Dead species coming back alive

[ChrisRackauckas]

This was noted in the MWE https://github.com/HelgavonLichtenstein/Food-Webs by @HelgavonLichtenstein.

I created a debugging script https://github.com/HelgavonLichtenstein/Food-Webs/pull/2 to see what's going on. The end result is captured in:

(A\b)[101] # -2.6218322568017613e-23
(sparse(A)\b)[101] # -0.0 

Basically, the linear solver introduces a numerical error which then revives a dead quantity. It's dead because:

function condition(out, bioS, t, integrator)
    # extinction threshold for species
    out[1:(num_plant+num_animal)] .= bioS[(num_nutrient+1):(index_vessel-1)] .- 1e-6
end

function affect!(integrator, event_idx)
    integrator.p[1][event_idx+num_nutrient] = 0.0
    integrator.u[event_idx+num_nutrient] = 0.0
    @show event_idx[], integrator.t
end

enforces u == 0 and du == 0 for that component, yet it can still revive because:

  if repeat_step
    linres = dolinsolve(integrator, cache.linsolve; A = nothing, b = _vec(linsolve_tmp),
                        du = cache.fsalfirst, u = u, p = p, t = t, weight = weight, solverdata = (;gamma = dtgamma))
  else
    linres = dolinsolve(integrator, cache.linsolve; A = W, b = _vec(linsolve_tmp),
                        du = cache.fsalfirst, u = u, p = p, t = t, weight = weight, solverdata = (;gamma = dtgamma))
  end

  @inbounds @simd ivdep for i in eachindex(u)
    k1[i] = -linres.u[i]
  end
  integrator.destats.nsolve += 1

  @inbounds @simd ivdep for i in eachindex(u)
    u[i] = uprev[i] + a21*k1[i]
  end
  @show u[101], uprev[101], k1[101]

in the numerical error of k1 introduced by the factorization. Sparse matrices can impose this as a true zero, though that can lose performance for smaller sizes. The right answer is probably just doing u[101] = 0 in the ODE, at least for performance.

[ChrisRackauckas]

Interestingly, the only way for a user to have a chance against this is to have mutation, so score 1 point for the lack of safety in mutation!

function dBdT(dB, bioS, p, t)

    # extinction_parameter[1], D[2], S[3], K[4], v[5], r[6], X[7], num_nutrient[8], num_plant[9], num_animal[10],
    # num_vessel_types[11], bm[12], foodWeb[13], b[14], q[15], ω[16], c[17], h[18], e[19], target_species[20],
    # catch_max[21], b0V[22], μ[23], elasticity[24], clearance_V_type[25], harvested_species[26], weighted_fish_price[27]

    dB .= 0.0 # if removed results in [CVODES ERROR]  CVode
              # At t = 0 and h = 0.412902, the corrector convergence test failed repeatedly or with |h| = hmin.
    catch_F = zeros(num_vessel_types)

    for i in (num_nutrient+1):(index_vessel-1)
        if iszero(p[1][i])
            bioS[i] = 0.0 #safety against https://github.com/SciML/OrdinaryDiffEq.jl/issues/1651
        end
    end

while this is usually not a good idea, in this case we know that the error is <eps() and so the error estimate won't find it, so in this case it's a good idea as it will effectively correct the linear solver error.

[ChrisRackauckas]

For reference:

A = [
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(A\b)[101] # -2.6218322568017613e-23
(sparse(A)\b)[101] # -0.0