Scientific Deep Ensemble for 1D Advection-Diffusion-Reaction¶

Notebook: DeepEnsemble_AdvectionDiffusionReaction1D_Tutorial.ipynb

This tutorial uses DeepEnsembleRegressor on a steady 1D advection-diffusion-reaction boundary-value problem. The ensemble learns a pointwise surrogate for the PDE response and visualizes epistemic uncertainty bands over the spatial coordinate.

Key ideas: - coordinate-plus-parameter regression for a scientific PDE surrogate, - parameter-space OOD shift through sharper forcing and stronger transport, - predictive mean and ensemble spread as the uncertainty signal.

Primary references: - Lakshminarayanan, Pritzel, Blundell (2017), Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles. NeurIPS proceedings - Hansen, Salamon (1990), Neural Network Ensembles. DOI: 10.1109/34.58871