# A novel Trunk Branch-net PINN for flow and heat transfer prediction in porous medium

arXiv: https://arxiv.org/abs/2501.16362 · HTML: https://mlsanity.com/paper/2501.16362/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 59 references that are in the map.
- First posted on arXiv 21 Jan 2025.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Deep Learning of Subsurface Flow via Theory-guided Neural Network](https://mlsanity.com/paper/1911.00103/) (2019)
- [Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media](https://mlsanity.com/paper/2203.01514/) (2022)
- [Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks](https://mlsanity.com/paper/2209.03276/) (2022)

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

- [Hierarchical rank-evolving representation for physics-informed neural networks](https://mlsanity.com/paper/2608.09483/) (2026)

## Abstract (arXiv)

A novel Trunk-Branch (TB)-net physics-informed neural network (PINN) architecture is developed, which is a PINN-based method incorporating trunk and branch nets to capture both global and local features. The aim is to solve four main classes of problems: forward flow problem, forward heat transfer problem, inverse heat transfer problem, and transfer learning problem within the porous medium, which are notoriously complex that could not be handled by origin PINN. In the proposed TB-net PINN architecture, a Fully-connected Neural Network (FNN) is used as the trunk net, followed by separated FNNs as the branch nets with respect to outputs, and automatic differentiation is performed for partial derivatives of outputs with respect to inputs by considering various physical loss. The effectiveness and flexibility of the novel TB-net PINN architecture is demonstrated through a collection of forward problems, and transfer learning validates the feasibility of resource reuse. Combining with the superiority over traditional numerical methods in solving inverse problems, the proposed TB-net PINN shows its great potential for practical engineering applications.