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 - The authors would like to thank the National Center for Supercomputing Applications (NCSA) at the University of Illinois, and particularly its Research Consulting Directorate, the Industry Program, and the Center for Artificial Intelligence Innovation (CAII) for their support and hardware resources. This research is a part of the Delta research computing project, which is supported by the National Science Foundation (award OCI 2005572) and the State of Illinois, as well as the Illinois Computes program supported by the University of Illinois Urbana-Champaign and the University of Illinois System. Finally, the authors would like to thank Professors George Karniadakis, Lu Lu, and the Crunch team at Brown, whose original work with DeepONets inspired this research.
Funding is provided by the National Science Foundation (Grant No. OCI 2005572).
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 -