Pretraining a Neural Operator in Lower Dimensions

• URL: http://arxiv.org/abs/2407.17616v2
• Date: Tue, 19 Nov 2024 21:08:20 GMT
• Title: Pretraining a Neural Operator in Lower Dimensions
• Authors: AmirPouya Hemmasian, Amir Barati Farimani,
• Abstract summary: We aim to Pretrain neural PDE solvers on Lower Dimensional PDEs (PreLowD) where data collection is the least expensive. We evaluate the effectiveness of this pretraining strategy in similar PDEs in higher dimensions. Our work sheds light on the effect of the fine-tuning configuration to make the most of this pretraining strategy.
• Score: 7.136205674624813
• License:
• Abstract: There has recently been increasing attention towards developing foundational neural Partial Differential Equation (PDE) solvers and neural operators through large-scale pretraining. However, unlike vision and language models that make use of abundant and inexpensive (unlabeled) data for pretraining, these neural solvers usually rely on simulated PDE data, which can be costly to obtain, especially for high-dimensional PDEs. In this work, we aim to Pretrain neural PDE solvers on Lower Dimensional PDEs (PreLowD) where data collection is the least expensive. We evaluated the effectiveness of this pretraining strategy in similar PDEs in higher dimensions. We use the Factorized Fourier Neural Operator (FFNO) due to having the necessary flexibility to be applied to PDE data of arbitrary spatial dimensions and reuse trained parameters in lower dimensions. In addition, our work sheds light on the effect of the fine-tuning configuration to make the most of this pretraining strategy. Code is available at https://github.com/BaratiLab/PreLowD.

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