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

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