Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics

• URL: http://arxiv.org/abs/2512.11090v1
• Date: Thu, 11 Dec 2025 20:06:45 GMT
• Title: Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics
• Authors: Biraj Dahal, Jiahui Cheng, Hao Liu, Rongjie Lai, Wenjing Liao,
• Abstract summary: WeldNet is a data-driven nonlinear model reduction framework to build a low-dimensional model for complex evolution systems.<n>We develop a mathematical theory establishing the representation power of WeldNet under the manifold hypothesis.
• Score: 9.777339863468487
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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