A novel data generation scheme for surrogate modelling with deep operator networks
This work addresses a bottleneck in deploying operator-based surrogate models for practical applications, offering a widely applicable method to reduce data generation costs, though it is incremental as it builds on existing DeepONet frameworks.
The authors tackled the high computational cost of generating training data for DeepONet surrogate models by proposing a novel data generation scheme that avoids solving PDEs directly, instead using Gaussian Process Regression to generate output fields and finite differences to compute input sources, achieving significant reduction in computational cost.
Operator-based neural network architectures such as DeepONets have emerged as a promising tool for the surrogate modeling of physical systems. In general, towards operator surrogate modeling, the training data is generated by solving the PDEs using techniques such as Finite Element Method (FEM). The computationally intensive nature of data generation is one of the biggest bottleneck in deploying these surrogate models for practical applications. In this study, we propose a novel methodology to alleviate the computational burden associated with training data generation for DeepONets. Unlike existing literature, the proposed framework for data generation does not use any partial differential equation integration strategy, thereby significantly reducing the computational cost associated with generating training dataset for DeepONet. In the proposed strategy, first, the output field is generated randomly, satisfying the boundary conditions using Gaussian Process Regression (GPR). From the output field, the input source field can be calculated easily using finite difference techniques. The proposed methodology can be extended to other operator learning methods, making the approach widely applicable. To validate the proposed approach, we employ the heat equations as the model problem and develop the surrogate model for numerous boundary value problems.