pbdl-book/notation.md

# 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 |

## Summary of the most important abbreviations:

| ABbreviation | Meaning |
| --- | --- |
| CNN | Convolutional neural network |
| DL | Deep learning |
| NN | Neural network |
| PBDL | Physics-based deep learning |



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