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

TL;DR

WeldNet is a novel data-driven nonlinear model reduction framework that uses windowed auto-encoders and propagator networks to efficiently learn and simulate complex, high-dimensional dynamical systems.

Contribution

The paper introduces WeldNet, a new approach combining windowed auto-encoders and transcoders for scalable nonlinear model reduction with theoretical guarantees.

Findings

Outperforms traditional projection-based methods

Effectively captures nonlinear latent structures

Handles long-horizon dynamics efficiently

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.