TY - JOUR

T1 - Predictions of transient vector solution fields with sequential deep operator network

AU - He, Junyan

AU - Kushwaha, Shashank

AU - Park, Jaewan

AU - Koric, Seid

AU - Abueidda, Diab

AU - Jasiuk, Iwona

N1 - Publisher Copyright:
© The Author(s) 2024.

PY - 2024/8

Y1 - 2024/8

N2 - The deep operator network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models in the branch of DeepONet to predict final solutions given time-dependent inputs. In the current work, the S-DeepONet architecture is extended by modifying the information combination mechanism between the branch and trunk networks to simultaneously predict vector solutions with multiple components at multiple time steps of the evolution history, which is the first in the literature using DeepONets. Two example problems, one on transient fluid flow and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the model to handle different physics problems. The use of a trained S-DeepONet model in inverse parameter identification via the genetic algorithm is shown to demonstrate the application of the model. In almost all cases, the trained model achieved an R2 value of above 0.99 and a relative L2 error of less than 10% with only 3200 training data points, indicating superior accuracy. The vector S-DeepONet model, having only 0.4% more parameters than a scalar model, can predict two output components simultaneously at an accuracy similar to the two independently trained scalar models with a 20.8% faster training time. The S-DeepONet inference is at least three orders of magnitude faster than direct numerical simulations, and inverse parameter identifications using the trained model are highly efficient and accurate.

AB - The deep operator network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models in the branch of DeepONet to predict final solutions given time-dependent inputs. In the current work, the S-DeepONet architecture is extended by modifying the information combination mechanism between the branch and trunk networks to simultaneously predict vector solutions with multiple components at multiple time steps of the evolution history, which is the first in the literature using DeepONets. Two example problems, one on transient fluid flow and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the model to handle different physics problems. The use of a trained S-DeepONet model in inverse parameter identification via the genetic algorithm is shown to demonstrate the application of the model. In almost all cases, the trained model achieved an R2 value of above 0.99 and a relative L2 error of less than 10% with only 3200 training data points, indicating superior accuracy. The vector S-DeepONet model, having only 0.4% more parameters than a scalar model, can predict two output components simultaneously at an accuracy similar to the two independently trained scalar models with a 20.8% faster training time. The S-DeepONet inference is at least three orders of magnitude faster than direct numerical simulations, and inverse parameter identifications using the trained model are highly efficient and accurate.

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U2 - 10.1007/s00707-024-03991-2

DO - 10.1007/s00707-024-03991-2

M3 - Article

AN - SCOPUS:85195636642

SN - 0001-5970

VL - 235

SP - 5257

EP - 5272

JO - Acta Mechanica

JF - Acta Mechanica

IS - 8

ER -