MPIPN: A Multi Physics-Informed PointNet for solving parametric
  acoustic-structure systems
Chu Wang Jinhong Wu Yanzhi Wang Zhijian Zha Qi Zhou
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.