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The procedure for estimating parameters in a parabolic partial differential equation is very inefficient. How can I speed it up?

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The procedure for estimating parameters in a parabolic partial differential equation is very inefficient. How can I speed it up?

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PDE models should be used only after more approximate (ODE) models have provided good estimates for the parameters. A limited number of parameters (two or three) can be fine-tuned using the more complete PDE model.

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