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Graph Neural Networks (GNNs) have recently caught great attention and achieved significant progress in graph-level applications. In this paper, we propose a framework for graph neural networks with multiresolution Haar-like wavelets, or…

Microstructures, i.e., architected materials, are designed today, typically, by maximizing an objective, such as bulk modulus, subject to a volume constraint. However, in many applications, it is often more appropriate to impose constraints…

We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures…

Multi-Grid Back-Projection (MGBP) is a fully-convolutional network architecture that can learn to restore images and videos with upscaling artifacts. Using the same strategy of multi-grid partial differential equation (PDE) solvers this…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as…

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…

Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large…

In the literature, there exist several studies on symbol-based multigrid methods for the solution of linear systems having structured coefficient matrices. In particular, the convergence analysis for such methods has been obtained in an…

Designing spectral convolutional networks is a formidable task in graph learning. In traditional spectral graph neural networks (GNNs), polynomial-based methods are commonly used to design filters via the Laplacian matrix. In practical…

Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…

Sleep staging based on electroencephalogram (EEG) plays an important role in the clinical diagnosis and treatment of sleep disorders. In order to emancipate human experts from heavy labeling work, deep neural networks have been employed to…

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, with a training objective that makes them approximately sample in proportion to a given reward…

In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations. Training deep neural…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

Multinomial Logit (MNL) is one of the most popular discrete choice models and has been widely used to model ranking data. However, there is a long-standing technical challenge of learning MNL from many real-world ranking data: exact…

This paper provides a unified and detailed presentation of root-node style algebraic multigrid (AMG). Algebraic multigrid is a popular and effective iterative method for solving large, sparse linear systems that arise from discretizing…

The prediction of physicochemical properties from molecular structures is a crucial task for artificial intelligence aided molecular design. A growing number of Graph Neural Networks (GNNs) have been proposed to address this challenge.…

Rapid development of big data and high-performance computing have encouraged explosive studies of deep learning in geoscience. However, most studies only take single-type data as input, frittering away invaluable multisource, multi-scale…