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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11090 |
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| _version_ | 1866917140958806016 |
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| author | Dahal, Biraj Cheng, Jiahui Liu, Hao Lai, Rongjie Liao, Wenjing |
| author_facet | Dahal, Biraj Cheng, Jiahui Liu, Hao Lai, Rongjie Liao, Wenjing |
| contents | Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we propose WeldNet: Windowed Encoders for Learning Dynamics, a data-driven nonlinear model reduction framework to build a low-dimensional surrogate model for complex evolution systems. Given time-dependent training data, we split the time domain into multiple overlapping windows, within which nonlinear dimension reduction is performed by auto-encoders to capture latent codes. Once a low-dimensional representation of the data is learned, a propagator network is trained to capture the evolution of the latent codes in each window, and a transcoder is trained to connect the latent codes between adjacent windows. The proposed windowed decomposition significantly simplifies propagator training by breaking long-horizon dynamics into multiple short, manageable segments, while the transcoders ensure consistency across windows. In addition to the algorithmic framework, we develop a mathematical theory establishing the representation power of WeldNet under the manifold hypothesis, justifying the success of nonlinear model reduction via deep autoencoder-based architectures. Our numerical experiments on various differential equations indicate that WeldNet can capture nonlinear latent structures and their underlying dynamics, outperforming both traditional projection-based approaches and recently developed nonlinear model reduction methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics Dahal, Biraj Cheng, Jiahui Liu, Hao Lai, Rongjie Liao, Wenjing Machine Learning Numerical Analysis Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we propose WeldNet: Windowed Encoders for Learning Dynamics, a data-driven nonlinear model reduction framework to build a low-dimensional surrogate model for complex evolution systems. Given time-dependent training data, we split the time domain into multiple overlapping windows, within which nonlinear dimension reduction is performed by auto-encoders to capture latent codes. Once a low-dimensional representation of the data is learned, a propagator network is trained to capture the evolution of the latent codes in each window, and a transcoder is trained to connect the latent codes between adjacent windows. The proposed windowed decomposition significantly simplifies propagator training by breaking long-horizon dynamics into multiple short, manageable segments, while the transcoders ensure consistency across windows. In addition to the algorithmic framework, we develop a mathematical theory establishing the representation power of WeldNet under the manifold hypothesis, justifying the success of nonlinear model reduction via deep autoencoder-based architectures. Our numerical experiments on various differential equations indicate that WeldNet can capture nonlinear latent structures and their underlying dynamics, outperforming both traditional projection-based approaches and recently developed nonlinear model reduction methods. |
| title | Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2512.11090 |