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The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers. This paper studies…

Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the…

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational…

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a…

Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…

While the deployment of neural networks, yielding impressive results, becomes more prevalent in various applications, their interpretability and understanding remain a critical challenge. Network inversion, a technique that aims to…

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived…

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…

Matrix completion is one of the key problems in signal processing and machine learning, with applications ranging from image pro- cessing and data gathering to classification and recommender sys- tems. Recently, deep neural networks have…

This work presents a methodology to predict a near-optimal spacing function, which defines the element sizes, suitable to perform steady RANS turbulent viscous flow simulations. The strategy aims at utilising existing high fidelity…

Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…

This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to…

Many machine learning algorithms can be interpreted as procedures for estimating functions defined on the data distribution. In this paper we present a conceptual framework that formulates a wide range of learning problems as variational…

The present work proposes an inflow turbulence generation strategy using deep learning methods. This is achieved with the help of an autoencoder architecture with two different types of operational layers in the latent-space: a fully…

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…

The architecture of a neural network and the selection of its activation function are both fundamental to its performance. Equally vital is ensuring these two elements are well-matched, as their alignment is key to achieving effective…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…