Ingot

Optimizer

Target problem

Ingot targets expensive, noisy, small-data, multi-objective, constrained sequential experiments. Optical-lens molding fits this problem: every run consumes equipment, material, and inspection capacity; process variation exists; parameter dimension is limited; objectives and safety outcomes are measurable.

Why not an LLM or a deep network

  • An LLM has no calibrated numerical uncertainty and does not generate recipes.
  • Deep networks usually need more data than one campaign can provide.
  • A GP provides both a mean and uncertainty in small data.
  • Bayesian optimization balances exploration and exploitation with that uncertainty.

LLMs may explain, retrieve, or draft structured intent. Deterministic numerical code makes recommendations.

Two-stage surrogate

Quality depends on the realized trajectory, not only the setpoint:

control settings x
  ├─ GP₁: x → realized process features z
  └─ GP₂: [x, z] → objectives y and safety outcomes c

GP₂ trains on measured features. For a new recipe, GP₁ predicts trajectory features before GP₂ evaluates quality.

Only process features common to all training observations enter the current model, avoiding implicit missing-value fabrication.

Objectives

Supported shapes:

  • less than or equal to specification;
  • greater than or equal to specification;
  • target ± tolerance;
  • acceptable range;
  • objective weights.

For multiple objectives, normalized specification utility enters qLogNEHVI to improve the constrained Pareto front.

Constraints

Parameter constraints

Bounds and linear <= / >= rules filter candidate generation.

Outcome constraints

Crack rate, residual stress, and similar constraints are additional GP outputs and acquisition constraints. Safety-critical outcomes also require:

P(outcome satisfies limit | current evidence) ≥ minimum safety probability

Candidates below the threshold are not returned.

Cold start

  • Without safety outcomes, use Sobol space-filling points.
  • With safety outcomes, require a verified safe baseline.
  • Keep initial exploration inside a trust region around that baseline.
  • Switch to the BoTorch GP engine after three observations.

Pending experiments

Unobserved Planned, Approved, and Running settings become X_pending and are removed from the candidate set. Repeated clicks and parallel execution do not duplicate experiments.

Stateless protocol

The optimizer stores no campaign. Every request supplies:

  • variables, objectives, and constraints;
  • all valid observations;
  • pending points;
  • batch size and seed.

The response includes settings, objective and constraint predictions, feasibility, acquisition value, model version, and rationale. Platform persists the snapshot and result.

Current limits

  • The trajectory surrogate currently feeds posterior means, not the full trajectory posterior, into the quality model.
  • GP 95% intervals are approximate and are not a factory guarantee.
  • Cross-product multi-task GP is not complete.
  • Physical features exist, but a calibrated grey-box prior mean is not complete.
  • Real replay must measure calibration, regret, and experiments-to-specification.