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This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications using a consistent neural message passing layer. As the name implies, the focus is on enabling scalable operations that satisfy…

Convolutional neural networks (CNNs) have dramatically improved the accuracy of tasks such as object recognition, image segmentation and interactive speech systems. CNNs require large amounts of computing resources because ofcomputationally…

In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The…

Despite their success, modern convolutional neural networks (CNNs) exhibit fundamental limitations, including data inefficiency, poor out-of-distribution generalization, and vulnerability to adversarial perturbations. These shortcomings can…

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned…

There is an increasing convergence between biologically plausible computational models of inference and learning with local update rules and the global gradient-based optimization of neural network models employed in machine learning. One…

We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network,…

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…

A commonly used heuristic in non-convex optimization is Normalized Gradient Descent (NGD) - a variant of gradient descent in which only the direction of the gradient is taken into account and its magnitude ignored. We analyze this heuristic…

A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…

To better address challenging issues of the irregularity and inhomogeneity inherently present in 3D point clouds, researchers have been shifting their focus from the design of hand-craft point feature towards the learning of 3D point…

With more and more data being collected, data-driven modeling methods have been gaining in popularity in recent years. While physically sound, classical gray-box models are often cumbersome to identify and scale, and their accuracy might be…

Despite impressive progress in video generation, existing models remain limited to surface-level plausibility, lacking a coherent and unified understanding of the world. Prior approaches typically incorporate only a single form of…

Traditional convolution layers are specifically designed to exploit the natural data representation of images -- a fixed and regular grid. However, unstructured data like 3D point clouds containing irregular neighborhoods constantly breaks…

Point cloud filtering, the main bottleneck of which is removing noise (outliers) while preserving geometric features, is a fundamental problem in 3D field. The two-step schemes involving normal estimation and position update have been shown…

In automotive applications, frequency modulated continuous wave (FMCW) radar is an established technology to determine the distance, velocity and angle of objects in the vicinity of the vehicle. The quality of predictions might be seriously…

Route alignment design in surveying and transportation engineering frequently involves fixed waypoint constraints, where a path must precisely traverse specific coordinates. While existing literature primarily relies on geometric…

We propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of the equal-sized graph matching or subgraph matching, finds wide…

Graph Convolutional Network (GCN) are widely used in Graph Anomaly Detection (GAD) due to their natural compatibility with graph structures, resulting in significant performance improvements. However, most researchers approach GAD as a…