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smaller cleanup

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2021-03-10 12:48:24 +08:00
parent 8556fa6c96
commit 627c7746e8
3 changed files with 10 additions and 1 deletions
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8
diffphys-code-burgers.ipynb
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@@ -182,6 +182,14 @@
"Now we have our simulation graph in TF, we can use TF to give us a gradient for the initial state for the loss. All we need to do is run `tf.gradients(loss, [state_in.velocity.data]`, which will give us a \n", "Now we have our simulation graph in TF, we can use TF to give us a gradient for the initial state for the loss. All we need to do is run `tf.gradients(loss, [state_in.velocity.data]`, which will give us a \n",
"\n", "\n",
"Thus now we have \"search direction\" for each velocity variable. Based on a linear approximation, the gradient tells us how to change each of them to increase the loss function (gradients _always_ point \"upwards\"). In the following code block, we're additionally saving all these gradients in a list called `grads`, such that we can visualize them later on. (Normally, we could discard each gradient after performing an update step.)\n", "Thus now we have \"search direction\" for each velocity variable. Based on a linear approximation, the gradient tells us how to change each of them to increase the loss function (gradients _always_ point \"upwards\"). In the following code block, we're additionally saving all these gradients in a list called `grads`, such that we can visualize them later on. (Normally, we could discard each gradient after performing an update step.)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Optimization \n",
"\n", "\n",
"Based on the gradient, we can now take a step in the opposite direction to bring the loss down (instead of increasing it). Below we're using a learning rate `LR=5` for this step. Afterwards, we're re-evaluating the loss for the updated state to check how we did. " "Based on the gradient, we can now take a step in the opposite direction to bring the loss down (instead of increasing it). Below we're using a learning rate `LR=5` for this step. Afterwards, we're re-evaluating the loss for the updated state to check how we did. "
] ]

2
diffphys-control.ipynb
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@@ -41,7 +41,7 @@
"$\n", "$\n",
"\\newcommand{\\pde}{\\mathcal{P}}\n", "\\newcommand{\\pde}{\\mathcal{P}}\n",
"\\newcommand{\\net}{\\mathrm{CFE}}\n", "\\newcommand{\\net}{\\mathrm{CFE}}\n",
"\\mathbf{u}_{n},d_{n} = \\pdec(\\net(\\pdec(\\net(\\cdots \\pdec(\\net( \\mathbf{u}_0,d_0 ))\\cdots)))) = (\\pdec\\net)^n ( \\mathbf{u}_0,d_0 ) .\n", "\\mathbf{u}_{n},d_{n} = \\pde(\\net(~\\pde(\\net(\\cdots \\pde(\\net( \\mathbf{u}_0,d_0 ))\\cdots)))) = (\\pde\\net)^n ( \\mathbf{u}_0,d_0 ) .\n",
"$\n", "$\n",
"\n", "\n",
"minimizes the loss above. The $\\mathrm{OP}$ network is a predictor that determines the action of the $\\mathrm{CFE}$ network given the target $d^*$, i.e., $\\mathrm{OP}(\\mathbf{u},d,d^*)=d_{OP}$,\n", "minimizes the loss above. The $\\mathrm{OP}$ network is a predictor that determines the action of the $\\mathrm{CFE}$ network given the target $d^*$, i.e., $\\mathrm{OP}(\\mathbf{u},d,d^*)=d_{OP}$,\n",

1
intro.md
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@@ -87,6 +87,7 @@ See also... Test link: {doc}`supervised`
- PINNs: often need weighting of added loss terms for different parts - PINNs: often need weighting of added loss terms for different parts
- DP intro, check transpose of Jacobians in equations - DP intro, check transpose of Jacobians in equations
- DP control, show targets at bottom? - DP control, show targets at bottom?
- finish pictures...
## TODOs , Planned content ## TODOs , Planned content