rtx-fsi: ECSW phase-2 offline study — POD subspace confirmed, hyperreduction refuted at this resolution

fsi3_ecsw_offline.rs (env-gated on RTX_ECSW_SNAP; committed default is
a no-op) measures the three pre-registered quantities on the harvested
run-7 flag trajectory, with a numbering self-check (clamped-DOF
displacement exactly 0.0 across all 3,294 snapshots).

Measured: (1) the flapping manifold compresses 560 free DOFs to 12-20
POD modes at ~0.5% held-out rms projection error — the subspace
exists. (2) ECSW has NOTHING TO EXPLOIT on the 70-element flag: the
NNLS residual sits at single-element scale until nearly every element
joins (31 el -> 10%, 51 -> 10%, 67 -> 2.5%, 70 -> 1e-15; held-out ==
training everywhere; cycle-only manifold identical) — each macroscopic
Quad8 carries non-redundant virtual work, so no sub-percent sample
smaller than the mesh exists. (3) full reduced assembly 548 us/eval;
ECSW at best 1.4x at a useless 10% residual.

ReducedNonlinearModel gains assemble_reduced_force (the measured
quantity). The campaign's >=10x structural gate cannot come from
hyperreduction at the validated resolution — recorded in the campaign
doc with the re-scope options.

Co-Authored-By: Claude Fable 5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01X2GmJXeQ2njUecEKiJZ1G2

crates/specialized/rtx-fea/src/mor/reduced.rs

@@ -245,6 +245,28 @@ impl<'a> ReducedNonlinearModel<'a> {
         self.active.len()
     }
 
+    /// Assemble the weighted reduced internal force `Σ w_e V_e' f_e(u)`
+    /// over the active element set at a full free-DOF displacement — the
+    /// per-Newton-iteration cost ECSW reduces, exposed for wall-clock
+    /// measurement (full-active vs sampled model on the same states).
+    pub fn assemble_reduced_force(
+        &self,
+        free_displacement: &DVector<f64>,
+    ) -> FeaResult<DVector<f64>> {
+        let modes = self.basis.ncols();
+        let spatial_dim = self.mesh.spatial_dimension;
+        let mut force = DVector::zeros(modes);
+        for &(index, weight) in &self.active {
+            let reduced = self.operators[index].reduced_internal_force(
+                self.materials,
+                spatial_dim,
+                free_displacement,
+            )?;
+            force += reduced * weight;
+        }
+        Ok(force)
+    }
+
     /// Newton in reduced coordinates: solve
     /// `V' f_int(V q) = V' f_ext` and return the expanded free-DOF
     /// displacement `V q`.