Related papers: Combining high-order metric interpolation and geom…

In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization model. The proposed scheme has the advantage of not needing to…

This paper focuses on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the…

In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…

Accurate camera models are essential for photogrammetry applications such as 3D mapping and object localization, particularly for long distances. Various stereo-camera based 3D localization methods are available but are limited to few…

In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…

Conservation laws, in for example, electromagnetism, solid and fluid mechanics, allow an exact discrete representation in terms of line, surface and volume integrals. We develop high order interpolants, from any basis that is a partition of…

Distributed optimization is widely used in large-scale and privacy-preserving machine learning, where each agent stores a local objective and communicates only with its neighbors in a connected network. We study decentralized second-order…

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…

Interference detection of arbitrary geometric objects is not a trivial task due to the heavy computational load imposed by implementation issues. The hierarchically structured bounding boxes help us to quickly isolate the contour of…

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not…

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

Many machine learning models operate on images, but ignore the fact that images are 2D projections formed by 3D geometry interacting with light, in a process called rendering. Enabling ML models to understand image formation might be key…

Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with…

After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands. When compressing, it is desirable to preserve the original model's per-example decisions (e.g., to go beyond top-1…

We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…

Unsupervised multi-object representation learning depends on inductive biases to guide the discovery of object-centric representations that generalize. However, we observe that methods for learning these representations are either…

Texture synthesis models are important tools for understanding visual processing. In particular, statistical approaches based on neurally relevant features have been instrumental in understanding aspects of visual perception and of neural…

Learning-based 3D reconstruction methods have shown impressive results. However, most methods require 3D supervision which is often hard to obtain for real-world datasets. Recently, several works have proposed differentiable rendering…