Fixing SDE algorithms (EM and SIEA) for Metal #380
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| _saveat = get(prob.kwargs, :saveat, nothing) | ||
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| saveat = _saveat === nothing ? saveat : _saveat |
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this should be retained
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| # no need for n; just advance until t reaches t1 | ||
| # tolerance avoids off-by-one from fp error | ||
| tol = eps(Tt) * abs(t1) + Tt(1e-7) * dt | ||
| while t + dt <= t1 + tol | ||
| uprev = u | ||
| u = uprev + f(uprev, p, t) * dt + sqdt * g(uprev, p, t) .* randn(typeof(u0)) | ||
| t += dt | ||
| end | ||
| if saveat === nothing && !save_everystep | ||
| @inbounds us[2] = u | ||
| @inbounds ts[2] = t |
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Suggested change
| # no need for n; just advance until t reaches t1 | |
| # tolerance avoids off-by-one from fp error | |
| tol = eps(Tt) * abs(t1) + Tt(1e-7) * dt | |
| while t + dt <= t1 + tol | |
| uprev = u | |
| u = uprev + f(uprev, p, t) * dt + sqdt * g(uprev, p, t) .* randn(typeof(u0)) | |
| t += dt | |
| end | |
| if saveat === nothing && !save_everystep | |
| @inbounds us[2] = u | |
| @inbounds ts[2] = t | |
| while t <= t1 + tol | |
| uprev = u | |
| u = uprev + f(uprev, p, t) * dt + sqdt * g(uprev, p, t) .* randn(typeof(u0)) | |
| t += dt | |
| end | |
| if saveat === nothing && !save_everystep | |
| @inbounds us[2] = u | |
| @inbounds ts[2] = t |
Needs to stop one step earlier otherwise the final point will be saved twice
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| elseif saveat !== nothing | ||
| while cur_t <= length(saveat) && saveat[cur_t] <= t | ||
| savet = saveat[cur_t] | ||
| Θ = (savet - (t - dt)) / dt | ||
| # Linear Interpolation | ||
| @inbounds us[cur_t] = uprev + (u - uprev) * Θ | ||
| @inbounds ts[cur_t] = savet | ||
| cur_t += 1 | ||
| end | ||
| else |
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This isn't right, the linear interpolation code is needed. The else branch doesn't actually support saveat or use it
modified: src/ensemblegpukernel/perform_step/gpu_siea_perform_step.jl
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I rewrote the fix to change as little as possible compared to before. |
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The last step isn't correct with this because of accumulation error, for example 0.1+0.10.1 != 0.3 because it is larger. So the last step should at least be corrected to match the tspan[2] |
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#383 is a more correct way here |
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Add any other context about the problem here.
With the suggested code changes the algorithms run using Metal (when saveat is not specified).
Code was generated with the help of AI. Given that I am no expert, code could require review.