Implementation of Neural Operator Learning in Digital Twin Systems

Kobayashi, Kazuma; Daniell, James; Kumar, Dinesh; Alam, Syed Bahauddin

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https://hdl.handle.net/2142/121819 Copy

Description

Title

Implementation of Neural Operator Learning in Digital Twin Systems

Author(s)

• Kobayashi, Kazuma
• Daniell, James
• Kumar, Dinesh
• Alam, Syed Bahauddin

Issue Date

2023

Keyword(s)

• Digital twin
• Neural operator
• Surrogate modeling

Abstract

Digital twin (DT) technology is attracting attention in various fields and is expected to be applied in the nuclear sector. According to the U.S. Nuclear Regulatory Commission (NRC), there are three vital components for realizing and implementing a DT system: (i) advanced sensors and instrumentation for real- time temporal synchronization, (ii) modeling and simulation, and (iii) data and information management. This study focuses on the modeling methods and introduces the surrogate modeling technique using Deep Operator neural Network (DeepONet) [1] to enable real-time and faster predictions for the Digital Twin systems. With modern computational advancements and statistical analysis methods, the utilization of neural networks as partial differential equation (PDE) solvers has been studied. In particular, physics- informed neural networks (PINN) [2], have achieved great success in hybrid modeling with the laws of physics and data. The method builds a surrogate model of the system by training a neural network with scattered sensor data from measurement and imposing boundary and initial conditions. Therefore, the application to dynamic systems is a challenge, as the network needs to be re-trained by acquiring training data again when the initial or boundary conditions change. Unfortunately, this leads to the slower prediction and not applicable for real-time and on-the-fly prediction. To solve this challenge, the use of state-of-the- art DeepONet learning method is proposed. Unlike conventional neural networks such as PINN and Multi- fidelity neural networks (MFNN), which map functions from input variables, DeepONet aims to map the relationship between input and output functions by leveraging two distinct networks. The input functions here are, for example, time-dependent initial conditions and boundary conditions. The output function can then be regarded as the system's response to those conditions. The advantage of DeepONet lies in its generalization capabilities. A single model can obtain the system response under various conditions without re-training with all possible input and output function patterns. To demonstrate the capability of DeepONet in nuclear systems and real-time DT applicability, the surrogate model of neutron flux distribution in a 2D geometry was developed. The pairs of distributed neutron sources following a Gaussian function and the corresponding neutron flux distribution in the geometry, computed with a Monte Carlo-based simulation, were employed as training data. The results show that the surrogate model exhibits excellent prediction accuracy, with an R2 score of over 9×10-1 and a mean squared error (MSE) of less than 10-2 for the unseen test data, leading to the generalization of the DT systems. In addition, the simulation takes approximately 30 seconds of computation time for a given input function, whereas the pre-trained model could obtain more than ~100 times faster predictions. These results show that DeepONet has high potential as a surrogate modeling method for constituting a DT for nuclear systems.

Type of Resource

text

Language

eng

Handle URL

https://hdl.handle.net/2142/121819

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