Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to generate. To reduce or even eliminate the dependency on high-fidelity data, we propose a novel multi-fidelity architecture which is based on a feature space shared by the low- and high-fidelity solutions. In the feature space, the projections of the low-fidelity and high-fidelity solutions are adjacent by constraining their relative distance. The feature space is represented with an encoder and its mapping to the original solution space is effected through a decoder. The proposed multi-fidelity approach is validated on forward and inverse problems for steady and unsteady problems described by partial differential equations.

翻译：物理信息神经网络已作为求解偏微分方程的替代方法出现。然而，对于复杂问题，此类网络的训练仍可能依赖于生成成本高昂的高保真度数据。为降低甚至消除对高保真度数据的依赖，我们提出了一种新颖的多保真度架构，该架构基于低保真度与高保真度解共享的特征空间。在特征空间中，通过约束低保真度与高保真度解投影的相对距离，使其彼此邻近。该特征空间由编码器表示，并通过解码器实现向原始解空间的映射。所提出的多保真度方法在由偏微分方程描述的稳态与非稳态问题的正问题及反问题中得到了验证。