43 lines
1.5 KiB
Markdown
43 lines
1.5 KiB
Markdown
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# Notation and Abbreviations
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## Math notation:
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| Symbol | Meaning |
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| --- | --- |
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| $A$ | matrix |
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| $\eta$ | learning rate or step size |
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| $\Gamma$ | boundary of computational domain $\Omega$ |
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| $f^{*}$ | generic function to be approximated, typically unknown |
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| $f$ | approximate version of $f^{*}$ |
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| $\Omega$ | computational domain |
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| $\mathcal P^*$ | continuous/ideal physical model |
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| $\mathcal P$ | discretized physical model, PDE |
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| $\theta$ | neural network params |
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| $t$ | time dimension |
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| $\mathbf{u}$ | vector-valued velocity |
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| $x$ | neural network input or spatial coordinate |
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| $y$ | neural network output |
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| $y^*$ | learning targets: ground truth, reference or observation data |
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## Summary of the most important abbreviations:
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| Abbreviation | Meaning |
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| --- | --- |
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| AI | Mysterious buzzword popping up in all kinds of places these days |
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| BNN | Bayesian neural network |
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| CNN | Convolutional neural network (specific NN architecure) |
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| DDPM | Denoising diffusion probabilistic models (diffusion modeling variant) |
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| DL | Deep Learning |
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| FM | Flow matching (diffusion modeling variant) |
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| FNO | Fourier neural operator (specific NN architecure) |
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| GD | (steepest) Gradient Descent |
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| MLP | Multi-Layer Perceptron, a neural network with fully connected layers |
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| NN | Neural network (a generic one, in contrast to, e.g., a CNN or MLP) |
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| PDE | Partial Differential Equation |
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| PBDL | Physics-Based Deep Learning |
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| SGD | Stochastic Gradient Descent |
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