# BubbleNet: Inferring micro-bubble dynamics with semi-physics-informed deep learning

arXiv: https://arxiv.org/abs/2105.07179 · HTML: https://mlsanity.com/paper/2105.07179/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 72 references that are in the map.
- First posted on arXiv 15 May 2021.

## Builds on (most cited first, 16 of 16)

- [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)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics](https://mlsanity.com/paper/1712.03641/) (2017)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Deep Learning in Alzheimer's disease: Diagnostic Classification and Prognostic Prediction using Neuroimaging Data](https://mlsanity.com/paper/1905.00931/) (2019)

## Built on by (most cited first, 4 of 4)

- [Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates](https://mlsanity.com/paper/2405.17260/) (2024)
- [Stress Predictions in Polycrystal Plasticity using Graph Neural Networks with Subgraph Training](https://mlsanity.com/paper/2409.05169/) (2024)
- [Scalable Physics-Informed Neural Differential Equations and Data-Driven Algorithms for HVAC Systems](https://mlsanity.com/paper/2604.18438/) (2026)
- [Open datasets and machine learning for two-phase heat transfer: a review following a spatial-temporal taxonomy](https://mlsanity.com/paper/2605.23037/) (2026)

## Abstract (arXiv)

Micro-bubbles and bubbly flows are widely observed and applied in chemical engineering, medicine, involves deformation, rupture, and collision of bubbles, phase mixture, etc. We study bubble dynamics by setting up two numerical simulation cases: bubbly flow with a single bubble and multiple bubbles, both confined in the microchannel, with parameters corresponding to their medical backgrounds. Both the cases have their medical background applications. Multiphase flow simulation requires high computation accuracy due to possible component losses that may be caused by sparse meshing during the computation. Hence, data-driven methods can be adopted as an useful tool. Based on physics-informed neural networks (PINNs), we propose a novel deep learning framework BubbleNet, which entails three main parts: deep neural networks (DNN) with sub nets for predicting different physics fields; the semi-physics-informed part, with only the fluid continuum condition and the pressure Poisson equation P encoded within; the time discretized normalizer (TDN), an algorithm to normalize field data per time step before training. We apply the traditional DNN and our BubbleNet to train the coarsened simulation data and predict the physics fields of both the two bubbly flow cases. The BubbleNets are trained for both with and without P, from which we conclude that the 'physics-informed' part can serve as inner supervision. Results indicate our framework can predict the physics fields more accurately, estimating the prediction absolute errors. Our deep learning predictions outperform traditional numerical methods computed with similar data density meshing. The proposed network can potentially be applied to many other engineering fields.