Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs

• URL: http://arxiv.org/abs/2509.16395v1
• Date: Fri, 19 Sep 2025 20:17:31 GMT
• Title: Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs
• Authors: Jiahao Zhang, Shiheng Zhang, Guang Lin,
• Abstract summary: We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains parameter evolution to a low-rank subspace.<n>LR-EDNN achieves comparable accuracy with substantially fewer trainable parameters and reduced computational cost.
• Score: 11.156869211296156
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains parameter evolution to a low-rank subspace, thereby reducing the effective dimensionality of training while preserving solution accuracy. The low-rank tangent subspace is defined layer-wise by the singular value decomposition (SVD) of the current network weights, and the resulting update is obtained by solving a well-posed, tractable linear system within this subspace. This design augments the underlying numerical solver with a parameter efficient EDNN component without requiring full fine-tuning of all network weights. We evaluate LR-EDNN on representative PDE problems and compare it against corresponding baselines. Across cases, LR-EDNN achieves comparable accuracy with substantially fewer trainable parameters and reduced computational cost. These results indicate that low-rank constraints on parameter velocities, rather than full-space updates, provide a practical path toward scalable, efficient, and reproducible scientific machine learning for PDEs.

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