TY - JOUR
T1 - Improved generalization with deep neural operators for engineering systems: Path towards digital twin
AU - Kobayashi, Kazuma
AU - Alam, Syed Bahauddin
PY - 2024/5
Y1 - 2024/5
N2 - Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural Networks (NN), which directly approximate functions, ONets specialize in approximating mathematical operators, enhancing their efficacy in addressing complex PDEs.In this work, we evaluate the capabilities of Deep Operator Networks (DeepONets), an ONets implementation using a branch–trunk architecture. Three test cases are studied: a system of ODEs, a general diffusion system, and the convection–diffusion Burgers’ equation. It is demonstrated that DeepONets can accurately learn the solution operators, achieving prediction accuracy (R
2) scores above 0.96 for the ODE and diffusion problems over the observed domain while achieving zero-shot (without retraining) capability. More importantly, when evaluated on unseen scenarios (zero-shot feature), the trained models exhibit excellent generalization ability. This underscores ONets’ vital niche for surrogate modeling and digital twin development across physical systems. While convection–diffusion poses a greater challenge, the results confirm the promise of ONets and motivate further enhancements to the DeepONet algorithm. This work represents an important step towards unlocking the potential of digital twins through robust and generalizable surrogates.
AB - Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural Networks (NN), which directly approximate functions, ONets specialize in approximating mathematical operators, enhancing their efficacy in addressing complex PDEs.In this work, we evaluate the capabilities of Deep Operator Networks (DeepONets), an ONets implementation using a branch–trunk architecture. Three test cases are studied: a system of ODEs, a general diffusion system, and the convection–diffusion Burgers’ equation. It is demonstrated that DeepONets can accurately learn the solution operators, achieving prediction accuracy (R
2) scores above 0.96 for the ODE and diffusion problems over the observed domain while achieving zero-shot (without retraining) capability. More importantly, when evaluated on unseen scenarios (zero-shot feature), the trained models exhibit excellent generalization ability. This underscores ONets’ vital niche for surrogate modeling and digital twin development across physical systems. While convection–diffusion poses a greater challenge, the results confirm the promise of ONets and motivate further enhancements to the DeepONet algorithm. This work represents an important step towards unlocking the potential of digital twins through robust and generalizable surrogates.
KW - Neural operator
KW - Digital twin
KW - Retraining
KW - Surrogate modeling
UR - http://www.scopus.com/inward/record.url?scp=85182976582&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85182976582&partnerID=8YFLogxK
U2 - 10.1016/j.engappai.2024.107844
DO - 10.1016/j.engappai.2024.107844
M3 - Article
SN - 0952-1976
VL - 131
JO - Engineering Applications of Artificial Intelligence
JF - Engineering Applications of Artificial Intelligence
M1 - 107844
ER -