  As a promising framework for resolving partial differential equations (PDEs),
physics-informed neural networks (PINNs) have received widespread attention
from industrial and scientific fields. However, lack of expressive ability and
initialization pathology issues are found to prevent the application of PINNs
in complex PDEs. In this work, we propose Element-wise Multiplication Based
Physics-informed Neural Networks (EM-PINNs) to resolve these issues. The
element-wise multiplication operation is adopted to transform features into
high-dimensional, non-linear spaces, which effectively enhance the expressive
capability of PINNs. Benefiting from element-wise multiplication operation,
EM-PINNs can eliminate the initialization pathologies of PINNs. The proposed
structure is verified on various benchmarks. The results show that EM-PINNs
have strong expressive ability.
