The Fabry–Pérot (FP) cavity is the essential component of an ultra-stable laser (USL) for gravitational wave detection, which couples multiple physics fields (optical/thermal/mechanical) and requires ultra-high precision. Aiming at the deficiency of the current single physical field optimization, a multi-physics and multi-objective optimization method for fixing the cubic FP cavity based on data learning is proposed in this paper. A multi-physics coupling model for the cubic FP cavity is established and the performance is obtained via finite element analysis. The key performance indices (V, $w_F$, $w_F$) and key design variables (d, l, F) are determined considering the features of the FP cavity. Different data learning models (NN, RSF, KRG) are established and compared based on 49 sets of data acquired by orthogonal experiments, with the results showing that the neural network has the best performance. NSGA-II is adopted as the optimization algorithm, the Pareto optimal front is obtained, and the optimal combination of design variables is finally determined as $\{5,32,250\}$. The performance after optimization proves to be greatly improved, with the displacement under the fixing force and vibration test both decreased by more than 60%. The proposed optimization strategy can help in the design of the FP cavity, and could enlighten other optimization fields as well.

Fabry-Pérto (FP) cavity is the essential component of ultra-stable laser (USL) for gravitational wave detection, which couples multi-physic (Optical/Thermal/Mechanics) fields and requires ultra-high precision. To satisfy the requirements of precise and efficient design, a multi-physic coupling optimization method for fixing cubic FP cavity based on data learning is proposed. A multi-physic model for the cubic FP cavity is established and the performance is obtained by finite element analysis. The key performance indices (V, wF, wF) and key design variables (d, l, F) are determined considering the features of the FP cavity. The 49 sets of data by orthogonal experiment are acquired for the establishment and comparison of different data learning models (NN, RSF, KRG). The result turns out that the neural network has the best performance. Based on NSGA-II, the Pareto optimal front is obtained and the optimal combination of design variables is finally determined as {5,32,250}. The performance after optimization has proven to be a great improvement, of which the displacement under the fixing force and vibration test are decreased by more than 60%. The optimization strategy can not only help the design of the FP cavity but also enlighten other optimization fields.