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This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random…

Large-scale or high-resolution geologic models usually comprise a huge number of grid blocks, which can be computationally demanding and time-consuming to solve with numerical simulators. Therefore, it is advantageous to upscale geologic…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…

Harmonic retrieval techniques are the foundation of radio channel sounding, estimation, and modeling. This paper introduces a Deep Learning approach for joint delay- and Doppler estimation from frequency and time samples of a radio channel…

Deep neural networks are a powerful tool for feature learning and extraction given their ability to model high-level abstractions in highly complex data. One area worth exploring in feature learning and extraction using deep neural networks…

We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…

Graph convolution operators bring the advantages of deep learning to a variety of graph and mesh processing tasks previously deemed out of reach. With their continued success comes the desire to design more powerful architectures, often by…

Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks…

An evolving area of research in deep learning is the study of architectures and inductive biases that support the learning of relational feature representations. In this paper, we address the challenge of learning representations of…

We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…

We propose Deep Hierarchical Machine (DHM), a model inspired from the divide-and-conquer strategy while emphasizing representation learning ability and flexibility. A stochastic routing framework as used by recent deep neural…

Machine Learning (ML)-based unfolding methods have enabled high-dimensional and unbinned differential cross section measurements. While a suite of such methods has been proposed, most focus exclusively on the challenge of statistically…

We investigate the dependence of the approximation capacity of deep residual networks on its depth in a continuous dynamical systems setting. This can be formulated as the general problem of quantifying the minimal time-horizon required to…