Related papers: Capturing the Diffusive Behavior of the Multiscale…

Human Activity Recognition (HAR) based on motion sensors has drawn a lot of attention over the last few years, since perceiving the human status enables context-aware applications to adapt their services on users' needs. However, motion…

In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network (DNN) utilizes a multiple scaling technique to convert high…

Recent advances in vision transformers (ViTs) have demonstrated the advantage of global modeling capabilities, prompting widespread integration of large-kernel convolutions for enlarging the effective receptive field (ERF). However, the…

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic…

Highly distributed training of Deep Neural Networks (DNNs) on future compute platforms (offering 100 of TeraOps/s of computational capacity) is expected to be severely communication constrained. To overcome this limitation, new gradient…

When designing Convolutional Neural Networks (CNNs), one must select the size\break of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible…

Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…

Recently, learned image compression methods have made remarkable achievements, some of which have outperformed the traditional image codec VVC. The advantages of learned image compression methods over traditional image codecs can be largely…

Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…

Long-term time series forecasting plays an important role in various real-world scenarios. Recent deep learning methods for long-term series forecasting tend to capture the intricate patterns of time series by decomposition-based or…

We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based to a micro-macro decomposition of the unknown, coupled with a stabilization procedure. The numerical method is…

Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning…

Deep neural networks that approximate nonlinear function-to-function mappings, i.e., operators, which are called DeepONet, have been demonstrated in recent articles to be capable of encoding entire PDE control methodologies, such as…

Despite the remarkable success of deep learning in pattern recognition, deep network models face the problem of training a large number of parameters. In this paper, we propose and evaluate a novel multi-path wavelet neural network…

We propose a novel layer-wise parameterization for convolutional neural networks (CNNs) that includes built-in robustness guarantees by enforcing a prescribed Lipschitz bound. Each layer in our parameterization is designed to satisfy a…

Self-Organized Operational Neural Networks (Self-ONNs) have recently been proposed as new-generation neural network models with nonlinear learning units, i.e., the generative neurons that yield an elegant level of diversity; however, like…

In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…

We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We…

Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field are towards representing…

This paper presents a multiple length-scale asymptotic analysis for transport problems in 1-D diffusive random media. This analysis shows that the Levermore-Pomraning (LP) equations can be adjusted in order to achieve the correct asymptotic…