# Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows

arXiv: https://arxiv.org/abs/2211.00214 · HTML: https://mlsanity.com/paper/2211.00214/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations](https://mlsanity.com/paper/1804.07010/) (2018)
- [A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations](https://mlsanity.com/paper/1809.02362/) (2018)
- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [Physical Symmetries Embedded in Neural Networks](https://mlsanity.com/paper/1904.08991/) (2019)
- [Hamiltonian neural networks for solving equations of motion](https://mlsanity.com/paper/2001.11107/) (2020)
- [Unsupervised Neural Networks for Quantum Eigenvalue Problems](https://mlsanity.com/paper/2010.05075/) (2020)
- [Unsupervised Reservoir Computing for Solving Ordinary Differential Equations](https://mlsanity.com/paper/2108.11417/) (2021)
- [DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networks](https://mlsanity.com/paper/2209.07081/) (2022)

## Built on by (most cited first, 12 of 12)

- [Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains](https://mlsanity.com/paper/2302.04954/) (2023)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [Understanding and Mitigating Extrapolation Failures in Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.09478/) (2023)
- [Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space](https://mlsanity.com/paper/2501.12116/) (2025)
- [Adaptive Physics-informed Neural Networks: A Survey](https://mlsanity.com/paper/2503.18181/) (2025)
- [One-Shot Transfer Learning for Nonlinear ODEs](https://mlsanity.com/paper/2311.14931/) (2023)
- [Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networks](https://mlsanity.com/paper/2507.22370/) (2025)
- [Conditioning on PDE Parameters to Generalise Deep Learning Emulation of Stochastic and Chaotic Dynamics](https://mlsanity.com/paper/2509.09599/) (2025)
- [Bayesian quantum sensing using graybox machine learning](https://mlsanity.com/paper/2601.17465/) (2026)
- [Learning embeddings of non-linear PDEs: the Burgers' equation](https://mlsanity.com/paper/2603.07812/) (2026)
- [Physics-Informed Neural Embeddings of PDE Solution Families](https://mlsanity.com/paper/2607.06348/) (2026)
- [Physics-Informed Neural Networks to Infer the Perpendicular Energy Conductivity in the Scrape-Off Layer of Stellarator Devices](https://mlsanity.com/paper/2609.11628/) (2026)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning approach for PINNs and introduce a multi-head model to efficiently obtain accurate solutions to nonlinear systems of ordinary differential equations with random potentials. In particular, we apply the method to simulate stochastic branched flows, a universal phenomenon in random wave dynamics. Finally, we compare the results achieved by feed forward and GAN-based PINNs on two physically relevant transfer learning tasks and show that our methods provide significant computational speedups in comparison to standard PINNs trained from scratch.