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In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
Controlling nonlinear stochastic dynamical systems involves substantial challenges when the dynamics contain unknown and unstructured nonlinear state-dependent terms. For such complex systems, deep neural networks can serve as powerful…
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…
A critically important, ubiquitous, and yet poorly understood ingredient in modern deep networks (DNs) is batch normalization (BN), which centers and normalizes the feature maps. To date, only limited progress has been made understanding…
Precision scaling has emerged as a popular technique to optimize the compute and storage requirements of Deep Neural Networks (DNNs). Efforts toward creating ultra-low-precision (sub-8-bit) DNNs suggest that the minimum precision required…
This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary integral equations…
We present a technique for developing a network of re-used features, where the topology is formed using a coarse learning method, that allows gradient-descent fine tuning, known as an Abstract Deep Network (ADN). New features are built…
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…
In this paper, we propose a generalization of the Batch Normalization (BN) algorithm, diminishing batch normalization (DBN), where we update the BN parameters in a diminishing moving average way. BN is very effective in accelerating the…
We propose a novel deep learning tool in order to study the evolution of dark energy models. The aim is to combine two architectures: the Recurrent Neural Networks (RNN) and the Bayesian Neural Networks (BNN), we named this full network as…
We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
Over the past few years, deep neural networks (DNNs) have achieved tremendous success and have been continuously applied in many application domains. However, during the practical deployment in the industrial tasks, DNNs are found to be…
Utilizing physics-informed neural networks (PINN) to solve partial differential equations (PDEs) becomes a hot issue and also shows its great powers, but still suffers from the dilemmas of limited predicted accuracy in the sampling domain…
We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…
Deep Learning has the hierarchical network architecture to represent the complicated features of input patterns. Such architecture is well known to represent higher learning capability compared with some conventional models if the best set…
Deep neural networks (DNN) have been a de facto standard for nowadays biometric recognition solutions. A serious, but still overlooked problem in these DNN-based recognition systems is their vulnerability against adversarial attacks.…
This paper introduces deep neural networks (DNNs) as add-on blocks to baseline feedback control systems to enhance tracking performance of arbitrary desired trajectories. The DNNs are trained to adapt the reference signals to the feedback…
Convolutional neural networks (CNNs) are deep learning frameworks which are well-known for their notable performance in classification tasks. Hence, many skeleton-based action recognition and segmentation (SBARS) algorithms benefit from…