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Modelling long-range dependencies is critical for scene understanding tasks in computer vision. Although CNNs have excelled in many vision tasks, they are still limited in capturing long-range structured relationships as they typically…

We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…

Message-passing based approaches form the default backbone of most learning architectures on graph-structured data. However, the rapid progress of modern deep learning architectures in other domains, particularly sequence modeling, raises…

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in…

While (message-passing) graph neural networks have clear limitations in approximating permutation-equivariant functions over graphs or general relational data, more expressive, higher-order graph neural networks do not scale to large…

This paper pertains to an emerging machine learning paradigm: learning higher-order functions, i.e. functions whose inputs are functions themselves, $\textit{particularly when these inputs are Neural Networks (NNs)}$. With the growing…

The Matrix-Element Method (MEM) has long been a cornerstone of data analysis in high-energy physics. It leverages theoretical knowledge of parton-level processes and symmetries to evaluate the likelihood of observed events. In parallel, the…

Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…

Equivariant Graph neural Networks (EGNs) are powerful in characterizing the dynamics of multi-body physical systems. Existing EGNs conduct flat message passing, which, yet, is unable to capture the spatial/dynamical hierarchy for complex…

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

Anatomical mesh segmentation requires models that operate directly on irregular surface geometry while remaining robust to arbitrary patient pose and mesh resolution variation. Existing task-specific mesh and point-cloud methods are not…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited…

Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…

Unsupervised attributed graph representation learning is challenging since both structural and feature information are required to be represented in the latent space. Existing methods concentrate on learning latent representation via…

Predicting the evolution of a representative sample of a material with microstructure is a fundamental problem in homogenization. In this work we propose a graph convolutional neural network that utilizes the discretized representation of…

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with…

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…