Airfoil Inverse Design Using a Deep Neural Net with an Explainable Attention Mechanism

The data-driven inverse design approach has advantages over traditional methods that require domain knowledge, many constraints, and empirical formulas. However, because deep learning models are basically black-box models, that is, uninterpretable models, explaining the causal relationship between the input and output using them is difficult. This reduces the reliability of inverse design approaches based on deep learning. Therefore, in this study, an airfoil inverse design using an explainable deep neural network was developed. The airfoil shape parameters were predicted using the pressure coefficient distribution. Because the distribution is considered as undirected sequence data, a bidirectional long short-term memory was used as the base of the network. To provide explainability to the network, we utilized two types of attention-applied network architectures: single-attention and multi-attention. This makes the network more accurate and explainable with good convergence. Consequently, a purely data-driven inverse design approach that does not require domain experience was established. Furthermore, a self-explanatory network without additional data mining was modeled. This attention-applied network performed predictions not only to obtain the airfoil geometry but also to determine the correlation between airfoil geometry and the local pressure distribution. The correlation obtained from the network was shown to properly reflect the physics of flow, thereby confirming that the present approach can be used to analyze physical phenomena, particularly those whose mechanisms have not yet been identified.