Caelum: Self-Evolving Compilation of Forward–Inverse CAE Optimizers

Inverse design is the promise of learned physics surrogates: differentiate through the surrogate, and simulation data becomes better geometry. Realizing it on a new dataset still demands a hand-built pipeline and dozens of expert decisions. The common remedy is to pretrain one large model across regimes. Yet CAE data is proprietary and rarely poolable, so specializing to each dataset is the more practical path. We present Caelum, a self-evolving compiler for this setting: from a raw CAE dataset it emits one deployable forward–inverse optimizer that predicts physical fields and reshapes geometry through them, specialized to its dataset and never leaving its owner. Our key insight is that build expertise is itself learnable. A simulation label costs a solver run, but an alternative build decision costs only retraining on data already in hand, so counterfactual build sweeps turn fifteen datasets into hundreds of process-rewarded preference pairs. Confirmed lessons harden into rules and precedents, and rule-residual preference optimization (RRPO) then tunes the language model only on decisions no rule can answer. Caelum ships every optimizer end-to-end across fifteen datasets from four physics domains. On frozen decision boards it answers every regime probe that frontier models miss and cuts the decision loss from 22.4 R2 points to 0.1. Design-loop construction becomes a self-evolving compilation process.