K. Iyer, A. Morris, B. Zenger, K. Karnath, B.A. Orkild, O. Korshak, S. Elhabian. Statistical Shape Modeling of Biventricular Anatomy with Shared Boundaries, Subtitled arXiv:2209.02706v1, 2022.
Statistical shape modeling (SSM) is a valuable and powerful tool to generate a detailed representation of complex anatomy that enables quantitative analysis and the comparison of shapes and their variations. SSM applies mathematics, statistics, and computing to parse the shape into a quantitative representation (such as correspondence points or landmarks) that will help answer various questions about the anatomical variations across the population. Complex anatomical structures have many diverse parts with varying interactions or intricate architecture. For example, the heart is a four-chambered anatomy with several shared boundaries between chambers. Coordinated and efficient contraction of the chambers of the heart is necessary to adequately perfuse end organs throughout the body. Subtle shape changes within these shared boundaries of the heart can indicate potential pathological changes that lead to uncoordinated contraction and poor end-organ perfusion. Early detection and robust quantification could provide insight into ideal treatment techniques and intervention timing. However, existing SSM approaches fall short of explicitly modeling the statistics of shared boundaries. In this paper, we present a general and flexible data-driven approach for building statistical shape models of multi-organ anatomies with shared boundaries that captures morphological and alignment changes of individual anatomies and their shared boundary surfaces throughout the population. We demonstrate the effectiveness of the proposed methods using a biventricular heart dataset by developing shape models that consistently parameterize the cardiac biventricular structure and the interventricular septum (shared boundary surface) across the population data.
M.H. Jensen, S. Joshi, S. Sommer. Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces: Sampling and Metric Estimation, In Algorithms, Vol. 15, No. 8, 2022.
We present schemes for simulating Brownian bridges on complete and connected Lie groups and homogeneous spaces. We use this to construct an estimation scheme for recovering an unknown left- or right-invariant Riemannian metric on the Lie group from samples. We subsequently show how pushing forward the distributions generated by Brownian motions on the group results in distributions on homogeneous spaces that exhibit a non-trivial covariance structure. The pushforward measure gives rise to new non-parametric families of distributions on commonly occurring spaces such as spheres and symmetric positive tensors. We extend the estimation scheme to fit these distributions to homogeneous space-valued data. We demonstrate both the simulation schemes and estimation procedures on Lie groups and homogenous spaces, including SPD(3)=GL+(3)/SO(3) and S2=SO(3)/SO(2).
X. Jiang, Z. Li, R. Missel, Md. Zaman, B. Zenger, W. W. Good, R. S. MacLeod, J. L. Sapp, L. Wang. Few-Shot Generation of Personalized Neural Surrogates for Cardiac Simulation via Bayesian Meta-learning, In Medical Image Computing and Computer Assisted Intervention -- MICCAI 2022, Springer Nature Switzerland, pp. 46--56. 2022.
Clinical adoption of personalized virtual heart simulations faces challenges in model personalization and expensive computation. While an ideal solution is an efficient neural surrogate that at the same time is personalized to an individual subject, the state-of-the-art is either concerned with personalizing an expensive simulation model, or learning an efficient yet generic surrogate. This paper presents a completely new concept to achieve personalized neural surrogates in a single coherent framework of meta-learning (metaPNS). Instead of learning a single neural surrogate, we pursue the process of learning a personalized neural surrogate using a small amount of context data from a subject, in a novel formulation of few-shot generative modeling underpinned by: 1) a set-conditioned neural surrogate for cardiac simulation that, conditioned on subject-specific context data, learns to generate query simulations not included in the context set, and 2) a meta-model of amortized variational inference that learns to condition the neural surrogate via simple feed-forward embedding of context data. As test time, metaPNS delivers a personalized neural surrogate by fast feed-forward embedding of a small and flexible number of data available from an individual, achieving -- for the first time -- personalization and surrogate construction for expensive simulations in one end-to-end learning framework. Synthetic and real-data experiments demonstrated that metaPNS was able to improve personalization and predictive accuracy in comparison to conventionally-optimized cardiac simulation models, at a fraction of computation.
