| \(\mathbf{x}\) |
State vector / field |
| \(\mathbf{y}\) |
Observations |
| \(\mathbf{m}\) |
Binary observation mask |
| \(\mathcal{H}\) |
Observation operator |
| \(\varphi_\theta\) |
Learned prior (autoencoder) |
| \(\Psi_\phi\) |
Gradient modulator (ConvLSTM) |
| \(J\) |
Variational (energy) cost |
| \(J_{obs}\) |
Observation cost |
| \(J_{prior}\) |
Prior cost |
| \(\lambda\) |
Prior weight |
| \(\alpha\) |
Gradient step-size |
| \(K\) |
Number of solver steps |
| \(B\) |
Batch size |
| \(T\) |
Number of time steps |
| \(N\) |
Spatial size (1-D) |
| \(H, W\) |
Spatial height / width (2-D) |
| \(C\) |
Number of channels (multivariate) |
| \(\odot\) |
Element-wise product |
| \(*\) |
Convolution |
| \(\sigma(\cdot)\) |
Sigmoid activation |