Tutorials¶

These guides summarize each notebook and link directly to source notebooks in GitHub.

Tutorial Families¶

Deep Ensembles¶

• Deep Ensemble + 1D ADR
• Heteroscedastic Deep Ensemble + 1D ADR
• Deep Ensemble Classifier + Elasticity Failure Map
• Multi-Output Deep Ensemble + Elastic Bar
• Heteroscedastic Multi-Output Deep Ensemble + Transport2D
• Legacy: Deep Ensembles + Parametric Poisson1D
• Full method docs: /methods/deep-ensembles/
• Notebook family directory: notebooks/ensembles/

Variational Inference¶

• Bayes by Backprop guide
• Heteroscedastic Bayes by Backprop + ADR1D
• Multi-Output Bayes by Backprop + Elastic Bar
• Heteroscedastic Multi-Output Bayes by Backprop + Transport2D
• Last-Layer VI + Heat2D Classification
• Full method docs: /methods/variational-inference/
• Notebook family directory: notebooks/vi/

Laplace Approximation¶

• Laplace comparison guide
• Full method docs: /methods/laplace/
• Notebook directory: notebooks/laplace/

MCMC / SGLD¶

• SGLD guide
• Full method docs: /methods/mcmc-sgld/
• Notebook: notebooks/SGLD_Tutorial.ipynb

MC Dropout¶

• MC Dropout guide
• Full method docs: /methods/mc-dropout/
• Notebook: notebooks/MC_Dropout_Tutorial.ipynb

Gaussian Processes¶

• Gaussian Processes guide
• Full method docs: /methods/gaussian-processes/
• Notebook directory: notebooks/gp/

Scientific ML / Operator Learning¶

• DeepONet + Burgers + Laplace guide
• Uses the reusable DeepONet2D model together with the existing Laplace backends
• Notebook: notebooks/sciml/operators/DeepONet_Burgers_Laplace_Tutorial.ipynb
• DeepONet + 1D Poisson + Laplace guide
• Uses the reusable DeepONet1D model for a field-to-field 1D operator-learning problem with shaded UQ bands
• Notebook: notebooks/sciml/operators/DeepONet_Poisson1D_Laplace_Tutorial.ipynb
• FNO3D + 3D Heat + Laplace guide
• Uses the reusable FNO3D model for a 3D field-to-field heat-diffusion surrogate with slice-based uncertainty maps
• Notebook: notebooks/sciml/operators/FNO3D_Heat_Laplace_Tutorial.ipynb
• FNO2D + Darcy Flow + Laplace guide
• Uses the reusable FNO2D model for a 2D Darcy operator surrogate with three input fields and Laplace uncertainty maps
• Notebook: notebooks/sciml/operators/FNO2D_Darcy_Laplace_Tutorial.ipynb
• CNN / ResNet + Heat2D UQ guide
• Uses CNNRegressor2D and ResNetRegressor2D on a 2D heat source-to-solution map with MC Dropout and optional ensembles
• Notebook: notebooks/sciml/spatial/CNN_ResNet_Heat2D_UQ_Tutorial.ipynb
• UNet + Diffusion2D UQ guide
• Uses UNet2D for 2D field-to-field diffusion prediction with stochastic uncertainty bands/maps
• Notebook: notebooks/sciml/spatial/UNet_Diffusion2D_UQ_Tutorial.ipynb
• Conditional Diffusion + Heat2D guide
• Uses ConditionalUNet2D for sparse-sensor heat-field reconstruction with sample-based predictive uncertainty
• Notebook: notebooks/sciml/generative/ConditionalDiffusion_Heat2D_Tutorial.ipynb
• PINN + Poisson + Laplace guide
• Uses PINN1D and PINN2D for physics-informed Poisson problems with last-layer Laplace uncertainty
• Notebook: notebooks/sciml/pinns/PINN_Poisson_Laplace_Tutorial.ipynb

Graph Neural Operators¶

• Graph Operator + Gray-Scott + Deep Ensembles
• Uses GraphNeuralOperator2D on Gray-Scott reaction-diffusion data from The Well when available, with a synthetic quick-mode fallback for local execution
• Notebook: notebooks/graphs/GraphOperator_GrayScott_Ensemble_Tutorial.ipynb

Notebook Source Directory¶

• Notebook guide: notebooks/README.md
• Variational Inference notebooks: notebooks/vi/
• Ensemble notebooks: notebooks/ensembles/
• Laplace notebooks: notebooks/laplace/
• Gaussian Process notebooks: notebooks/gp/
• Scientific ML notebooks: notebooks/sciml/
• Graph notebooks: notebooks/graphs/