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We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of fiber based materials, and pore network models of porous materials. Nevertheless, the…
The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry…
Real-world geometry and 3D vision tasks are replete with challenging symmetries that defy tractable analytical expression. In this paper, we introduce Neural Isometries, an autoencoder framework which learns to map the observation space to…
Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization…
Understanding structure-property relationships in complex materials requires integrating complementary measurements across multiple length scales. Here we propose an interpretable "multimodal" machine learning framework that unifies…
Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…
In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…
To facilitate rational molecular and materials design, this research proposes an integrated computational framework that combines stochastic simulation, ab initio quantum chemistry, and molecular docking. The suggested workflow allows…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
A spatiotemporal deep learning framework is proposed that is capable of 2D full-field prediction of fracture in concrete mesostructures. This framework not only predicts fractures but also captures the entire history of the fracture…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…
Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point correspondences via the geodesic boundary value problem, solving…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…