{"ID":2869010,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.16395","arxiv_id":"2509.16395","title":"Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs","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.","short_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 dimen...","url_abs":"https://arxiv.org/abs/2509.16395","url_pdf":"https://arxiv.org/pdf/2509.16395v1","authors":"[\"Jiahao Zhang\",\"Shiheng Zhang\",\"Guang Lin\"]","published":"2025-09-19T20:17:31Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}