Meshes are used to represent complex objects in high fidelity physics simulators across a variety of domains, such as radar sensing and aerodynamics. There is growing interest in using neural networks to accelerate physics simulations, and also a growing body of work on applying neural networks directly to irregular mesh data. Since multiple mesh topologies can represent the same object, mesh augmentation is typically required to handle topological variation when training neural networks. Due to the sensitivity of physics simulators to small changes in mesh shape, it is challenging to use these augmentations when training neural network-based physics simulators. In this work, we show that variations in mesh topology can significantly reduce the performance of neural network simulators. We evaluate whether pretraining can be used to address this issue, and find that employing an established autoencoder pretraining technique with graph embedding models reduces the sensitivity of neural network simulators to variations in mesh topology. Finally, we highlight future research directions that may further reduce neural simulator sensitivity to mesh topology.

Many modeling tasks from disparate domains can be framed the same way, computing spherical signals from geometric inputs, for example, computing the radar response of different objects or navigating through an environment. This paper introduces G2Sphere, a general method for mapping object geometries to spherical signals. G2Sphere operates entirely in Fourier space, encoding geometric structure into latent Fourier features using equivariant neural networks and outputting the Fourier coefficients of the continuous target signal, which can be evaluated at any resolution. By utilizing a hybrid GNN-spherical CNN architecture, our method achieves much higher frequency output signal than comparable equivariant GNNs and avoids hand-engineered geometry features used previously by purely spherical methods. We perform experiments on various challenging domains including radar response modeling, aerodynamic drag prediction, and policy learning for manipulation and navigation. We find that G2Sphere outperforms competitive baselines in terms of accuracy and inference time, and we demonstrate that equivariance and Fourier features lead to improved sample efficiency and generalization.The source code is available at: https://github.com/ColinKohler/geometry2sphere.

This research focuses on improving the robustness of machine learning systems to natural variations and distribution shifts. A design trade space is presented, and various methods are compared, including adversarial training, data augmentation techniques, and novel approaches inspired by model-based robust optimization formulations.

Accurate epidemiological models require parameter estimates that account for mobility patterns and social network structure. We demonstrate the effectiveness of probabilistic programming for parameter inference in these models. We consider an agent-based simulation that represents mobility networks as degree-corrected stochastic block models, whose parameters we estimate from cell phone co-location data. We then use probabilistic program inference methods to approximate the distribution over disease transmission parameters conditioned on reported cases and deaths. Our experiments demonstrate that the resulting models improve the quality of fit in multiple geographies relative to baselines that do not model network topology.

Most network analysis is conducted on existing incomplete samples of much larger complete, fully observed graphs. For example, many researchers obtain graphs from online data repositories without knowing how these graphs were collected. Thus, these graphs can be poor representations of the fully observed networks. More complete data would lead to more accurate analyses, but data acquisition can be at best costly and at worst error-prone. For example, think of an adversary that deliberately poisons the answer to a query. Given a query budget for identifying additional nodes and edges, how can one improve the observed graph sample so that it is a more accurate representation of the complete, fully observed network? How does the approach change if one is interested in learning the best function (e.g. node classifier) on the network for a down-stream task? This is a novel problem that is related to, but distinct from, topics such as graph sampling and crawling. Given the prevailing use of graph samples in the research literature, this problem is of considerable importance, even though it has been ignored. In this tutorial, we discuss latent biases in incomplete networks and present methods for enriching such networks through active probing of nodes and edges. We focus on active learning and sequential decision-making formulations of this problem (a.k.a. the network discovery problem). We present distinctions between learning to grow the network (a.k.a. active exploration) vs. learning the "best" function on the network (a.k.a. active learning). In addition, we will discuss issues surrounding adversarial machine learning when querying for more data to reduce incompleteness.

A new approach for targeted graph sampling is proposed in which graph sampling and classification occur together, and content-based homophily is exploited to achieve improved classification performance. The application of network discovery of relevant content is considered using an approach that may be generalized to a broad class of vertex properties. The resulting procedure provides the initial step of a graph analytic processing chain whose performance is directly affected by the quality of graph sampling. The performance of the algorithm is measured with real network data and content observed on a social media site. Precision-Recall performance improvements of 30% are demonstrated with this dataset, compared to a baseline approach that does not exploit homophily. Because real-world graphs grow exponentially, this performance improvement may have a significant impact on graph analytic algorithms with sensitivities to the graph sampling quality.

Topic modeling continues to grow as a popular technique for finding hidden patterns, as well as grouping collections of new types of text and non-text data. Recent years have witnessed a growing body of work in developing metrics and techniques for evaluating the quality of topic models and the topics they generate. This is particularly true for text data where significant attention has been given to the semantic interpretability of topics using measures such as coherence. It has been shown however that topic assessments based on coherence metrics do not always align well with human judgment. Other efforts have examined the utility of information-theoretic distance metrics for evaluating topic quality in connection with semantic interpretability. Although there has been progress in evaluating interpretability of topics, the existing intrinsic evaluation metrics do not address some of the other aspects of concern in topic modeling such as: the number of topics to select, the ability to align topics from different models, and assessing the quality of training data. Here we propose an alternative metric for characterizing topic quality that addresses all three aforementioned issues. Our approach is based on clustering topics, and using the silhouette measure, a popular clustering index, for characterizing the quality of topics. We illustrate the utility of this approach in addressing the other topic modeling concerns noted above. Since this metric is not focused on interpretability, we believe it can be applied more broadly to text as well as non-text data. In this paper however we focus on the application of this metric to archival and non-archival text data.

Enterprise computer networks are filled with users performing a variety of tasks, ranging from business-critical tasks to personal interest browsing. Due to this multi-modal distribution of behaviors, it is non-trivial to automatically discern which behaviors are business-relevant and which are not. Additionally, it is difficult to infer communities of interest within the enterprise, even given an organizational mapping. In this work, we present a two-step framework for classifying user behavior within an enterprise in a data-driven way. As a first step, we use a latent topic model on active search queries to identify types of behaviors and topics of interest associated with a given user. We then leverage the information about user's assigned role within the organization to extract relevant topics which are most reflective of self-organizing communities of interest. We demonstrate that our framework is able to identify rich communities of interest that are better representations of how users interact and assemble in an enterprise setting.