mlsanityData to 7 Oct 2026

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

arXiv 2211.00214 ↗First posted 1 Nov 2022cs.LG physics.comp-phcited by 12

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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.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 10 of its 18 references that are in the map. First posted on arXiv 1 Nov 2022.

Builds on

10 of 18 references.

References · 10

  1. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  2. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  3. 2018A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equationscited by 55
  4. 2018Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equationscited by 54
  5. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  6. 2019Physical Symmetries Embedded in Neural Networkscited by 40
  7. 2020Hamiltonian neural networks for solving equations of motioncited by 33
  8. 2020Unsupervised Neural Networks for Quantum Eigenvalue Problemscited by 15
  9. 2021Unsupervised Reservoir Computing for Solving Ordinary Differential Equationscited by 11
  10. 2022DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networkscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 5; 2026: 4.

12 papers.

  1. 2023Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domainscited by 14
  2. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  3. 2023Understanding and Mitigating Extrapolation Failures in Physics-Informed Neural Networkscited by 8
  4. 2025Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Spacecited by 6
  5. 2025Adaptive Physics-informed Neural Networks: A Surveycited by 5
  6. 2023One-Shot Transfer Learning for Nonlinear ODEscited by 3
  7. 2025Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networkscited by 0
  8. 2025Conditioning on PDE Parameters to Generalise Deep Learning Emulation of Stochastic and Chaotic Dynamicscited by 0
  9. 2026Bayesian quantum sensing using graybox machine learningcited by 0
  10. 2026Learning embeddings of non-linear PDEs: the Burgers' equationcited by 0
  11. 2026Physics-Informed Neural Embeddings of PDE Solution Familiescited by 0
  12. 2026Physics-Informed Neural Networks to Infer the Perpendicular Energy Conductivity in the Scrape-Off Layer of Stellarator Devicescited by 0