Add correction inference metrics and optional correction netCDF output

[jpdunc23]

Steppers can apply correctors (e.g. ocean heat content, global dryness) that adjust the network's raw output each step, but today there is no way to see how much a trained model relies on its corrector. This PR adds normalized-space metrics of the correction (output − uncorrected) to the inference aggregators and an optional denormalized correction netCDF, on by default behind aggregator config flags. It builds on the StepOutput.uncorrected plumbing from #1283 (PR1, base branch) and additionally carries that shadow up to the aggregators on a time-aware diagnostics carriage. The uncorrected/-prefixed error metrics from #1222 are intentionally dropped in favor of metrics of the correction itself.

Per review on #1283, the consumer-facing plumbing that surfaces the pre-correction shadow on prediction data was moved out of that PR into this one, and reworked into an opaque, encapsulated carriage (rather than a raw uncorrected field) so it cannot be silently dropped by BatchData/PairedData methods.

Changes:

• fme.ace.data_loading.step_diagnostics.StepDiagnostics (new) — an opaque, time-aware carriage holding the per-step uncorrected series (today the only diagnostic). It validates its leading sample dim and exposes the structure-preserving operations (device movement, time slicing, ensemble broadcast, spatial scatter, pin-memory) so the container can be forwarded and time-sliced alongside data without BatchData inspecting its contents.
• fme.ace.data_loading.batch_data — BatchData.step_diagnostics / PairedData.step_diagnostics optional fields (following the data_mask/stepper_state precedent), threaded through every structure-preserving method via the container protocol and time-sliced by the time-touching methods, so compute_derived_variables and friends cannot silently drop or misalign it.
• fme.ace.stepper.single_module.Stepper.predict — stacks the per-step StepOutput.uncorrected shadows into a forward-step-aligned series, wraps it in StepDiagnostics, and attaches it to the final prediction after the IC-windowing pipeline.
• fme.ace.aggregator.inference.correction (new) — CorrectionTimeMeanAggregator (time_mean_norm/correction_magnitude/{var} area-weighted global mean of the time-mean of |normalized correction|, a channel_mean over corrected variables only, and the signed time_mean_norm/correction_map/{var} image), CorrectionMeanAggregator (mean_norm/weighted_correction_magnitude/{var} and mean_norm/weighted_correction_std/{var} per-step series), and a shared CorrectionRecorder. Corrections are normalize(output) − normalize(uncorrected) per corrected key using the network normalizer.
• fme.ace.aggregator.inference.main — log_correction_metrics: bool = True on both InferenceEvaluatorAggregatorConfig and InferenceAggregatorConfig; the recorder is wired into both aggregators' record/summary/time-series/diagnostics paths. Correction metrics merge into the existing time_mean_norm / mean_norm groups (and are the only members of those groups for no-target inference). The no-target aggregator now accepts the stepper's network normalizer; correction metrics are skipped when no normalizer is supplied (backward compatible).
• fme.ace.inference.inference — passes stepper.normalizer.normalize into the no-target aggregator build.
• fme.ace.inference.data_writer.main — save_correction_files: bool = False on DataWriterConfig writes autoregressive_corrections.nc with the denormalized correction time series for the sparse corrected variables, respecting the save-names subset and time-coarsening, via a single-source writer in PairedDataWriter.

Availability: time-mean metrics in all inference types; time-series metrics only in standalone evaluator and no-target inference (inline training drops them via the existing enable_time_series path). Defaults preserve current behavior except the newly logged metrics for corrector-equipped runs; correction-file saving is off by default.

• Tests added
• If dependencies changed, "deps only" image rebuilt and "latest_deps_only_image.txt" file updated

Tests: test_batch_data parametrized tests asserting step_diagnostics survives every structure-preserving method (including compute_derived_variables) on both BatchData and PairedData, the absent/None pass-through, post-init sample-dim validation, scatter, and pin-memory; aggregator unit tests asserting exact magnitude/std/map/channel_mean values for a constant-offset correction plus the flag-off and no-corrector silence paths; writer tests for the sparse denormalized file including time-coarsening and the empty-without-corrector case; config validation/defaults tests; and an end-to-end train+inference test (test_train_and_inference_correction_metrics) asserting time-mean correction metrics appear in inline training inference with the per-step series dropped, the per-step series appear in standalone inference, and autoregressive_corrections.nc is written.

Stacked on #1283 (PR1) — base branch is feature/step-output; retarget to main once that merges.

Resolves #1272

🤖 Generated with Claude Code

[jpdunc23]

Agent chose StepDiagnostic as opposed to @mcgibbon 's original StepMetrics, reasoning "since the payload is diagnostic input, not a metric".

[mcgibbon]

Issue: I think this can't distinguish between a value with a zero-correction from the corrector, and a value that isn't affected by the corrector. If true, this could easily lead to bugs like under-estimation of means by dropping zero entries, if we use this as a sentinel for variables the corrector doesn't touch.