Why inverse-surrogate ML model failed in practical jumper design?
Why inverse-surrogate learning sounds promising—but breaks in practice
Inverse engineering with a learned generator looks elegant: feed system conditions and targets in, get a geometry out. In theory, you encode all engineering requirements as differentiable losses and let the model learn the trade-offs. In practice—especially for jumper configuration—manufacturing limits, discrete choices, and non-negotiable constraints collide with a single differentiable objective. The result is loss functions that are hard to tune, easy to game, and brittle at inference. This article explains why the inverse-surrogate approach is ill-suited here and why a forward-only, constraint-filtering workflow aligns better with how engineers actually design jumpers.
The inverse design workflow in detail
Let \(S \in \mathbb{R}^{25}\) denote the system variables. Let \(G \in \mathbb{R}^{7}\) be the seven segment lengths that parameterize the jumper geometry. The frozen forward model \(f_\phi\) maps the scaled concatenation \(X = [G, S] \in \mathbb{R}^{32}\) to two unity values \(U \in \mathbb{R}^2\).
In an inverse-surrogate setup, one trains a learnable inverse model \(g_\theta\) that proposes a geometry given system variables and design intents. The inverse network outputs a geometry proposal \(G = g_\theta(\cdot)\). The forward pass applies the same feature scaling and evaluates unity via \(U = f_\phi(\operatorname{scale}([G, S]))\).
The training objective is a scalar loss \(\mathcal{L}(\theta; \cdot)\). Parameters solve
\[\min_{\theta} \, \mathbb{E}[\, \mathcal{L}(\theta; S, D, m, u^*, \Delta h, z)\,].\]
The gradient follows the chain rule through the frozen forward model and the inverse generator,
\[\nabla_{\theta} \, \mathcal{L} = \frac{\partial \mathcal{L}}{\partial U} \cdot \frac{\partial U}{\partial X} \cdot \frac{\partial X}{\partial G} \cdot \frac{\partial G}{\partial \theta}, \quad U = f_\phi(X),\; X = [G,S],\; G = g_\theta(\cdot).\]
A prototypical loss—and how it becomes a minefield
A realistic loss aggregates several objectives with weights:
\[\mathcal{L} = w_u\,\mathcal{L}_{\text{unity}} + w_{\text{span}}\,\mathcal{L}_{\text{span}} + w_h\,\mathcal{L}_{\text{height}} + w_b\,\mathcal{L}_{\text{belly}} + w_s\,\mathcal{L}_{\text{sym}} + w_d\,\mathcal{L}_{\text{div}}.\]
With \(U = f_\phi(\operatorname{scale}([G,S]))\) and \(u_{\max} = \max(U_1, U_2)\):
\[\mathcal{L}_{\text{unity}} = \mathbf{1}_{\text{moderate}}(S)\, (u_{\max} - u^*)^2 + \mathbf{1}_{\text{extreme}}(S)\, u_{\max}^2.\]
The span requirement keeps \(s(G) = g_2 + g_4 + g_6\) within tolerance of \(D\):
\[\mathcal{L}_{\text{span}}(G,D) = \Bigg(\max\!\Big\{0, \frac{|s(G) - D|}{D+\delta} - \varepsilon\Big\}\Bigg)^2.\]
A hard height cap \(H_{\max}\) with \(H(G) = g_1 + g_3 + g_5 + g_7\):
\[\mathcal{L}_{\text{height}}(G) = [ H(G) - H_{\max} ]_+^2, \quad [x]_+ = \max(x,0).\]
Belly clearance inequality \(B(G,S) \ge B_{\min}\) as a surrogate:
\[\mathcal{L}_{\text{belly}}(G,S) = [ B_{\min} - B(G,S) ]_+^2.\]
Symmetry when hubs are nearly level:
\[\mathcal{L}_{\text{sym}}(G, \Delta h) = \mathbf{1}_{\{|\Delta h|<\tau\}}\, |g_3 - g_5|.\]
Diversity across a batch:
\[\mathcal{L}_{\text{div}}(\{G_i\}) = \frac{1}{B}\sum_{i=1}^B \exp\!\left(-\frac{\min_{j\ne i} \lVert G_i - G_j \rVert_2}{\sigma}\right).\]
Despite careful formulation, competing terms often lead to brittle optimization and designs that exploit the loss rather than meet engineering rules.
Why balancing these terms is intrinsically brittle
Objectives embody incompatible incentives (unity rewards flexibility; manufacturability caps height; span alignment can fight height, etc.). A single scalar objective cannot encode lexicographic engineering practice—feasible first, then optimal—without either zeroing gradients outside feasibility (stalling learning) or allowing violations inside the loss (failures at inference under shift).
A forward-only workflow that matches engineering practice
Use a forward-only approach: search under hard constraints and select the best feasible design by clear priorities. Enforce exact rules (height cap, span tolerance, discrete stock options, belly clearance, symmetry policies) with validators, generate candidates within bounds (sampling, templates, proposal samplers), evaluate in batch with the frozen forward model, and select lexicographically (feasible → minimize \(\max(U)\) → tie-break by height/material/robustness). If no feasible design exists, report it explicitly.
Conclusion
Inverse-surrogate training forces soft penalties and straight-through projections onto inherently discrete, non-smooth constraints, yielding brittle optimization and infeasible outputs. A forward-only pipeline with hard filters and principled search reflects actual engineering practice and provides dependable results for jumper configuration design.