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We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…
In recent years, deep learning based methods have shown success in essential medical image analysis tasks such as segmentation. Post-processing and refining the results of segmentation is a common practice to decrease the misclassifications…
Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
Machine learning (ML) has shown significant promise in studying complex geophysical dynamical systems, including turbulence and climate processes. Such systems often display sensitive dependence on initial conditions, reflected in positive…
Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…
In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train…
Leveraging geodesic distances and the geometrical information they convey is key for many data-oriented applications in imaging. Geodesic distance computation has been used for long for image segmentation using Image based metrics. We…
Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…
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…
Longitudinal MRIs are often used to capture the gradual deterioration of brain structure and function caused by aging or neurological diseases. Analyzing this data via machine learning generally requires a large number of ground-truth…
Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map…
Monitoring awkward postures is a proactive prevention for Musculoskeletal Disorders (MSDs)in construction. Machine Learning (ML) models have shown promising results for posture recognition from Wearable Sensors. However, further…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…
Machine learning (ML) is revolutionizing protein structural analysis, including an important subproblem of predicting protein residue contact maps, i.e., which amino-acid residues are in close spatial proximity given the amino-acid sequence…
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured…
Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…
Machine unlearning (MU) has emerged to enhance the privacy and trustworthiness of deep neural networks. Approximate MU is a practical method for large-scale models. Our investigation into approximate MU starts with identifying the steepest…