arXiv subjects

Daniel J. Laky

Publications and source records attributed to Daniel J. Laky.

2 recordsLinked to original sources

arXiv2026

Optimal Experimental Design using Eigenvalue-Based Criteria with Pyomo.DoE

Digital twins require high-quality data to achieve predictive capability, but time and resource limitations make efficient experiment design essential. Model-based design of experiments can address this challenge, especially when coupled with equation-oriented optimization and first-principles models. Pyomo.DoE is a software package for optimal experimental design of high-fidelity, equation-oriented models; however, embedding linear algebra operations such as matrix inversion and eigenvalue computation within these optimization problems remains difficult. This work extends Pyomo.DoE with callback-based capabilities that enable rigorous computation of eigenvalue-based design metrics, including minimum eigenvalue optimality (E-optimality) and condition number optimality (ME-optimality), within equation-oriented optimization frameworks. These additions allow experimental design to focus directly on poorly informed or numerically problematic parameter directions. We also present a new experiment-creation modeling abstraction for intrusive uncertainty quantification in Pyomo that reduces user modeling effort by aligning model and software abstractions across the digital twin workflow. In addition, a brief tutorial on experimental design metrics is provided in the methodology and supplementary information. Overall, this work expands the range of practical optimal design criteria available in Pyomo.DoE and improves the workflow for building and refining high-value digital twins.

math.OC↗

arXiv2023

A Fast and Scalable Computational Topology Framework for the Euler Characteristic

The Euler characteristic (EC) is a powerful topological descriptor that can be used to quantify the shape of data objects that are represented as fields/manifolds. Fast methods for computing the EC are required to enable processing of high-throughput data and real-time implementations. This represents a challenge when processing high-resolution 2D field data (e.g., images) and 3D field data (e.g., video, hyperspectral images, and space-time data obtained from fluid dynamics and molecular simulations). In this work, we present parallel algorithms (and software implementations) to enable fast computations of the EC for 2D and 3D fields using vertex contributions. We test the proposed algorithms using synthetic data objects and data objects arising in real applications such as microscopy, 3D molecular dynamics simulations, and hyperspectral images. Results show that the proposed implementation can compute the EC a couple of orders of magnitude faster than ${\tt GUDHI}$ (an off-the-shelf and state-of-the art tool) and at speeds comparable to ${\tt CHUNKYEuler}$ (a tool tailored to scalable computation of the EC). The vertex contributions approach is flexible in that it compute the EC as well as other topological descriptors such as perimeter, area, and volume (${\tt CHUNKYEuler}$ can only compute the EC). Scalability with respect to memory use is also addressed by providing low-memory versions of the algorithms; this enables processing of data objects beyond the size of dynamic memory. All data and software needed for reproducing the results are shared as open-source code.

cs.CG↗