1.5 KiB
1.5 KiB
Notation and Abbreviations
Math notation:
| Symbol | Meaning |
|---|---|
| A | matrix |
| \eta | learning rate or step size |
| \Gamma | boundary of computational domain \Omega |
| f^{*} | generic function to be approximated, typically unknown |
| f | approximate version of f^{*} |
| \Omega | computational domain |
| \mathcal P^* | continuous/ideal physical model |
| \mathcal P | discretized physical model, PDE |
| \theta | neural network params |
| t | time dimension |
| \mathbf{u} | vector-valued velocity |
| x | neural network input or spatial coordinate |
| y | neural network output |
| y^* | learning targets: ground truth, reference or observation data |
Summary of the most important abbreviations:
| Abbreviation | Meaning |
|---|---|
| AI | Mysterious buzzword popping up in all kinds of places these days |
| BNN | Bayesian neural network |
| CNN | Convolutional neural network (specific NN architecure) |
| DDPM | Denoising diffusion probabilistic models (diffusion modeling variant) |
| DL | Deep Learning |
| FM | Flow matching (diffusion modeling variant) |
| FNO | Fourier neural operator (specific NN architecure) |
| GD | (steepest) Gradient Descent |
| MLP | Multi-Layer Perceptron, a neural network with fully connected layers |
| NN | Neural network (a generic one, in contrast to, e.g., a CNN or MLP) |
| PDE | Partial Differential Equation |
| PBDL | Physics-Based Deep Learning |
| SGD | Stochastic Gradient Descent |