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 |