X. Jiang, M. Toloubidokhti, J. Bergquist, B. Zenger, w. Good, R.S. MacLeod, L. Wang. Improving Generalization by Learning Geometry-Dependent and Physics-Based Reconstruction of Image Sequences, In IEEE Transactions on Medical Imaging, 2022.
Deep neural networks have shown promise in image reconstruction tasks, although often on the premise of large amounts of training data. In this paper, we present a new approach to exploit the geometry and physics underlying electrocardiographic imaging (ECGI) to learn efficiently with a relatively small dataset. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then explicitly model the geometry-dependent physics in between the two domains via a bipartite graph over their graphical embeddings. We applied the resulting network to reconstruct electrical activity on the heart surface from body-surface potentials. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the network to generalize across geometrical changes underlying the data using less than 10% of training data and fewer variations of training geometry in comparison to its Euclidean alternatives. In both simulation and real-data experiments, we further demonstrated its ability to be quickly fine-tuned to new geometry using a modest amount of data.
X. Jiang, J. Tate, J. Bergquist, A. Narayan, R. MacLeod, L. Wang. Uncertainty Quantification of Cardiac Position on Deep Graph Network ECGI, In Computing in Cardiology, Vol. 49, 2022.
Subject-specific geometry such as cardiac position and torso size plays an important role in electrocardiographic imaging (ECGI). Previously, we introduced a graph-based neural network (GNN) that is dependent on patient-specific geometry to improve reconstruction accuracy. However, geometric uncertainty, including changes in cardiac position and torso size, has not been addressed in network-based methods. In this study, we estimate geometrical uncertainty on GNN by applying uncertainty quantification with polynomial chaos emulators (PCE). To estimate the effect of geometric variation from common motions, we evaluated the model on samples generated by different heart torso geometries. The experiments shows that the GNN is less sensitive to heart position and torso shape and helps us direct development of similar models to account of possible variability.
R. Kamali, K. Gillete, J. Tate, D. A. Abhyankar, D. J. Dosdall, G. Plank, T. J. Bunch, R. S. Macleod & R. Ranjan . Treatment Planning for Atrial Fibrillation Using Patient-Specific Models Showing the Importance of Fibrillatory-Areas, In Annals of Biomedical Engineering, Springer, 2022.
Computational models have made it possible to study the effect of fibrosis and scar on atrial fibrillation (AF) and plan future personalized treatments. Here, we study the effect of area available for fibrillatory waves to sustain AF. Then we use it to plan for AF ablation to improve procedural outcomes. CARPentry was used to create patient-specific models to determine the association between the size of residual contiguous areas available for AF wavefronts to propagate and sustain AF [fibrillatory area (FA)] after ablation with procedural outcomes. The FA was quantified in a novel manner accounting for gaps in ablation lines. We selected 30 persistent AF patients with known ablation outcomes. We divided the atrial surface into five areas based on ablation scar pattern and anatomical landmarks and calculated the FAs. We validated the models based on clinical outcomes and suggested future ablation lines that minimize the FAs and terminate rotor activities in simulations. We also simulated the effects of three common antiarrhythmic drugs. In the patient-specific models, the predicted arrhythmias matched the clinical outcomes in 25 of 30 patients (accuracy 83.33%). The average largest FA (FAmax) in the recurrence group was 8517 ± 1444 vs. 6772 ± 1531 mm2 in the no recurrence group (p < 0.004). The final FAs after adding the suggested ablation lines in the AF recurrence group reduced the average FAmax from 8517 ± 1444 to 6168 ± 1358 mm2 (p < 0.001) and stopped the sustained rotor activity. Simulations also correctly anticipated the effect of antiarrhythmic drugs in 5 out of 6 patients who used drug therapy post unsuccessful ablation (accuracy 83.33%). Sizes of FAs available for AF wavefronts to propagate are important determinants for ablation outcomes. FA size in combination with computational simulations can be used to direct ablation in persistent AF to minimize the critical mass required to sustain recurrent AF.
