arXiv subjects

David Lenz

Publications and source records attributed to David Lenz.

23 records · Page 2Linked to original sources

arXiv2022

Adaptive Regularization of B-Spline Models for Scientific Data

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model regularization (i.e., smoothing) has traditionally been used to minimize these oscillations; unfortunately, it is sometimes impossible to sufficiently remove unwanted artifacts without smoothing away key features of the data set. In this article, we present a method of model regularization that preserves significant features of a data set while minimizing artificial oscillations. Our method varies the strength of a smoothing parameter throughout the domain automatically, removing artifacts in poorly-constrained regions while leaving other regions unchanged. The behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations.

math.NA↗

arXiv2022

Technology Mapping Using WebAI: The Case of 3D Printing

The diffusion of new technologies is crucial for the realization of social and economic returns to innovation. Tracking and mapping technology diffusion is, however, typically limited by the extent to which we can observe technology adoption. This study uses website texts to train a multilingual language model ensemble to map technology diffusion for the case of 3D printing. The study identifies relevant actors and their roles in the diffusion process. The results show that besides manufacturers, service provider, retailers, and information providers play an important role. The geographic distribution of adoption intensity suggests that regional 3D-printing intensity is driven by experienced lead users and the presence of technical universities. The overall adoption intensity varies by sector and firm size. These patterns indicate that the approach of using webAI provides a useful and novel tool for technology mapping which adds to existing measures based on patents or survey data.

econ.GN↗

arXiv2021

Construction of 4D Simplex Space-Time Meshes for Local Bisection Schemes

Adaptive mesh refinement is a key component of efficient unstructured space-time finite element methods. Underlying any adaptive mesh refinement scheme is, of course, a method for local refinement of simplices. However, simplex bisection algorithms in dimension greater than three have strict mesh preconditions which can be hard to satisfy. We prove that certain four-dimensional simplex space-time meshes can be handled with a relaxed precondition. Namely, we prove that if a tetrahedral mesh is 4-colorable, then we can produce a 4D simplex mesh which always satisfies the bisection precondition. We also briefly discuss strategies to handle tetrahedral meshes which are not 4-colorable.

math.NA↗

arXiv2021

FTK: A Simplicial Spacetime Meshing Framework for Robust and Scalable Feature Tracking

We present the Feature Tracking Kit (FTK), a framework that simplifies, scales, and delivers various feature-tracking algorithms for scientific data. The key of FTK is our high-dimensional simplicial meshing scheme that generalizes both regular and unstructured spatial meshes to spacetime while tessellating spacetime mesh elements into simplices. The benefits of using simplicial spacetime meshes include (1) reducing ambiguity cases for feature extraction and tracking, (2) simplifying the handling of degeneracies using symbolic perturbations, and (3) enabling scalable and parallel processing. The use of simplicial spacetime meshing simplifies and improves the implementation of several feature-tracking algorithms for critical points, quantum vortices, and isosurfaces. As a software framework, FTK provides end users with VTK/ParaView filters, Python bindings, a command line interface, and programming interfaces for feature-tracking applications. We demonstrate use cases as well as scalability studies through both synthetic data and scientific applications including Tokamak, fluid dynamics, and superconductivity simulations. We also conduct end-to-end performance studies on the Summit supercomputer. FTK is open-sourced under the MIT license: https://github.com/hguo/ftk

cs.GR↗

arXiv2020

Fourier-Informed Knot Placement Schemes for B-Spline Approximation

Fitting B-splines to discrete data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently and robustly approximated with B-splines by analyzing the Fourier spectrum of the data. Our method uses a collection of spectral filters to produce different indicator functions that guide effective knot placement. In particular, we describe how spectral filters can be used to compute high-order derivatives, smoothed versions of noisy data, and the locations of jump discontinuities. Our knot placement method can combine one or more of these indicators to place knots that align with the qualitative features of the data, leading to accurate B-spline approximations without needing many knots. The method we introduce is direct and does not require any intermediate B-spline fitting before choosing the final knot vector. Aside from a fast Fourier transform to transfer to and from Fourier space, the method runs in linear time with very little communication. The method is applied to several test cases in one and two dimensions, including data sets with jump discontinuities and noise. These tests show that the method can fit discontinuous data without spurious oscillations and remains accurate in the presence of noise.

math.NA↗