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We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…

With the advancements made in deep learning, computer vision problems like object detection and segmentation have seen a great improvement in performance. However, in many real-world applications such as autonomous driving vehicles, the…

We examine the zero-temperature Metropolis Monte Carlo algorithm as a tool for training a neural network by minimizing a loss function. We find that, as expected on theoretical grounds and shown empirically by other authors, Metropolis…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

As Deep Learning continues to yield successful applications in Computer Vision, the ability to quantify all forms of uncertainty is a paramount requirement for its safe and reliable deployment in the real-world. In this work, we leverage…

The rapid progress in quantum computing (QC) and machine learning (ML) has attracted growing attention, prompting extensive research into quantum machine learning (QML) algorithms to solve diverse and complex problems. Designing…

The control of complex systems is of critical importance in many branches of science, engineering, and industry. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy…

Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…

Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a…

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…

Simulation of turbulent flows at high Reynolds number is a computationally challenging task relevant to a large number of engineering and scientific applications in diverse fields such as climate science, aerodynamics, and combustion.…

The increasing capabilities of Machine Learning (ML) models go hand in hand with an immense amount of data and computational power required for training. Therefore, training is usually outsourced into HPC facilities, where we have started…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep learning, most prominently its lack of trustworthiness, may…

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

We propose a framework for training neural networks that are coupled with partial differential equations (PDEs) in a parallel computing environment. Unlike most distributed computing frameworks for deep neural networks, our focus is to…

Aqueous solubility is a valuable yet challenging property to predict. Computing solubility using first-principles methods requires accounting for the competing effects of entropy and enthalpy, resulting in long computations for relatively…