Tutorial: Heteroscedastic Multi-Output Bayes by Backprop on Transport2D¶

Notebook: HeteroscedasticMultiOutput_BayesByBackprop_Transport2D_Tutorial.ipynb

Scientific problem¶

A pointwise 2D transport field with two outputs: concentration and flux magnitude, both observed with input-dependent noise.

Input and output¶

• input: (x, y) plus transport parameters
• output: [c(x, y), |\nabla c(x, y)|] and corresponding predicted variances

UQ method¶

• HeteroscedasticMultiOutputBayesByBackpropRegressor
• predict_vi_uq(...) returns multi-output epistemic and aleatoric terms

Why this notebook exists¶

This is the most complete regression VI example in the package: multi-output, Bayesian weight uncertainty, and input-dependent noise in one workflow.