V. Keshavarzzadeh, R.M. Kirby, A. Narayan. Variational Inference for Nonlinear Inverse Problems via Neural Net Kernels: Comparison to Bayesian Neural Networks, Application to Topology Optimization, Subtitled arXiv:2205.03681, 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.
D. Klotzl, T. Krake, Y. Zhou, I. Hotz, B. Wang, D. Weiskopf. Local Bilinear Computation of Jacobi Sets, In The Visual Computer, 2022.
We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.
D. Klötzl, T. Krake, Y. Zhou, J. Stober, K. Schulte, I. Hotz, B. Wang, D. Weiskopf. Reduced Connectivity for Local Bilinear Jacobi Sets, Subtitled arXiv:2208.07148, 2022.
We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological structure of the local bilinear method is utilized, which is given by the nerve complex of the traditional piecewise linear method. Since the nerve complex consists of higher-dimensional simplices, the local bilinear method (visually represented by the 1-skeleton of the nerve complex) leads to clutter via crossings of line segments. Therefore, we propose a homotopy-equivalent representation that uses different collapses and edge contractions to remove such artifacts. Our new connectivity method is easy to implement, comes with only little overhead, and results in a less cluttered representation.
R. Lanfredi, J.D. Schroeder, T. Tasdizen. Localization supervision of chest x-ray classifiers using label-specific eye-tracking annotation, Subtitled arXiv:2207.09771, 2022.
Convolutional neural networks (CNNs) have been successfully applied to chest x-ray (CXR) images. Moreover, annotated bounding boxes have been shown to improve the interpretability of a CNN in terms of localizing abnormalities. However, only a few relatively small CXR datasets containing bounding boxes are available, and collecting them is very costly. Opportunely, eye-tracking (ET) data can be collected in a non-intrusive way during the clinical workflow of a radiologist. We use ET data recorded from radiologists while dictating CXR reports to train CNNs. We extract snippets from the ET data by associating them with the dictation of keywords and use them to supervise the localization of abnormalities. We show that this method improves a model's interpretability without impacting its image-level classification.
D. Lange, S. Sahai, J.M. Phillips, A. Lex. Ferret: Reviewing Tabular Datasets for Manipulation, Subtitled OSF Preprint, 2022.
How do we ensure the veracity of science? The act of manipulating or fabricating scientific data has led to many high-profile fraud cases and retractions. Detecting manipulated data, however, is a challenging and time-consuming endeavor. Automated detection methods are limited due to the diversity of data types and manipulation techniques. Furthermore, patterns automatically flagged as suspicious can have reasonable explanations. Instead, we propose a nuanced approach where experts analyze tabular datasets, eg, as part of the peer-review process, using a guided, interactive visualization approach. In this paper, we present an analysis of how manipulated datasets are created and the artifacts these techniques generate. Based on these findings, we propose a suite of visualization methods to surface potential irregularities. We have implemented these methods in Ferret, a visualization tool for data forensics work. Ferret makes potential data issues salient and provides guidance on spotting signs of tampering and differentiating them from truthful data.
Z. Li, S. Liu, X. Yu, K. Bhavya, J. Cao, J. Diffenderfer, P.T. Bremer, V. Pascucci. “Understanding Robustness Lottery”: A Comparative Visual Analysis of Neural Network Pruning Approaches, Subtitled arXiv preprint arXiv:2206.07918, 2022.
