Iteratively running through list of parameter sets with ParametricNDSolve - wolfram-mathematica

Question

So I have the below code
perturb1 =
x'[t] == mu1*x[t] + x[t]*(a*x[t] + b*y[t] + c*z[t]) +
x[t]*eps1 * (UnitStep[t - 1.5] - UnitStep[t - 2.5]);
perturb2 =
y'[t] == mu2*y[t] + y[t]*(d*x[t] + e*y[t] + f*z[t]) +
y[t]*eps2 * (UnitStep[t - 1.5] - UnitStep[t - 2.5]);
perturb3 =
z'[t] == mu3*z[t] + z[t]*(g*x[t] + h*y[t] + i*z[t]) +
z[t]*eps3 * (UnitStep[t - 1.5] - UnitStep[t - 2.5]);
perturbSol = ParametricNDSolve[
{perturb1, perturb2, perturb3, x[0] == 0.25, y[0] == 0.4,
z[0] == 0.35},
{x[t], y[t], z[t]},
{t, 0, 500},
{mu1, mu2, mu3, a, b, c, d, e, f, g, h, i, eps1, eps2, eps3}
];
Evaluate[x[t][#] /. perturbSol] & /# parameterSets
parameterSets is a list of 5000+ elements of the form {mu1, mu2, mu3, a, b, c, d, e, f, g, h, i, eps1, eps2, eps3} (but with numerical values). What I'm trying to do is to evaluate the parametric function using each parameter set. When I do as above, I get the error
ParametricNDSolve: Too many parameters in {mu1,mu2,mu3,a,b,c,d,e,f,g,h,i,eps1,eps2,eps3} to be filled from {{0.9,0.9,0.9,-2,-1,-1,-1,-2,-1,-1,-1,-2,-2,-2,-2}}.
So it seems that it's because, with a single value, you would evaluate the function as follows:
Evaluate[x[t][0.9,0.9,0.9,-2,-1,-1,-1,-2,-1,-1,-1,-2,-2,-2,-2]/.perturbSol]
Whereas when using Map on parameterSets, it does this:
Evaluate[x[t][{0.9,0.9,0.9,-2,-1,-1,-1,-2,-1,-1,-1,-2,-2,-2,-2}]/.perturbSol]
i.e. it's applying the function to a list of 15 parameters, rather than to the 15 parameters separated by commas.
Is there any elegant solution to this? I tried flatten around the #, which didn't do anything (as I sort of expected). I guess one way is to write #1,#2,#3 etc in the square brackets but that's pretty messy.
Any better way to do this?
Many thanks,
H

Answer 1

Probably, you want something along the lines of
u = ParametricNDSolveValue[{perturb1, perturb2, perturb3,
x[0] == 0.25, y[0] == 0.4, z[0] == 0.35}, {x, y, z}, {t, 0,
500}, {mu1, mu2, mu3, a, b, c, d, e, f, g, h, i, eps1, eps2,
eps3}];
parameterSets = RandomReal[{-1, 1}, {3, 15}];
(u[##])[[1]][t] & ### parameterSets