6
I think it is better to use NDSolve for this. Having to integrate random function is not practical. (after activate, etc...) and will be very slow.
I used the noise[t] function from this answer Continuous noise representation and plugged it as input to the ode. Here is second order ode example using it (you can change the ode to the first order one you had ...
4
A wonderful function for that is PolyharmonicSplineInterpolation.
fun=ResourceFunction["PolyharmonicSplineInterpolation"][data,Compiled->True];
fun[6.55,2.08,1.51]
(* -0.00221661 *)
The weakness is that my computer needed almost two minutes to make the interpolacan above. Now I can make the nice plot below.
Plot3D[fun[x,y,1.02],{x,4,8},{y,1,3}]
3
You could try somthing like this. Using a MeshRegion as domain guarantess that the optimization algorithm won't leave the domain of definition of f1 and f2. (Using f1 and f2 for extrapolation might do crazy things.) Not having the data, I cannot check whether this works...
R1 = ConvexHullMesh[data1[[All, 1]]];
R2 = ConvexHullMesh[data2[[All, 1]]];
R = ...
2
Your data is the form f(x,y,z)= loss, so we need to use ListContourPlot3Dand change the data {{x,y,z},loss} to {x,y,z,loss}
ListContourPlot3D[Flatten /@ data, PlotRange -> All, Contours -> 20,
PlotLegends -> "Expressions", Mesh -> None,
MaxPlotPoints -> Automatic]
And the gradient of interpolation function for example at point {...
2
The data is 4 dimensional, x, y, z, value. One way to visualize would be to use ListPlot3D for x, y, z and a ColorFunction based on the Interpolation for the values. e.g.
ListPlot3D[data[[All, 1]],
ColorFunction -> Function[{x, y, z}, ColorData["TemperatureMap"]@func[x, y, z]],
ColorFunctionScaling -> False,
ImageSize -> 500]
1
Some fake data
SeedRandom[42];
timeWind11=MovingAverage[Sort@RandomReal[1,51+9],10];
lammdaWind11=MovingAverage[RandomReal[1,51+9],10];
your current interpolations
lammdaWind11I = ListInterpolation[lammdaWind11];
timeWind11I = ListInterpolation[timeWind11];
Show[
ListPlot[{timeWind11,lammdaWind11},PlotStyle->{Red,Blue},PlotTheme->"Scientific&...
1
Let us create some data and interpolate it
data = Table[{{t}, {Sin[1 t], Sin[2 t], Sin[3 t], Sin[4 t]}}, {t, 0, 1, 0.01}];
f = Interpolation[data]
Now you can do some ParametricPlots
ParametricPlot[{x^y - z w^4, Sin[x y z w]} /. {x -> f[t][[1]],
y -> f[t][[2]], z -> f[t][[3]], w -> f[t][[4]]}, {t, 0, 1}]
or simply plot
Plot[f[t], {t, 0, 1}]
...
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