Model Architectures¶
Deep-UQ separates predictive architectures from uncertainty methods. This page is the canonical inventory of model families available in the package, while the UQ method pages describe how posterior or predictive uncertainty is computed.
For convolutional backbones, the primary UQ paths are MC Dropout and Deep Ensembles. For coordinate-input PINNs, the primary UQ path is last-layer Laplace because the current Laplace implementation integrates naturally with final nn.Linear heads.
Legend: ✓ supported, ✗ not the primary path.
Dense / Parametric Models¶
These models operate on vectors or coordinate-augmented point inputs and are a natural fit for classical regression baselines, ensembles, and PINN-style training.
| Model | 1D | 2D | 3D | Laplace | MC Dropout | Deep Ensemble | Primary Use | Notebook |
|---|---|---|---|---|---|---|---|---|
MLP | ✓ | ✓ | ✗ | ✓ | ✓ | ✓ | Parametric regression / classification | Deep Ensembles |
PINN1D | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ | 1D physics-informed PDE surrogate | PINN + Poisson |
PINN2D | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | 2D physics-informed PDE surrogate | PINN + Poisson |
Spatial Convolutional Models¶
These are field-to-field backbones for regular scientific grids. Their main UQ story in Deep-UQ is stochastic inference through dropout or population-level uncertainty through ensembles.
| Model | 1D | 2D | 3D | Laplace | MC Dropout | Deep Ensemble | Primary Use | Notebook |
|---|---|---|---|---|---|---|---|---|
CNNRegressor2D | ✗ | ✓ | ✗ | ✗ | ✓ | ✓ | Compact 2D PDE surrogate baseline | CNN / ResNet + Heat2D |
ResNetRegressor2D | ✗ | ✓ | ✗ | ✗ | ✓ | ✓ | Stronger residual 2D surrogate baseline | CNN / ResNet + Heat2D |
UNet2D | ✗ | ✓ | ✗ | ✗ | ✓ | ✓ | Multi-scale 2D field-to-field surrogate | UNet + Diffusion2D |
UNet3D | ✗ | ✗ | ✓ | ✗ | ✓ | ✓ | Volumetric 3D field surrogate backbone | UNet + Diffusion2D |
Operator-Learning Models¶
These models learn mappings between whole fields. DeepONet uses separate branch and trunk networks, while FNO performs global spectral mixing on regular grids.
| Model | 1D | 2D | 3D | Laplace | MC Dropout | Deep Ensemble | Primary Use | Notebook |
|---|---|---|---|---|---|---|---|---|
DeepONet1D | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ | 1D field-to-field operator learning | DeepONet + 1D Poisson |
DeepONet2D | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | 2D field-to-field operator learning | DeepONet + Burgers |
FNO2D | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | 2D Darcy / regular-grid PDE surrogate | FNO2D + Darcy |
FNO3D | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | 3D periodic PDE surrogate | FNO3D + 3D Heat |
Graph Operator Models¶
These models treat a regular grid as a graph and use local message passing instead of global spectral mixing. They are a good bridge between grid-based operator learning and future unstructured-mesh models.
| Model | 1D | 2D | 3D | Laplace | MC Dropout | Deep Ensemble | Primary Use | Notebook |
|---|---|---|---|---|---|---|---|---|
GraphNeuralOperator2D | ✗ | ✓ | ✗ | ✓ | ✗ | ✓ | Grid-as-graph operator learning for reaction-diffusion and mesh-style surrogates | Graph Operator + Gray-Scott |
Generative / Diffusion Models¶
These models represent uncertainty through the spread of generated conditional samples rather than by wrapping a deterministic predictor with Laplace, dropout, or ensembles.
| Model | 1D | 2D | 3D | Laplace | MC Dropout | Deep Ensemble | Primary Use | Notebook |
|---|---|---|---|---|---|---|---|---|
ConditionalUNet2D | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | Conditional field reconstruction with sample-based UQ | Conditional Diffusion + Heat2D |
Gaussian Process Models¶
The GP family is function-space Bayesian from the start, so the uncertainty story is native rather than layered on after training.
| Model | 1D | 2D | 3D | Laplace | MC Dropout | Deep Ensemble | Primary Use | Notebook |
|---|---|---|---|---|---|---|---|---|
| GP regressors / classifiers | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | Kernel-based Bayesian modeling | Gaussian Processes |
Deep Ensemble Method Note¶
DeepEnsembleWrapper is a UQ method, not a predictive model class. It can wrap any compatible deterministic backbone and is the primary ensemble-based uncertainty path for MLP, CNNRegressor2D, ResNetRegressor2D, UNet2D, and UNet3D.