Temporal Extrapolation and Reliable Generalization via Temporal Neural Operator (TNO) for Geologic Carbon Storage

Summary We introduce the Temporal Neural Operator (TNO), a novel operator learning framework for learning the operator of parametric time-dependent PDEs. The TNO leverages the U-DeepONet architecture along with an additional U-Net path to process initial conditions. The TNO also utilizes temporal bundling training scheme to achieve state-of-art generalization and temporal extrapolation performance. Temporal bundling was shown to be effective in reducing error accumulation in temporal extrapolation, as well as reducing the training and prediction time as it reduces the number of solver calls.