@@ -10,7 +10,7 @@ The central goal of these methods is to use existing numerical solvers, and equi
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them with functionality to compute gradients with respect to their inputs.
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them with functionality to compute gradients with respect to their inputs.
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Once this is realized for all operators of a simulation, we can leverage
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Once this is realized for all operators of a simulation, we can leverage
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the autodiff functionality of DL frameworks with backpropagation to let gradient
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the autodiff functionality of DL frameworks with backpropagation to let gradient
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information flow from from a simulator into an NN and vice versa. This has numerous
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information flow from a simulator into an NN and vice versa. This has numerous
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advantages such as improved learning feedback and generalization, as we'll outline below.
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advantages such as improved learning feedback and generalization, as we'll outline below.
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In contrast to physics-informed loss functions, it also enables handling more complex
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In contrast to physics-informed loss functions, it also enables handling more complex
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@@ -117,7 +117,7 @@
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"source": [
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"source": [
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"def step(velocity, smoke, pressure, dt=1.0, buoyancy_factor=1.0):\n",
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"def step(velocity, smoke, pressure, dt=1.0, buoyancy_factor=1.0):\n",
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" smoke = advect.semi_lagrangian(smoke, velocity, dt) + INFLOW\n",
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" smoke = advect.semi_lagrangian(smoke, velocity, dt) + INFLOW\n",
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" buoyancy_force = smoke * (0, buoyancy_factor) >> velocity # resamples smoke to velocity sample points\n",
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" buoyancy_force = (smoke * (0, buoyancy_factor)).at(velocity) # resamples smoke to velocity sample points\n",
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" velocity = advect.semi_lagrangian(velocity, velocity, dt) + dt * buoyancy_force\n",
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" velocity = advect.semi_lagrangian(velocity, velocity, dt) + dt * buoyancy_force\n",
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" velocity = diffuse.explicit(velocity, NU, dt)\n",
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" velocity = diffuse.explicit(velocity, NU, dt)\n",
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" velocity, pressure = fluid.make_incompressible(velocity)\n",
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" velocity, pressure = fluid.make_incompressible(velocity)\n",
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@@ -527,4 +527,4 @@
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},
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},
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"nbformat": 4,
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"nbformat": 4,
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"nbformat_minor": 1
|
"nbformat_minor": 1
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||||||
}
|
}
|
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|
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Reference in New Issue
Block a user