Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations

Understand

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics.

• DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent prediction capabilities.
• Having said that, being set in a deterministic framework exposes DeepONet architecture to the risk of overfitting, poor generalization and in its unaltered form, it is incapable of quantifying the uncertainties associated with its predictions.
• We propose in this paper, a Variational Bayes DeepONet (VB-DeepONet) for operator learning, which can alleviate these limitations of DeepONet architecture to a great extent and give user additional information regarding the associated uncertainty at the prediction stage.