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clarified tensor vs grid differences

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2024-11-05 13:56:27 +08:00
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overview-burgers-forw.ipynb
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@@ -95,7 +95,7 @@
"source": [ "source": [
"\n", "\n",
"Next, we initialize a 1D `velocity` grid from the `INITIAL` numpy array that was converted into a tensor.\n", "Next, we initialize a 1D `velocity` grid from the `INITIAL` numpy array that was converted into a tensor.\n",
"The extent of our domain $\\Omega$ is specifiied via the `bounds` parameter $[-1,1]$, and the grid uses periodic boundary conditions (`extrapolation.PERIODIC`). These two properties are the main difference between a tensor and a grid: the latter has boundary conditions and a physical extent.\n", "The extent of our domain $\\Omega$ is specifiied via the `bounds` parameter $[-1,1]$, and the grid uses periodic boundary conditions (`extrapolation.PERIODIC`). These two properties are the main difference between phiflow's tensor and grid objects: the latter has boundary conditions and a physical extent.\n",
"\n", "\n",
"Just to illustrate, we'll also print some info about the velocity object: it's a `phi.math` tensor with a size of 128. Note that the actual grid content is contained in the `values` of the grid. Below we're printing five entries by using the `numpy()` function to convert the content of the phiflow tensor into a numpy array. For tensors with more dimensions, we'd need to specify the additional dimenions here, e.g., `'y,x,vector'` for a 2D velocity field. (For tensors with a single dimensions we could leave it out.)" "Just to illustrate, we'll also print some info about the velocity object: it's a `phi.math` tensor with a size of 128. Note that the actual grid content is contained in the `values` of the grid. Below we're printing five entries by using the `numpy()` function to convert the content of the phiflow tensor into a numpy array. For tensors with more dimensions, we'd need to specify the additional dimenions here, e.g., `'y,x,vector'` for a 2D velocity field. (For tensors with a single dimensions we could leave it out.)"
] ]

13
references.bib
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@@ -1033,4 +1033,17 @@
} }
@article{lipman2022flow,
title={Flow matching for generative modeling},
author={Lipman, Yaron and Chen, Ricky TQ and Ben-Hamu, Heli and Nickel, Maximilian and Le, Matt},
journal={arXiv:2210.02747}, year={2022}
}
@article{liu2022rect,
title={Flow straight and fast: Learning to generate and transfer data with rectified flow},
author={Liu, Xingchao and Gong, Chengyue and Liu, Qiang},
journal={arXiv:2209.03003}, year={2022}
}