Bridging optical and thermoelastic simulations with surrogate models for system-level design

Automated co‑design of optics and mechanics under inhomogeneous thermoelastic loading, such as radiation heating or constrained thermal expansion, can require fast and physically meaningful separation of rigid‑body motion (RBM) from surface‑figure deviation (SFD) in mesh‑based point clouds originating from finite‑element analysis (FEA). For optical ray‑tracing, a polynomial prescription of the perturbed surface is desirable. We present a proof‑of‑concept inverse modelling approach that learns this separation directly from data generated by simulation‑driven Design of Experiments (DoE). Synthetic point clouds are created by sampling realistic RBM and freeform SFD ranges; inverse Gaussian‑process regressors are then trained in a two‑step hierarchy: individual single-output models first retrieve RBM, after which a single multioutput model estimates the polynomial SFD coefficients from the RBM‑corrected point cloud. To stress‑test robustness under prescription ambiguity, we employ XY‑polynomial bases for optical freeform surface prescription, whose correlated monomials typically complicate accurate RBM/SFD separation. External validation on independent datasets drawn from distinct DoEs shows that the hierarchical surrogate reliably recovers both RBM and SFD with high accuracy, with test cases exceeding 99.9999% accuracy on synthetic ground truth. This precision is compatible with six‑sigma process capability and enables millisecond‑scale retrieval suitable for inner loops of opto‑thermo‑mechanical optimisation, surrogate modelling of full optical systems, and compensator/control co‑design. Beyond accuracy, the method integrates cleanly with common optical and finite‑element toolchains via Python.