Improved Training of Physics-Informed Neural Networks with Model Ensembles

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review


Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training such physics-informed neural networks (PINNs) is notoriously difficult in practice since PINNs often converge to wrong solutions. In this paper, we address this problem by training an ensemble of PINNs. Our approach is motivated by the observation that individual PINN models find similar solutions in the vicinity of points with targets (e.g., observed data or initial conditions) while their solutions may substantially differ farther away from such points. Therefore, we propose to use the ensemble agreement as the criterion for gradual expansion of the solution interval, that is including new points for computing the loss derived from differential equations. Due to the flexibility of the domain expansion, our algorithm can easily incorporate measurements in arbitrary locations. In contrast to the existing PINN algorithms with time-adaptive strategies, the proposed algorithm does not need a predefined schedule of interval expansion and it treats time and space equally. We experimentally show that the proposed algorithm can stabilize PINN training and yield performance competitive to the recent variants of PINNs trained with time adaptation.

Original languageEnglish
Title of host publicationIJCNN 2023 - International Joint Conference on Neural Networks, Proceedings
ISBN (Electronic)978-1-6654-8867-9
Publication statusPublished - 2023
MoE publication typeA4 Conference publication
EventInternational Joint Conference on Neural Networks - Gold Coast, Australia
Duration: 18 Jun 202323 Jun 2023

Publication series

NameProceedings of International Joint Conference on Neural Networks
ISSN (Electronic)2161-4407


ConferenceInternational Joint Conference on Neural Networks
Abbreviated titleIJCNN
CityGold Coast


  • Label propagation
  • Model ensembles
  • Partial differential equations
  • Physics-informed neural networks


Dive into the research topics of 'Improved Training of Physics-Informed Neural Networks with Model Ensembles'. Together they form a unique fingerprint.

Cite this