Deep learning approaches have provided state-of-the-art performance in many applications by relying on extremely large and heavily overparameterized neural networks. However, such networks have been shown to be very brittle, not generalize well to new uses cases, and are often difficult if not impossible to deploy on resources limited platforms. Model pruning, i.e., reducing the size of the network, is a widely adopted strategy that can lead to more robust and generalizable network -- usually orders of magnitude smaller with the same or even improved performance. While there exist many heuristics for model pruning, our understanding of the pruning process remains limited. Empirical studies show that some heuristics improve performance while others can make models more brittle or have other side effects. This work aims to shed light on how different pruning methods alter the network's internal feature representation, and the corresponding impact on model performance. To provide a meaningful comparison and characterization of model feature space, we use three geometric metrics that are decomposed from the common adopted classification loss. With these metrics, we design a visualization system to highlight the impact of pruning on model prediction as well as the latent feature embedding. The proposed tool provides an environment for exploring and studying differences among pruning methods and between pruned and original model. By leveraging our visualization, the ML researchers can not only identify samples that are fragile to model pruning and data corruption but also obtain insights and explanations on how some pruned …
S. Li, R.M. Kirby, S. Zhe. Decomposing Temporal High-Order Interactions via Latent ODEs, 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.
S. Li, Z Wang, R.M. Kirby, S. Zhe. Infinite-Fidelity Coregionalization for Physical Simulation, Subtitled arXiv:2207.00678, 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.
Z. Li, T. Sun, H. Wang, B. Wang. Adaptive and Implicit Regularization for Matrix Completion, Subtitled arXiv preprint arXiv:2208.05640, 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.
S. Li, J.M. Phillips, X. Yu, R.M. Kirby, S. Zhe. Batch Multi-Fidelity Active Learning with Budget Constraints, Subtitled arXiv:2210.12704v1, 2022.
Learning functions with high-dimensional outputs is critical in many applications, such as physical simulation and engineering design. However, collecting training examples for these applications is often costly, e.g. by running numerical solvers. The recent work (Li et al., 2022) proposes the first multi-fidelity active learning approach for high-dimensional outputs, which can acquire examples at different fidelities to reduce the cost while improving the learning performance. However, this method only queries at one pair of fidelity and input at a time, and hence has a risk to bring in strongly correlated examples to reduce the learning efficiency. In this paper, we propose Batch Multi-Fidelity Active Learning with Budget Constraints (BMFAL-BC), which can promote the diversity of training examples to improve the benefit-cost ratio, while respecting a given budget constraint for batch queries. Hence, our method can be more practically useful. Specifically, we propose a novel batch acquisition function that measures the mutual information between a batch of multi-fidelity queries and the target function, so as to penalize highly correlated queries and encourages diversity. The optimization of the batch acquisition function is challenging in that it involves a combinatorial search over many fidelities while subject to the budget constraint. To address this challenge, we develop a weighted greedy algorithm that can sequentially identify each (fidelity, input) pair, while achieving a near -approximation of the optimum. We show the advantage of our method in several computational physics and engineering applications.
S. Li, M. Penwarden, R.M. Kirby, S. Zhe. Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks, Subtitled arXiv preprint arXiv:2210.12669, 2022.
Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, applying different PINNs to solve the equation in each subdomain and aligning the solution at the interface of the subdomains. Hence, they can further alleviate the problem complexity, reduce the computational cost, and allow parallelization. However, the performance of the multi-domain PINNs is sensitive to the choice of the interface conditions for solution alignment. While quite a few conditions have been proposed, there is no suggestion about how to select the conditions according to specific problems. To address this gap, we propose META Learning of Interface Conditions (METALIC), a simple, efficient yet powerful approach to dynamically determine the optimal interface conditions for solving a family of parametric PDEs. Specifically, we develop two contextual multi-arm bandit models. The first one applies to the entire training procedure, and online updates a Gaussian process (GP) reward surrogate that given the PDE parameters and interface conditions predicts the solution error. The second one partitions the training into two stages, one is the stochastic phase and the other deterministic phase; we update a GP surrogate for each phase to enable different condition selections at the two stages so as to further bolster the flexibility and performance. We have shown the advantage of METALIC on four bench-mark PDE families.
