rtx-fea: mor gains total-Lagrangian operators and a held-out ECSW residual

The mor scope was small-strain only ("geometrically linear") — a basis
trained on total-Lagrangian trajectories (the FSI flag marches
with_total_lagrangian) sampled through small-strain operators would
conserve the virtual work of the wrong force. ElementOperator now
carries a Formulation (SmallStrain | TotalLagrangian), the TL branch
mirroring NonlinearDynamicAnalysis exactly (SVK from Lame parameters,
total_lagrangian::internal_force_and_tangent); train_ecsw /
ReducedNonlinearModel::new keep their behavior and delegate, with
_formulated variants added. ecsw_residual evaluates a trained model's
||Cw - b||/||b|| on arbitrary snapshots — the held-out generalization
measurement; on the training set it reproduces training_residual to
1e-12 (pinned).

Verified sharply: identity-basis reduced TL solve vs a
tight-tolerance full TL solve agrees to 4.4e-15 (machine precision)
while small-strain operators land 1.1e-2 away at the same load — the
switch is exercised and exact. (At the default 1e-6 convergence
criteria the reference itself stops 1.7e-4 short; measured and
recorded in the test comment.)

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

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

@@ -13,17 +13,20 @@
 //! 4. [`reduced::ReducedNonlinearModel`] — Newton in reduced coordinates,
 //!    assembling only the sampled elements.
 //!
-//! Scope: geometrically linear, materially nonlinear (what the nonlinear
-//! analysis supports), homogeneous Dirichlet data. Lifting for
-//! inhomogeneous boundary values is not implemented and the basis is over
-//! the free DOFs only.
+//! Scope: homogeneous Dirichlet data; the basis is over the free DOFs
+//! only (lifting for inhomogeneous boundary values is not implemented).
+//! Kinematics are selected per [`reduced::Formulation`]: the original
+//! small-strain scope (geometrically linear, materially nonlinear), or
+//! total-Lagrangian Saint Venant–Kirchhoff matching
+//! `NonlinearDynamicAnalysis::with_total_lagrangian` — required when the
+//! snapshots come from a total-Lagrangian trajectory (the FSI flag).
 
 pub mod ecsw;
 pub mod nnls;
 pub mod pod;
 pub mod reduced;
 
-pub use ecsw::{EcswModel, train_ecsw};
+pub use ecsw::{EcswModel, ecsw_residual, train_ecsw, train_ecsw_formulated};
 pub use nnls::nnls;
 pub use pod::pod_basis;
-pub use reduced::ReducedNonlinearModel;
+pub use reduced::{Formulation, ReducedNonlinearModel};