1.2 KiB
1.2 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 |
|---|---|
| BNN | Bayesian neural network |
| CNN | Convolutional neural network |
| DL | Deep Learning |
| 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 |