Neural Networks for Threshold Dynamics Reconstruction
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912153593708544 |
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| author | Negrini, Elisa Gao, Almanzo Jiahe Bowering, Abigail Zhu, Wei Capogna, Luca |
| author_facet | Negrini, Elisa Gao, Almanzo Jiahe Bowering, Abigail Zhu, Wei Capogna, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural Networks for Threshold Dynamics Reconstruction Negrini, Elisa Gao, Almanzo Jiahe Bowering, Abigail Zhu, Wei Capogna, Luca Machine Learning Dynamical Systems 68T07 (Primary), 65P99, 37M05 (Secondary) 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. |
| title | Neural Networks for Threshold Dynamics Reconstruction |
| topic | Machine Learning Dynamical Systems 68T07 (Primary), 65P99, 37M05 (Secondary) |
| url | https://arxiv.org/abs/2412.09079 |