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Deep learning provides a versatile suite of methods for extracting structured information from complex datasets, enabling deeper understanding of underlying fluid dynamic phenomena. The field of turbulence modeling, in particular, benefits…

Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

Finding semantic correspondences is a challenging problem. With the breakthrough of CNNs stronger features are available for tasks like classification but not specifically for the requirements of semantic matching. In the following we…

We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…

Rapid development of big data and high-performance computing have encouraged explosive studies of deep learning in geoscience. However, most studies only take single-type data as input, frittering away invaluable multisource, multi-scale…

Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean…

We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}_2$ [1] to position-orientation space $\mathbb{M}_2 \cong \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance and…

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…

Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently using modern computational frameworks that mix symbolic…

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

Understanding the dynamic processes of the glassy system continues to be challenging. Recent advances have shown the power of graph neural networks (GNNs) for determining the correlation between structure and dynamics in the glassy system.…

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…

This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep…