# Notation and Abbreviations

## Contents

# 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 |