Model Card for PDEFormer1d

This contains the checkpoint of pretrained PDEFormer1d model

Model Details

Model Description

The dynamics of Partial Differential Equations (PDEs) are associated with a wide range of physical phenomena and engineering applications, such as wing design, electromagnetic field simulations, and stress analysis. These real-world engineering applications all require multiple invocations of PDE solvers. Although traditional methods of solving PDEs usually exhibit high accuracy, they often require substantial computational resources and time. However, to design a universal solver for all types of PDEs could be challenging. In recent years, the Neural Operator approach, which employs neural networks to learn data from a large number of PDE solutions to approximate the PDE operators, has significantly improved the speed of solving the forward problems of PDEs. At the same time, the trained neural network model can also serve as a differentiable surrogate model to address inverse problems. However, current neural operator methods still struggle to generalize to new types of PDEs, and training for new PDEs often faces high training costs and difficulties in data acquisition.

To address these issues, we introduce the PDEformer model, a neural operator model that can directly input any form of PDEs. After being trained on a large-scale dataset of one-dimensional PDEs, the PDEformer model can quickly and accurately solve any form of one-dimensional PDE forward problems, and its zero-shot prediction accuracy within the training data distribution is higher than that of any expert model trained specifically for one type of equation (such as FNO, DeepONet). The PDEformer requires no retraining for new problems within the equation coefficient distribution and can rapidly generalize to downstream tasks through few-shot learning with minimal data for cases outside the coefficient distribution. At the same time, the PDEformer can be directly applied to solving inverse problems. With further increases in dataset scale, the PDEformer is expected to become a foundational model for solving various PDE problems, propelling the development of scientific research and engineering applications.

Model Sources

• Repository: [https://github.com/mindspore-ai/mindscience/tree/master/MindFlow/applications/pdeformer1d]
• Paper [optional]: [https://arxiv.org/abs/2402.12652]
• Demo [optional]: [https://www.bilibili.com/video/BV1wm411C7Sq/]

Uses