A novel data generation scheme for surrogate modelling with deep
  operator networks
Shivam Choubey Birupaksha Pal Manish Agrawal
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.