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A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

In the last decade, special purpose computing systems, such as Neuromorphic computing, have become very popular in the field of computer vision and machine learning for classification tasks. In 2015, IBM's released the TrueNorth…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…

Deep neural networks (DNNs) have achieved remarkable success across diverse domains, but their performance can be severely degraded by noisy or corrupted training data. Conventional noise mitigation methods often rely on explicit…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

Deep convolutional neural network (DCNN) based supervised learning is a widely practiced approach for large-scale image classification. However, retraining these large networks to accommodate new, previously unseen data demands high…

Optimal control of parametric partial differential equations (PDEs) is crucial in many applications in engineering and science. In recent years, the progress in scientific machine learning has opened up new frontiers for the control of…

The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

Deep Convolutional Neural Networks (DCNNs) is currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful…

In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

Deep neural networks (DNNs) are emerging as a potential solution to solve NP-hard wireless resource allocation problems. However, in the presence of intricate constraints, e.g., users' quality-of-service (QoS) constraints, guaranteeing…

Bilevel hyperparameter optimization has received growing attention thanks to the fast development of machine learning. Due to the tremendous size of data sets, the scale of bilevel hyperparameter optimization problem could be extremely…

Deep neural networks (DNNs) are reshaping the field of information processing. With their exponential growth challenging existing electronic hardware, optical neural networks (ONNs) are emerging to process DNN tasks in the optical domain…

A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update…

Deep neural networks (DNNs) sustain high performance in today's data processing applications. DNN inference is resource-intensive thus is difficult to fit into a mobile device. An alternative is to offload the DNN inference to a cloud…

End-to-end performance estimation and measurement of deep neural network (DNN) systems become more important with increasing complexity of DNN systems consisting of hardware and software components. The methodology proposed in this paper…