  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.
