not obfuscate gradients such as adversarial training exist, but these approaches generally make assumptions about the attack such as its magnitude. We propose a classification model that does not obfuscate gradients and is robust by construction without assuming prior knowledge about the attack. Our method casts classification as an optimization problem where we "invert" a conditional generator trained on unperturbed, natural images to find the class that generates the closest sample to the query image. We hypothesize that a potential source of brittleness against adversarial attacks is the high-to-low-dimensional nature of feed-forward classifiers which allows an adversary to find small perturbations in the input space that lead to large changes in the output space. On the other hand, a generative model is typically a low-to-high-dimensional mapping. While the method is related to Defense-GAN, the use of a conditional generative model and inversion in our model instead of the feed-forward classifier is a critical difference. Unlike Defense-GAN, which was shown to generate obfuscated gradients that are easily circumvented, we show that our method does not obfuscate gradients. We demonstrate that our model is extremely robust against black-box attacks and has improved robustness against white-box attacks compared to naturally trained, feed-forward classifiers.