Related papers: Manifold embedding data-driven mechanics
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
Physical data are representations of the fundamental laws governing the Universe, hiding complex compositional structures often well captured by hierarchical graphs. Hyperbolic spaces are endowed with a non-Euclidean geometry that naturally…
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…
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
This paper introduces a new learning-based method, NASM, for anisotropic surface meshing. Our key idea is to propose a graph neural network to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve…
Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…
This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…
Bounding volumes are an established concept in computer graphics and vision tasks but have seen little change since their early inception. In this work, we study the use of neural networks as bounding volumes. Our key observation is that…
Many data representations are vectors of continuous values. In particular, deep learning embeddings are data-driven representations, typically either unconstrained in Euclidean space, or constrained to a hypersphere. These may also be…
Continual learning aims to efficiently learn from a non-stationary stream of data while avoiding forgetting the knowledge of old data. In many practical applications, data complies with non-Euclidean geometry. As such, the commonly used…
We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
We empirically demonstrate that a transformer pre-trained on country-scale unlabeled human mobility data learns embeddings capable, through fine-tuning, of developing a deep understanding of the target geography and its corresponding…
Recently, computational modeling has shifted towards the use of deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by…
Modeling non-Euclidean data is drawing extensive attention along with the unprecedented successes of deep neural networks in diverse fields. Particularly, a symmetric positive definite matrix is being actively studied in computer vision,…
Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the…
In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel,…