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With modern computational advancements and statistical analysis methods,machine learning algorithms have become a vital part of engineering modeling.Neural Operator Networks (ONets) is an emerging machine learning algorithm as a"faster surrogate" for approximating solutions to partial differentialequations (PDEs) due to their ability to approximate mathematical operatorsversus the direct approximation of Neural Networks (NN). ONets use theUniversal Approximation Theorem to map finite-dimensional inputs toinfinite-dimensional space using the branch-trunk architecture, which encodesdomain and feature information separately before using a dot product to combinethe information. ONets are expected to occupy a vital niche for surrogatemodeling in physical systems and Digital Twin (DT) development. Three testcases are evaluated using ONets for operator approximation, including a1-dimensional ordinary differential equations (ODE), general diffusion system,and convection-diffusion (Burger) system. Solutions for ODE and diffusionsystems yield accurate and reliable results (R2>0.95), while solutions forBurger systems need further refinement in the ONet algorithm.

Operator Learning Framework for Digital Twin and Complex Engineering Systems