# MPIPN: A Multi Physics-Informed PointNet for solving parametric acoustic-structure systems

arXiv: https://arxiv.org/abs/2403.01132 · HTML: https://mlsanity.com/paper/2403.01132/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 2 Mar 2024.

## Builds on (most cited first, 15 of 15)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains](https://mlsanity.com/paper/2007.11207/) (2020)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning](https://mlsanity.com/paper/2011.04602/) (2020)

## Built on by (most cited first, 1 of 1)

- [Physics-Informed Geometry-Aware Neural Operator](https://mlsanity.com/paper/2408.01600/) (2024)

## Abstract (arXiv)

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.