Machine learning is employed for solving physical systems governed by general nonlinear partial differential equations (PDEs). However, complex multi-physics systems such as acoustic-structure coupling are often described by a series of PDEs that incorporate variable physical quantities, which are referred to as parametric systems. There are lack of strategies for solving parametric systems governed by PDEs that involve explicit and implicit quantities. In this paper, a deep learning-based Multi Physics-Informed PointNet (MPIPN) is proposed for solving parametric acoustic-structure systems. First, the MPIPN induces an enhanced point-cloud architecture that encompasses explicit physical quantities and geometric features of computational domains. Then, the MPIPN extracts local and global features of the reconstructed point-cloud as parts of solving criteria of parametric systems, respectively. Besides, implicit physical quantities are embedded by encoding techniques as another part of solving criteria. Finally, all solving criteria that characterize parametric systems are amalgamated to form distinctive sequences as the input of the MPIPN, whose outputs are solutions of systems. The proposed framework is trained by adaptive physics-informed loss functions for corresponding computational domains. The framework is generalized to deal with new parametric conditions of systems. The effectiveness of the MPIPN is validated by applying it to solve steady parametric acoustic-structure coupling systems governed by the Helmholtz equations. An ablation experiment has been implemented to demonstrate the efficacy of physics-informed impact with a minority of supervised data. The proposed method yields reasonable precision across all computational domains under constant parametric conditions and changeable combinations of parametric conditions for acoustic-structure systems.

翻译：机器学习已被用于求解由一般非线性偏微分方程（PDEs）所支配的物理系统。然而，诸如声-结构耦合等复杂的多物理系统，通常由一系列包含可变物理量的偏微分方程描述，这类系统称为参数化系统。目前缺乏针对同时涉及显式与隐式量的偏微分方程所支配参数化系统的求解策略。本文提出了一种基于深度学习的多物理信息PointNet（MPIPN），用于求解参数化声-结构系统。首先，MPIPN引入了一种增强点云架构，该架构包含计算域的显式物理量及几何特征。然后，MPIPN分别提取重建后点云的局部与全局特征，作为参数化系统求解准则的一部分。此外，通过编码技术嵌入隐式物理量，作为求解准则的另一部分。最后，将表征参数化系统的所有求解准则融合为独特序列，作为MPIPN的输入，其输出即为系统解。所提框架通过针对相应计算域的自适应物理信息损失函数进行训练，并具备泛化能力以处理系统的新参数条件。通过将MPIPN应用于求解由亥姆霍兹方程支配的稳态参数化声-结构耦合系统，验证了其有效性。实施了消融实验，证明了在少量监督数据情况下物理信息影响的有效性。在声-结构系统的恒定参数条件及可变参数条件组合下，所提方法在所有计算域上均获得了合理的精度。