Related papers: Sharpening the shape analysis for higher-dimension…

Example-based mesh deformation methods are powerful tools for realistic shape editing. However, existing techniques typically combine all the example deformation modes, which can lead to overfitting, i.e. using a overly complicated model to…

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…

Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…

Statistical shape modeling (SSM) has recently taken advantage of advances in deep learning to alleviate the need for a time-consuming and expert-driven workflow of anatomy segmentation, shape registration, and the optimization of…

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often…

This paper addresses the challenge of geometric quality assurance in manufacturing, particularly when human assessment is required. It proposes using Blender, an open-source simulation tool, to create synthetic datasets for machine learning…

Mathematical models of physical systems are subject to many uncertainties such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that discrepancies between…

Optimization in engineering requires appropriate models. In this article, a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity…

We propose a new data analysis approach for the efficient post-processing of bundles of finite element data from numerical simulations. The approach is based on the mathematical principles of symmetry. We consider the case where simulations…

We construct a basis for effective operators responsible for interactions between the Standard Model and a dark sector composed of particles with spin less or equal to 1. Redundant operators are eliminated using dim-4 equations of motion.…

Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…

The `renormalon' or `dispersive' method for estimating non-perturbative corrections to QCD observables is reviewed. The corrections are power-suppressed, i.e. of the form $A/Q^p$ where $Q$ is the hard process momentum scale. The renormalon…

The shape control of deformable linear objects (DLOs) is challenging, since it is difficult to obtain the deformation models. Previous studies often approximate the models in purely offline or online ways. In this paper, we propose a scheme…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable…

One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…

In order to investigate correspondences between 3D shapes, many methods rely on a feature descriptor which is invariant under almost isometric transformations. An interesting class of models for such descriptors relies on partial…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

High-temperature dimensional reduction provides a systematic effective field theory framework for studying finite-temperature thermodynamics and cosmological phase transitions. While the matching of super-renormalizable operators in the…

Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…