From 5b588035be00dc8f4b5cb204b1f73eee4d78d1cf Mon Sep 17 00:00:00 2001 From: Michael Zingale Date: Sun, 12 Jan 2025 12:58:54 -0500 Subject: [PATCH] update the ODE integrators docs on tolerances (#1703) this regenerates the plot comparing tolerances and includes it now as a script under burn_cell --- Docs/source/ode_integrators.rst | 101 +- Docs/source/runtime_parameters.rst | 24 - Docs/source/tolerance-compare.png | Bin 0 -> 98705 bytes Docs/source/tolerances.png | Bin 323518 -> 0 bytes unit_test/burn_cell/compare_tolerances/README | 10 + .../burn_cell/compare_tolerances/plot-tols.py | 49 + .../compare_tolerances/run_tol_compare.sh | 20 + .../state_over_time_tol_a.txt | 1002 +++++++++++++++++ .../state_over_time_tol_b.txt | 1002 +++++++++++++++++ .../state_over_time_tol_c.txt | 1002 +++++++++++++++++ .../state_over_time_tol_d.txt | 1002 +++++++++++++++++ 11 files changed, 4155 insertions(+), 57 deletions(-) create mode 100644 Docs/source/tolerance-compare.png delete mode 100644 Docs/source/tolerances.png create mode 100644 unit_test/burn_cell/compare_tolerances/README create mode 100644 unit_test/burn_cell/compare_tolerances/plot-tols.py create mode 100755 unit_test/burn_cell/compare_tolerances/run_tol_compare.sh create mode 100644 unit_test/burn_cell/compare_tolerances/state_over_time_tol_a.txt create mode 100644 unit_test/burn_cell/compare_tolerances/state_over_time_tol_b.txt create mode 100644 unit_test/burn_cell/compare_tolerances/state_over_time_tol_c.txt create mode 100644 unit_test/burn_cell/compare_tolerances/state_over_time_tol_d.txt diff --git a/Docs/source/ode_integrators.rst b/Docs/source/ode_integrators.rst index fa7eb2b14c..37386399ae 100644 --- a/Docs/source/ode_integrators.rst +++ b/Docs/source/ode_integrators.rst @@ -146,46 +146,80 @@ Tolerances Tolerances dictate how accurate the ODE solver must be while solving equations during a simulation. Typically, the smaller the tolerance is, the more accurate the results will be. However, if the tolerance -is too small, the code may run for too long or the ODE solver will -never converge. In these simulations, ``rtol`` values will set the -relative tolerances and ``atol`` values will set the absolute tolerances -for the ODE solver. Often, one can find and set these values in an -input file for a simulation. - -:numref:`fig:tolerances` shows the results of a simple simulation using the -burn_cell unit test to determine -what tolerances are ideal for simulations. -For this investigation, it was assumed that a run with a tolerance of :math:`10^{-12}` -corresponded to an exact result, -so it is used as the basis for the rest of the tests. -From the figure, one can infer that the :math:`10^{-3}` and :math:`10^{-6}` tolerances -do not yield the most accurate results -because their relative error values are fairly large. -However, the test with a tolerance of :math:`10^{-9}` is accurate -and not so low that it takes incredible amounts of computer time, -so :math:`10^{-9}` should be used as the default tolerance in future simulations. +is too small, the code may run for too long, the ODE solver will +never converge, or it might require at timestep that underflows. + +.. index:: integrator.rtol_spec, integrator.rtol_enuc, integrator.atol_spec, integrator.atol_enuc + +There are separate tolerances for the mass fractions and the energy, +and there are both relative and absolute tolerances which act together. +The tolerances are: + +* ``integrator.rtol_spec`` : the relative tolerance for the species + (mass fractions when running with Strang and partial densities when + running with SDC). + +* ``integrator.rtol_enuc`` : the relative tolerance on the energy + (specific internal energy when running with Strang, internal energy + density when running with SDC). + +* ``integrator.atol_spec`` : the absolute tolerance for the species + (this is always interpreted in terms of mass fraction and the appropriate + density weighting will be added for SDC). + +* ``integrator.atol_enuc`` : the absolute tolerance for energy -- this + is generally not interesting, since the energy is so large and therefore + best served via a relative tolerance. + +The tolerances are combined, e.g. for species, as: + +.. math:: + + \epsilon_{\mathrm{total}, k} = \epsilon_\mathrm{abs} + \epsilon_\mathrm{rel} |X_k| + +so if the mass fraction, $X_k$, is very small, then the absolute tolerance +will set the error that the integrator tries to achieve. If the mass fraction +is large, $\mathcal{O}(1)$, then the relative tolerance dominates. + +Some suggestions when setting tolerances: + +.. index:: integrator.X_reject_buffer + +* If a burn does not converge with one type of Jacobian (analytic or + numerical) then it may do better with the other type. This can be + automated via the ``integrator.use_burn_retry`` mechanism described + above. + +* Sometimes a burn completes better if the absolute tolerances are + made even smaller -- this will require the integrator to track trace + species better which can help with equilibrium better. + +* The VODE integrator has additional logic meant to ensure that + species don't change too much per timestep. This is controlled by + ``integrator.X_reject_buffer``. If a species $k$, has a mass + fraction $X_k > \mbox{X_reject_buffer} \cdot \mbox{atol_spec}$ then + we reject a VODE timestep if the mass fraction changes by more than + a factor of 4 in a single VODE timestep and we try again. This is + all done internally to VODE. Making ``X_reject_buffer`` larger will + allow it to ignore more trace species. + +Below is a comparison of how the tolerances affect the nucleosynthesis. +This is run using ``burn_cell`` and the ``aprox13`` network. Four separate +runs were done, using tolerances of $10^{-3}$, $10^{-5}$, $10^{-8}$, and $10^{-12}$ +(all 4 tolerance parameters were set to the same value). The run with the tightest +tolerances ($10^{-12}$) was taken as the reference and relative errors were +computed with respect to it. The scripts for this are in ``Microphysics/unit_test/burn_cell/compare_tolerances/``. .. _fig:tolerances: -.. figure:: tolerances.png - :alt: Relative error plot +.. figure:: tolerance-compare.png + :alt: Relative error in mass fractions :width: 100% Relative error of runs with varying tolerances as compared to a run with an ODE tolerance of :math:`10^{-12}`. -The integration tolerances for the burn are controlled by -``rtol_spec`` and ``rtol_enuc``, -which are the relative error tolerances for -:eq:`eq:spec_integrate` and :eq:`eq:enuc_integrate`, -respectively. There are corresponding -``atol`` parameters for the absolute error tolerances. Note that -not all integrators handle error tolerances the same way—see the -sections below for integrator-specific information. - -The absolute error tolerances are set by default -to :math:`10^{-12}` for the species, and a relative tolerance of :math:`10^{-6}` -is used for the temperature and energy. - +We see that using a tolerance of $10^{-5}$ generally gives reasonable mass +fractions. Looser than this can produce large errors. Controlling Species $\sum_k X_k = 1$ ==================================== @@ -222,6 +256,7 @@ constraint on the intermediate states during the integration. This is enabled by default. + Retry Mechanism =============== diff --git a/Docs/source/runtime_parameters.rst b/Docs/source/runtime_parameters.rst index e35240cd42..1d8b4ef657 100644 --- a/Docs/source/runtime_parameters.rst +++ b/Docs/source/runtime_parameters.rst @@ -767,30 +767,6 @@ namespace: ``network`` -**NETWORK_DIR=he-burn.bak/he-burn-18a:** - -+---------------------------------------+---------------------------------------------------------+------------------------------+ -| parameter | description | default value | -+=======================================+=========================================================+==============================+ -| ``disable_p_C12_to_N13`` | | 0 | -+---------------------------------------+---------------------------------------------------------+------------------------------+ -| ``disable_He4_N13_to_p_O16`` | | 0 | -+---------------------------------------+---------------------------------------------------------+------------------------------+ - - - -**NETWORK_DIR=he-burn.bak/he-burn-22a:** - -+---------------------------------------+---------------------------------------------------------+------------------------------+ -| parameter | description | default value | -+=======================================+=========================================================+==============================+ -| ``disable_p_C12_to_N13`` | | 0 | -+---------------------------------------+---------------------------------------------------------+------------------------------+ -| ``disable_He4_N13_to_p_O16`` | | 0 | -+---------------------------------------+---------------------------------------------------------+------------------------------+ - - - **NETWORK_DIR=metal_chem:** +---------------------------------------+---------------------------------------------------------+------------------------------+ diff 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