StressPy: Geometric Stress Criterion (GSC)

stresspy is a reference Python implementation of the deterministic numerical core of the Geometric Stress Criterion (GSC). It decomposes model–data discrepancies into components that are locally accessible (tangent) and inaccessible (normal) through parameter variation.

1. Mathematical Background

At a specified parameter point $\hat{\theta}$, let $r = y - f(\hat{\theta})$ be the model–data discrepancy and $J = \left.\frac{\partial f}{\partial x}\right\vert{}_{\hat{\theta}}$ be the Jacobian with respect to parameter coordinates $x$.

After applying an observation-space whitening transformation $L$: $$r_W = Lr, \qquad J_W = LJ$$

If $U_r$ contains the retained left singular vectors of $J_W$, the orthogonal components are: $$r_{\parallel,W} = U_r U_r^\top r_W, \qquad r_{\perp,W} = r_W - r_{\parallel,W}$$

The reported stresses and normal fraction are: $$S_{\mathrm{total}} = \Vert{}r_W\Vert{}2^2, \quad S{\parallel} = \Vert{}r_{\parallel,W}\Vert{}2^2, \quad S{\perp} = \Vert{}r_{\perp,W}\Vert{}2^2, \quad F{\perp} = \frac{S_{\perp}}{S_{\mathrm{total}}}$$

The minimum-norm local repair vector $\Delta x$ satisfies: $$\Delta x = V_r \Sigma_r^{-1} U_r^\top r_W$$

Under the local linear approximation, $r - J \Delta x = r_\perp$.

2. Installation

pip install stresspy