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Tutorial: DeepONet + Burgers + Laplace

Notebook: DeepONet_Burgers_Laplace_Tutorial.ipynb

Purpose

Train a DeepONet-style surrogate for a small 2D viscous Burgers problem and quantify spatial epistemic uncertainty with the existing Laplace approximation tooling in Deep-UQ.

Data Setup

  • Scalar 2D viscous Burgers evolution on [0, 1]^2
  • Periodic boundary conditions
  • Smooth random initial conditions sampled from low-frequency Fourier modes
  • Operator target: map the initial field to the solution field at a fixed final time

Core Logic

  • Reusable DeepONet2D model with:
  • branch network for sampled input functions
  • trunk network for spatial coordinates
  • linear readout over fused branch/trunk features so last-layer Laplace is well-defined
  • MAP training with field-wise MSE loss
  • Last-layer Laplace on the trained model using LaplaceWrapper
  • Optional diag vs kron curvature comparison on the same fixed query grid

Expected Outputs

  • Burgers initial-condition and final-solution field plots
  • MAP prediction field and absolute error heatmap
  • Laplace predictive mean field
  • Epistemic uncertainty / standard-deviation heatmap over the 2D domain
  • Optional comparison of diag and kron uncertainty maps