Related papers: A multi-scale DNN algorithm for nonlinear elliptic…

The structure and weights of Deep Neural Networks (DNN) typically encode and contain very valuable information about the dataset that was used to train the network. One way to protect this information when DNN is published is to perform an…

Deep Neural Networks (DNNs) are rapidly gaining popularity in a variety of important domains. Formally, DNNs are complicated vector-valued functions which come in a variety of sizes and applications. Unfortunately, modern DNNs have been…

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

Although deeper and larger neural networks have achieved better performance, the complex network structure and increasing computational cost cannot meet the demands of many resource-constrained applications. Existing methods usually choose…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

The DBSCAN method for spatial clustering has received significant attention due to its applicability in a variety of data analysis tasks. There are fast sequential algorithms for DBSCAN in Euclidean space that take $O(n\log n)$ work for two…

In this paper, we propose a novel machine learning method based on an adaptive tensor neural network subspace for solving quasiperiodic elliptic problems. To this end, we first provide a theoretical analysis of the associated quasiperiodic…

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…

Deep neural network (DNN) partition is a research problem that involves splitting a DNN into multiple parts and offloading them to specific locations. Because of the recent advancement in multi-access edge computing and edge intelligence,…

Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

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…

Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…

Quantization of weights and activations in Deep Neural Networks (DNNs) is a powerful technique for network compression, and has enjoyed significant attention and success. However, much of the inference-time benefit of quantization is…

In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear…

The pioneer deep neural networks (DNNs) have emerged to be deeper or wider for improving their accuracy in various applications of artificial intelligence. However, DNNs are often too heavy to deploy in practice, and it is often required to…

We establish the existence of positive solutions for a nonlinear elliptic Dirichlet problem in dimension $N$ involving the $N$-Laplacian. The nonlinearity considered depends on the gradient of the unknown function and an exponential term.…

In this paper, a deep learning (DL)-based sphere decoding algorithm is proposed, where the radius of the decoding hypersphere is learned by a deep neural network (DNN). The performance achieved by the proposed algorithm is very close to the…

We studied the least-squares ReLU neural network (LSNN) method for solving linear advection-reaction equation with discontinuous solution in [Cai, Zhiqiang, Jingshuang Chen, and Min Liu. ``Least-squares ReLU neural network (LSNN) method for…

Different conflicting optimization criteria arise naturally in various Deep Learning scenarios. These can address different main tasks (i.e., in the setting of Multi-Task Learning), but also main and secondary tasks such as loss…