Improved generalization with deep neural operators for engineering systems: Path towards digital twin

Kazuma Kobayashi, Syed Bahauddin Alam

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number107844
JournalEngineering Applications of Artificial Intelligence
StatePublished - May 2024


  • Neural operator
  • Digital twin
  • Retraining
  • Surrogate modeling


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