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3D point clouds deep learning is a promising field of research that allows a neural network to learn features of point clouds directly, making it a robust tool for solving 3D scene understanding tasks. While recent works show that point…
To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density…
The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…
Geometric flows have proved to be a powerful geometric analysis tool, perhaps most notably in the study of 3-manifold topology, the differentiable sphere theorem, Hermitian-Yang-Mills connections and canonical Kaehler metrics. In the…
It has been repeatedly observed that convolutional architectures when applied to image understanding tasks learn oriented bandpass filters. A standard explanation of this result is that these filters reflect the structure of the images that…
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…
We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on…
This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely…
Many measurements or observations in computer vision and machine learning manifest as non-Euclidean data. While recent proposals (like spherical CNN) have extended a number of deep neural network architectures to manifold-valued data, and…
Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…
Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…
We focus on a convolutional neural network (CNN), which has recently been utilized for fluid flow analyses, from the perspective on the influence of various operations inside it by considering some canonical regression problems with fluid…
Geometric feature learning for 3D surfaces is critical for many applications in computer graphics and 3D vision. However, deep learning currently lags in hierarchical modeling of 3D surfaces due to the lack of required operations and/or…
Computational Fluid Dynamics (CFD) simulations are a very important tool for many industrial applications, such as aerodynamic optimization of engineering designs like cars shapes, airplanes parts etc. The output of such simulations, in…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
It is difficult to quantify structure-property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it…