Document Type
Article
Publication Date
2020
Publication Title
Inverse Problems and Imaging
Abstract
We introduce two convolutional neural network (CNN) architec- tures, inspired by the Merriman-Bence-Osher (MBO) algorithm and by cellular automatons, to model and learn threshold dynamics for front evolution from video data. The first model, termed the (single-dynamics) MBO network, learns a specific kernel and threshold for each input video without adapting to new dynamics, while the second, a meta-learning MBO network, generalizes across diverse threshold dynamics by adapting its parameters per input. Both models are evaluated on synthetic and real-world videos (ice melting and fire front propagation), with performance metrics indicating effective reconstruction and extrapolation of evolving boundaries, even under noisy conditions. Empirical results highlight the robustness of both networks across varied synthetic and real-world dynamics.
Keywords
threshold dynamics, cellular automaton, inverse problems, convolutional neural networks, deep learning
DOI
10.3934/ipi.2025023
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Rights
Licensed to Smith College and distributed CC-BY 4.0 under the Smith College Faculty Open Access Policy.
Version
Author's Accepted Manuscript
Recommended Citation
Negrini, Elisa; Gao, Almanzo Jiahe; Bowering, Abigail; Zhu, Wei; and Capogna, Luca, "Neural Networks for Threshold Dynamics Reconstruction" (2020). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/205