Improved Training of Physics-Informed Neural Networks with Model Ensembles

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference article in proceedingsScientificvertaisarvioitu

Abstrakti

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.

AlkuperäiskieliEnglanti
OtsikkoIJCNN 2023 - International Joint Conference on Neural Networks, Proceedings
KustantajaIEEE
ISBN (elektroninen)978-1-6654-8867-9
DOI - pysyväislinkit
TilaJulkaistu - 2023
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisussa
TapahtumaInternational Joint Conference on Neural Networks - Gold Coast, Austraalia
Kesto: 18 kesäk. 202323 kesäk. 2023

Julkaisusarja

NimiProceedings of International Joint Conference on Neural Networks
ISSN (elektroninen)2161-4407

Conference

ConferenceInternational Joint Conference on Neural Networks
LyhennettäIJCNN
Maa/AlueAustraalia
KaupunkiGold Coast
Ajanjakso18/06/202323/06/2023

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