Z. Li, H. Menon, K. Mohror, S. Liu, L. Guo, P.T. Bremer, V. Pascucci. A Visual Comparison of Silent Error Propagation, In IEEE Transactions on Visualization and Computer Graphics, IEEE, 2022.
High-performance computing (HPC) systems play a critical role in facilitating scientific discoveries. Their scale and complexity (e.g., the number of computational units and software stack) continue to grow as new systems are expected to process increasingly more data and reduce computing time. However, with more processing elements, the probability that these systems will experience a random bit-flip error that corrupts a program's output also increases, which is often recognized as silent data corruption. Analyzing the resiliency of HPC applications in extreme-scale computing to silent data corruption is crucial but difficult. An HPC application often contains a large number of computation units that need to be tested, and error propagation caused by error corruption is complex and difficult to interpret. To accommodate this challenge, we propose an interactive visualization system that helps HPC researchers understand the resiliency of HPC applications and compare their error propagation. Our system models an application's error propagation to study a program's resiliency by constructing and visualizing its fault tolerance boundary. Coordinating with multiple interactive designs, our system enables domain experts to efficiently explore the complicated spatial and temporal correlation between error propagations. At the end, the system integrated a nonmonotonic error propagation analysis with an adjustable graph propagation visualization to help domain experts examine the details of error propagation and answer such questions as why an error is mitigated or amplified by program execution.
Z. Liu, A. Narayan. A Stieltjes algorithm for generating multivariate orthogonal polynomials, Subtitled arXiv preprint arXiv:2202.04843, 2022.
Orthogonal polynomials of several variables have a vector-valued three-term recurrence relation, much like the corresponding one-dimensional relation. This relation requires only knowledge of certain recurrence matrices, and allows simple and stable evaluation of multivariate orthogonal polynomials. In the univariate case, various algorithms can evaluate the recurrence coefficients given the ability to compute polynomial moments, but such a procedure is absent in multiple dimensions. We present a new Multivariate Stieltjes (MS) algorithm that fills this gap in the multivariate case, allowing computation of recurrence matrices assuming moments are available. The algorithm is essentially explicit in two and three dimensions, but requires the numerical solution to a non-convex problem in more than three dimensions. Compared to direct Gram-Schmidt-type orthogonalization, we demonstrate on several examples in up to three dimensions that the MS algorithm is far more stable, and allows accurate computation of orthogonal bases in the multivariate setting, in contrast to direct orthogonalization approaches.
Y. Livnat, D. Maljovec, A. Gyulassy, B. Mouginot, V. Pascucci. A Novel Tree Visualization to Guide Interactive Exploration of Multi-dimensional Topological Hierarchies, Subtitled arXiv preprint arXiv:2208.06952, 2022.
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for studying this relationship, as phenomena of interest often appear naturally as fundamental features. The Morse-Smale complex captures a wide range of features by partitioning the domain of a scalar function into piecewise monotonic regions, while persistent homology provides a means to study these features at different scales of simplification. Previous works demonstrated how to compute such a representation and its usefulness to gain insight into multi-dimensional data. However, exploration of the multi-scale nature of the data was limited to selecting a single simplification threshold from a plot of region count. In this paper, we present a novel tree visualization that provides a concise overview of the entire hierarchy of topological features. The structure of the tree provides initial insights in terms of the distribution, size, and stability of all partitions. We use regression analysis to fit linear models in each partition, and develop local and relative measures to further assess uniqueness and the importance of each partition, especially with respect parents/children in the feature hierarchy. The expressiveness of the tree visualization becomes apparent when we encode such measures using colors, and the layout allows an unprecedented level of control over feature selection during exploration. For instance, selecting features from multiple scales of the hierarchy enables a more nuanced exploration. Finally, we …