I am currently building a library that can flexibly solve and optimize a variety of hydrological models (including some equations), which typically belongs to the ODEProblem. However, to ensure the flexibility of the library, I cannot build separate ODEFunction for different models. Therefore, I traverse all equations of a model to complete the computation of all input variables required to solve the ODEProblem in advance. But after building it, I found that my calculation method greatly affects the solving performance of the ODEProblem. The reference code is as follows:

```
# import pkg
using OrdinaryDiffEq
using Interpolations
using CSV
using DataFrames
using SciMLSensitivity
using BenchmarkTools
# read example data and interpolate them
file_path = "E:\\JlCode\\LumpedHydro.jl\\data\\exphydro\\01013500.csv"
data = CSV.File(file_path);
df = DataFrame(data);
ts = 1:10000
lday_vec = df[ts, "dayl(day)"]
prcp_vec = df[ts, "prcp(mm/day)"]
temp_vec = df[ts, "tmean(C)"]
flow_vec = df[ts, "flow(mm)"]
itp_method = SteffenMonotonicInterpolation()
itp_Lday = interpolate(ts, lday_vec, itp_method)
itp_P = interpolate(ts, prcp_vec, itp_method)
itp_T = interpolate(ts, temp_vec, itp_method)
```

Then there is the normal version

```
# this is the normal version of ODEProblem for OrdinaryDiffEq
step_fct(x) = (tanh(5.0 * x) + 1.0) * 0.5
# snow precipitation
Ps(P, T, Tmin) = step_fct(Tmin - T) * P
# rain precipitation
Pr(P, T, Tmin) = step_fct(T - Tmin) * P
# snow melt
M(S0, T, Df, Tmax) = step_fct(T - Tmax) * step_fct(S0) * minimum([S0, Df * (T - Tmax)])
# evapotranspiration
PET(T, Lday) = 29.8 * Lday * 0.611 * exp((17.3 * T) / (T + 237.3)) / (T + 273.2)
ET(S1, T, Lday, Smax) = step_fct(S1) * step_fct(S1 - Smax) * PET(T, Lday) + step_fct(S1) * step_fct(Smax - S1) * PET(T, Lday) * (S1 / Smax)
# base flow
Qb(S1, f, Smax, Qmax) = step_fct(S1) * step_fct(S1 - Smax) * Qmax + step_fct(S1) * step_fct(Smax - S1) * Qmax * exp(-f * (Smax - S1))
# peak flow
Qs(S1, Smax) = step_fct(S1) * step_fct(S1 - Smax) * (S1 - Smax)
function exp_hydro_optim_states!(dS, S, ps, t)
f, Smax, Qmax, Df, Tmax, Tmin = ps
Lday = itp_Lday(t)
P = itp_P(t)
T = itp_T(t)
Q_out = Qb(S[2], f, Smax, Qmax) + Qs(S[2], Smax)
dS[1] = Ps(P, T, Tmin) - M(S[1], T, Df, Tmax)
dS[2] = Pr(P, T, Tmin) + M(S[1], T, Df, Tmax) - ET(S[2], T, Lday, Smax) - Q_out
end
```

and a modified version to adapt to flexible solutions.

```
step_fct(x) = (tanh(5.0 * x) + 1.0) * 0.5
# snow precipitation
Ps(i, p) = step_fct(p[:Tmin] - i[:T]) * i[:P]
# rain precipitation
Pr(i, p) = step_fct(i[:T] - p[:Tmin]) * i[:P]
# snow melt
M(i, p) = step_fct(i[:T] - p[:Tmax]) * step_fct(i[:S0]) * minimum([i[:S0], p[:Df] * (i[:T] - p[:Tmax])])
# evapotranspiration
PET(i, p) = 29.8 * i[:Lday] * 0.611 * exp((17.3 * i[:T]) / (i[:T] + 237.3)) / (i[:T] + 273.2)
ET(i, p) = step_fct(i[:S1]) * step_fct(i[:S1] - p[:Smax]) * PET(i, p) + step_fct(i[:S1]) * step_fct(p[:Smax] - i[:S1]) * PET(i, p) * (i[:S1] / p[:Smax])
# base flow
Qb(i, p) = step_fct(i[:S1]) * step_fct(i[:S1] - p[:Smax]) * p[:Qmax] + step_fct(i[:S1]) * step_fct(p[:Smax] - i[:S1]) * p[:Qmax] * exp(-p[:f] * (p[:Smax] - i[:S1]))
# peak flow
Qs(i, p) = step_fct(i[:S1]) * step_fct(i[:S1] - p[:Smax]) * (i[:S1] - p[:Smax])
func_list = [Ps, Pr, M, PET, ET, Qb, Qs]
function exp_hydro_optim_states!(dS, S, ps, t)
p = namedtuple([:f, :Smax, :Qmax, :Df, :Tmax, :Tmin], collect(ps))
Lday = itp_Lday(t)
P = itp_P(t)
T = itp_T(t)
fluxes = (Lday=Lday, P=P, T=T, S0=S[1], S1=S[2])
for func in func_list
tmp_fluxes = namedtuple([nameof(func)], [func(fluxes, p)])
fluxes = merge(fluxes, tmp_fluxes)
end
dS[1] = fluxes[:Ps] - fluxes[:M]
dS[2] = fluxes[:Pr] + fluxes[:M] - fluxes[:ET] - fluxes[:Qb] - fluxes[:Qs]
end
```

In this modified code, I use namedtuple to store and continuously update the calculated variables, but this seems to seriously affect the performance of ODEProblem solving, see the performance comparison below.

```
t_out = 1:10000
prob = ODEProblem(exp_hydro_optim_states!, [0.0, 1303.004248], Float64.((t_out[1], maximum(t_out))))
@btime sol = solve(prob, Tsit5(), u0=[0.0, 1303.004248],
p=[0.01674478, 1709.461015, 18.46996175, 2.674548848, 0.175739196, -2.092959084],
saveat=t_out, reltol=1e-3, abstol=1e-3, sensealg=ForwardDiffSensitivity())
```

The computing performance of the normal version is:

```
14.956 ms (1006304 allocations: 20.71 MiB)
```

The modified version is:

```
451.091 ms (5540900 allocations: 180.06 MiB)
```

I would like to ask if there is a better solution here that ensures both code flexibility and, as much as possible, improves computational performance.

PS: I have tried building the ODEProblem using ModelingToolkit.jl, which does indeed solve this problem, but it has some limitations in parameter optimization.