full rerun BNN
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"without explicit viscosity, and with an additional transport equation for the marker density $d$ given by \n",
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"without explicit viscosity, and with an additional transport equation for the marker density $d$ given by \n",
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"$\\frac{\\partial d}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla d = 0$.\n",
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"$\\frac{\\partial d}{\\partial{t}} + \\mathbf{u} \\cdot \\nabla d = 0$.\n",
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"\n",
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"\n",
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"To summarize, we have a predictor $\\mathrm{OP}$ that gives us a direction, an actor $\\mathrm{CFE}$ that exerts a force on a physical model $\\mathcal{P}$. They all need to play hand in hand to reach a given target after $n$ iterations of the simulation. As apparent from this formulation, it's not a simple inverse problem, especially due to the fact that all three functions are non-linear. This is exactly why the gradients from the DP approach are so important. (The viewpoint above also indicates that _reinforcement learning_ is a potential option. In {doc}`reinflearn-code.ipynb` we'll compare DP with these alternatives.)\n",
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"To summarize, we have a predictor $\\mathrm{OP}$ that gives us a direction, an actor $\\mathrm{CFE}$ that exerts a force on a physical model $\\mathcal{P}$. They all need to play hand in hand to reach a given target after $n$ iterations of the simulation. As apparent from this formulation, it's not a simple inverse problem, especially due to the fact that all three functions are non-linear. This is exactly why the gradients from the DP approach are so important. (The viewpoint above also indicates that _reinforcement learning_ is a potential option. In {doc}`reinflearn-code` we'll compare DP with these alternatives.)\n",
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"\n"
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"\n"
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