I am finding some inconsistencies in getting NonlinearModelFit to work with the output of ParametricNDSolve. Here is an example that works (starting with a fresh Kernel):
eqs = {a'[t] == -k1 a[t] - k2 a[t]^2, b'[t] == k1 a[t] + k2 a[t]^2, a[0] == a0, b[0] == b0}; fixedparams = {k1 -> 1.2, b0 -> 0}; fns = {a, b}; params = {k2, a0}; solution = ParametricNDSolve[eqs /. fixedparams, fns, {t, 0, 5}, params] fitfn = a /. solution; paramsForDataSet = {k2 -> 1.263, a0 -> 0.0321}; dataset = {#, ((fitfn @@ params) /. paramsForDataSet)[#] + RandomVariate[NormalDistribution[0, 0.0002]]} & /@ Range[0, 5, 0.01]; ListPlot[dataset, PlotRange -> Full] Image may be NSFW.
Clik here to view.
initialGuess = {k2 -> 2.0, a0 -> 0.3}; tmp = Values@initialGuess; Dynamic@Column[{Show[ListPlot[dataset, PlotRange -> Full], Plot[(fitfn @@ tmp)[t], {t, 0, 5}, PlotRange -> Full, PlotStyle -> Red], PlotRange -> Full, ImageSize -> Large], ListPlot[{#1, #2 - (fitfn @@ tmp)[#1]} & @@@ dataset, PlotRange -> Full, AspectRatio -> 0.2, ImageSize -> Large]}] This last bit gives me a dynamically-updating plot of my fit and the residuals as it converges. Here is the fitting procedure:
result = NonlinearModelFit[dataset, (fitfn @@ params)[t], Evaluate[List @@@ initialGuess], t, StepMonitor :> (tmp = params)] tmp = Values@result["BestFitParameters"] Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
This looks great! But when I slightly complicate the model, it crashes the kernel on me. Again starting from a fresh kernel:
eqs = {a'[t] == -k1 a[t] - k2 a[t]^2, b'[t] == k1 a[t] + k2 a[t]^2, c[t] == q a[t] + r b[t], c[0] == q a0 + r b0, a[0] == a0, b[0] == b0}; fixedparams = {k1 -> 1.2, b0 -> 0}; fns = {a, b, c}; params = {k2, a0, q, r}; solution = ParametricNDSolve[eqs /. fixedparams, fns, {t, 0, 5}, params] fitfn = c /. solution; paramsForDataSet = {k2 -> 1.263, a0 -> 0.0321, q -> 0.341, r -> 0.8431}; dataset = {#, ((fitfn @@ params) /. paramsForDataSet)[#] + RandomVariate[NormalDistribution[0, 0.0002]]} & /@ Range[0, 5, 0.01]; ListPlot[dataset, PlotRange -> Full] Image may be NSFW.
Clik here to view.
initialGuess = {k2 -> 2.0, a0 -> 0.3, q -> 0.32, r -> 0.88}; tmp = Values@initialGuess; Dynamic@Column[{Show[ListPlot[dataset, PlotRange -> Full], Plot[(fitfn @@ tmp)[t], {t, 0, 5}, PlotRange -> Full, PlotStyle -> Red], PlotRange -> Full, ImageSize -> Large], ListPlot[{#1, #2 - (fitfn @@ tmp)[#1]} & @@@ dataset, PlotRange -> Full, AspectRatio -> 0.2, ImageSize -> Large]}] result = NonlinearModelFit[dataset, (fitfn @@ params)[t], Evaluate[List @@@ initialGuess], t, StepMonitor :> (tmp = params)] tmp = Values@result["BestFitParameters"] The only differences are:
- adding c[t] and c[0] to eqs
- adding c to fns
- adding q and r to params
- adding values for q and r to paramsForDataSet and to initialGuess
- changing fitfn to c instead of a
Everything else is identical, but this time the kernel crashes. Any suggestions would be most welcome.
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