Tutorial: Heteroscedastic Bayes by Backprop on ADR1D¶

Notebook: Heteroscedastic_BayesByBackprop_ADR1D_Tutorial.ipynb

Scientific problem¶

A manufactured 1D advection-diffusion-reaction field with spatially varying observation noise.

Input and output¶

• input: coordinate x plus ADR/source parameters
• output: scalar field value u(x) with predicted observation variance

UQ method¶

• HeteroscedasticBayesByBackpropRegressor
• predict_vi_uq(...) returns mean, epistemic_var, aleatoric_var, and total_var

Why this notebook exists¶

This is the cleanest VI example for separating model uncertainty from input-dependent noise in a scientific regression setting.