Sow in WhenEvent can't extract parameter value of ParametricNDSolve

Question

This is a problem I noticed when trying to answer this question. Just consider the following toy example:

test = ParametricNDSolveValue[{x'[t] == 1, x[0] == a, WhenEvent[t == 1, Sow@a]}, 
   x, {t, 0, 2}, a];
test@1; // Reap
(* {Null, {{a$224638}}} *)

This behavior becomes annoying when one wants to group the extracted value using the parameter a as a tag i.e. the 2nd argument of Sow.

How to understand this behavior? Is it possible to Sow the parameter value inside WhenEvent? If not, what's the best workaround for it?

Answer 1

Here is a workaround.

test = ParametricNDSolveValue[{x'[t] == 1, x[0] == a, b[0] == a, 
    WhenEvent[t == 1, Sow@b[t]]}, x, {t, 0, 2}, {a}, DiscreteVariables -> b];
Reap[test@1;][[2, 1, 1]]
(* 1. *)

and test@2 returns 2., as desired.

Answer 2

another workaround is to not use the parametric form:

test[a_] := NDSolveValue[{x'[t] == 1, x[0] == a, 
              WhenEvent[t == 1, Sow@a]}, x, {t, 0, 2}];
test[1]; // Reap

{Null, {{1}}}