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Resolve reduced derivative trend with a recorded four-step diagnostic grid

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This commit is contained in:
Emily Boudreaux
2026-09-17 10:09:24 -04:00
parent 2e31917269
commit b7ea1bdcf8
2 changed files with 36 additions and 1 deletions
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24
experiments/GRAVITY_REDUCTION_IMPLEMENTATION_2026-09-17.md
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@@ -91,3 +91,27 @@ The focused test source `tests/solver/gravity_reduction.cpp` covers:
These algebraic tests establish the reduction contract. They do not establish
FEM convergence, a faster implementation, or an additional virial-qualified
stellar equilibrium; those require the integrated runtime experiments.
## Resolved FEM difference sampling
The first frozen n=1.5 probe completed all gravity solves and preparations. Its
central-difference errors at steps 0.01, 0.001, and 0.0001 were respectively
`1.7761e-9`, `1.9661e-11`, and `7.1208e-11`. Only the first exceeded twenty times
the recorded arithmetic scale. The observed first-interval order was about
1.956, but the conservative checker correctly left the trend unresolved because
the finer endpoint did not meet its resolution criterion.
The diagnostic now uses the explicit, validated step array `{0.1, 0.03, 0.01,
0.001}` and records it in the summary. The larger steps test whether truncation
dominates sufficiently to reveal a central-difference trend; retaining 0.001
also preserves an independent small-step accuracy check. This adds one central
pair, hence at most four extra gravity correction solves under the existing
two-correction completion budget. The inner tolerance, prepared completion gate,
and checker thresholds are unchanged. There is no assumption that larger steps
will prepare successfully or automatically pass the trend check.
These remain finite-range empirical derivative checks. The recorded arithmetic
scale is heuristic, and a gravity residual bound by itself is not a bound on its
amplified effect in the retained equations. The larger grid is intended to
resolve a measurable trend without claiming such an unmeasured amplification
bound or interpreting floor-limited differences as derivative failures.

13
experiments/plateau_numerical_strategy_diagnostics.hpp
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@@ -19,6 +19,9 @@ struct NumericalStrategyProbeOptions final {
int restartLength{80};
int maximumCompletionCorrections{2};
double gravityCompletionTolerance{1.e-11};
// Coarser differences resolve truncation before cancellation dominates;
// the final small step independently checks derivative accuracy.
std::array<double, 4> reducedDifferenceSteps{.1, .03, .01, .001};
};
namespace numerical_strategy_detail {
@@ -55,6 +58,12 @@ void ProbeNumericalStrategies(
if (options.restartLength <= 0 || options.maximumCompletionCorrections <= 0 ||
!std::isfinite(options.gravityCompletionTolerance) || options.gravityCompletionTolerance <= 0.)
throw std::invalid_argument("Numerical strategy probes require valid inner and completion controls.");
double previousDifferenceStep = std::numeric_limits<double>::infinity();
for (const double step : options.reducedDifferenceSteps) {
if (!std::isfinite(step) || step <= 0. || step >= previousDifferenceStep)
throw std::invalid_argument("Reduced finite-difference steps must be finite, positive, and strictly decreasing.");
previousDifferenceStep = step;
}
int ranks = 0;
MPI_Comm_size(state.Problem().GetCommunicator(), &ranks);
if (ranks != 1 || !finiteElements.mesh || normalizedBase.Size() != state.Problem().StateSize() ||
@@ -92,6 +101,8 @@ void ProbeNumericalStrategies(
<< "\ninner_maximum_iterations," << options.inner.maximumIterations
<< "\ninner_restart_length," << options.restartLength
<< "\ngravity_completion_tolerance," << options.gravityCompletionTolerance << '\n';
for (std::size_t index = 0; index < options.reducedDifferenceSteps.size(); ++index)
summary << "reduced_difference_step_" << index << ',' << options.reducedDifferenceSteps[index] << '\n';
const double nan = std::numeric_limits<double>::quiet_NaN();
int preparationCount = 0;
double restorationError = 0.;
@@ -281,7 +292,7 @@ void ProbeNumericalStrategies(
<< "\nlifted_gravity_action_norm," << gravityResidual.Norml2()
<< "\nlifted_retained_action_difference," << d::Difference(retainedAction, reducedAction)
<< "\ncompleted_base_residual_norm," << completedBaseResidual.Norml2() << '\n';
for (const double alpha : {1.e-2, 1.e-3, 1.e-4}) {
for (const double alpha : options.reducedDifferenceSteps) {
std::array<mfem::Vector, 2> residuals{mfem::Vector(base.Size()), mfem::Vector(base.Size())};
std::array<bool, 2> completed{};
std::array<double, 2> gravityNorms{nan, nan};