Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network
CoRR(2023)
摘要
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 R^2 value of above 0.99 and a relative
L_2 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 is highly efficient and
accurate.
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