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Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part due to simulations…

The deployment of Deep Neural Networks (DNNs) on edge devices is hindered by the substantial gap between performance requirements and available processing power. While recent research has made significant strides in developing pruning…

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method…

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…

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…

We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dimensional PDEs, demonstrating both high accuracy and low…

Deep Neural Networks (DNNs) are being heavily utilized in modern applications and are putting energy-constraint devices to the test. To bypass high energy consumption issues, approximate computing has been employed in DNN accelerators to…

Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

Approximate Nearest-Neighbor Search (ANNS) efficiently finds data items whose embeddings are close to that of a given query in a high-dimensional space, aiming to balance accuracy with speed. Used in recommendation systems, image and video…

A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency…

Numerical experiments indicate that deep learning algorithms overcome the curse of dimensionality when approximating solutions of semilinear PDEs. For certain linear PDEs and semilinear PDEs with gradient-independent nonlinearities this has…

In this work, we present an adaptive adjoint-oriented neural network (adaptive AONN) for solving parametric optimal control problems governed by partial differential equations. The proposed method integrates deep adaptive sampling…

In Machine Learning, Artificial Neural Networks (ANNs) are a very powerful tool, broadly used in many applications. Often, the selected (deep) architectures include many layers, and therefore a large amount of parameters, which makes…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

Generalisation of a deep neural network (DNN) is one major concern when employing the deep learning approach for solving practical problems. In this paper we propose a new technique, named approximated orthonormal normalisation (AON), to…

Graph neural networks (GNN) has been successfully applied to operate on the graph-structured data. Given a specific scenario, rich human expertise and tremendous laborious trials are usually required to identify a suitable GNN architecture.…