Neural Networks for Threshold Dynamics Reconstruction

TL;DR

This paper presents CNN architectures inspired by MBO algorithms to model and learn threshold dynamics from video data, enabling effective boundary reconstruction and extrapolation in various scenarios.

Contribution

Introduces two CNN models, one specific and one meta-learning, for threshold dynamics reconstruction from videos, demonstrating robustness and generalization.

Findings

Effective boundary reconstruction in synthetic and real videos

Robust performance under noisy conditions

Meta-learning model generalizes across diverse dynamics

Abstract

We introduce two convolutional neural network (CNN) architectures, 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.