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Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…

Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…

A recurrent Neural Network (RNN) is trained to predict sound samples based on audio input augmented by control parameter information for pitch, volume, and instrument identification. During the generative phase following training, audio…

Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

Deep neural networks unlocked a vast range of new applications by solving tasks of which many were previously deemed as reserved to higher human intelligence. One of the developments enabling this success was a boost in computing power…

The radio wave propagation channel is central to the performance of wireless communication systems. In this paper, we introduce a novel machine learning-empowered methodology for wireless channel modeling. The key ingredients include a…

Numerous empirical evidence has corroborated that the noise plays a crucial rule in effective and efficient training of neural networks. The theory behind, however, is still largely unknown. This paper studies this fundamental problem…

We showed how to use trained neural networks to perform Bayesian reasoning in order to solve tasks outside their initial scope. Deep generative models provide prior knowledge, and classification/regression networks impose constraints. The…

For almost 70 years, researchers have typically selected the width of neural networks' layers either manually or through automated hyperparameter tuning methods such as grid search and, more recently, neural architecture search. This paper…

The emission rate of minority atmospheric gases is inferred by a new approach based on neural networks. The neural network applied is the multi-layer perceptron with backpropagation algorithm for learning. The identification of these…

In this article, we show that solving the system of linear equations by manipulating the kernel and the range space is equivalent to solving the problem of least squares error approximation. This establishes the ground for a gradient-free…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

We investigate the potential of stochastic neural networks for learning effective waveform-based acoustic models. The waveform-based setting, inherent to fully end-to-end speech recognition systems, is motivated by several comparative…

We develop a computing framework that leverages wave propagation within an interconnected network, where nodes and edges possess wave manipulation capabilities, such as frequency mixing or time delay. This computing paradigm can not only…

Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…

We obtain wavenumber-robust error bounds for the deep neural network (DNN) emulation of the solution to the time-harmonic, sound-soft acoustic scattering problem in the exterior of a smooth, convex obstacle in two physical dimensions. The…

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…