SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decomposition
This work addresses the inefficiency of PINNs for solving multiple PDEs, offering a domain-specific incremental improvement for computational physics and engineering applications.
The authors tackled the problem of solving a class of PDEs with PINNs by proposing SVD-PINNs, a transfer learning method that keeps singular vectors and optimizes singular values, achieving effectiveness on 10-dimensional linear parabolic and Allen-Cahn equations with close right-hand-side functions.
Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods. However, the most disadvantage of PINNs is that one neural network corresponds to one PDE. In practice, we usually need to solve a class of PDEs, not just one. With the explosive growth of deep learning, many useful techniques in general deep learning tasks are also suitable for PINNs. Transfer learning methods may reduce the cost for PINNs in solving a class of PDEs. In this paper, we proposed a transfer learning method of PINNs via keeping singular vectors and optimizing singular values (namely SVD-PINNs). Numerical experiments on high dimensional PDEs (10-d linear parabolic equations and 10-d Allen-Cahn equations) show that SVD-PINNs work for solving a class of PDEs with different but close right-hand-side functions.