Mixed-Precision Numerical Strategy

Where Kronos uses double, single, and reduced precision across simulation and training, and why precision is a correctness decision.

Precision is chosen per workload

L0 mixes numerical precisions deliberately. Precision trades accuracy against memory and speed, and the right point differs sharply between an implicit physics solve that must converge to a tight residual and a neural-network training run that tolerates noise. Kronos assigns precision per workload, not per machine.

Double precision for the physics core

Coupled MHD, Grad-Shafranov equilibria, and thermomechanics run in double precision. These are stiff, iterative, and sometimes chaotic; single precision would let rounding accumulate into a different converged state, which breaks reproducibility. For the certified core, double precision is non-negotiable.

Reduced precision for training

PINN, GNN, and surrogate training use mixed precision: reduced-precision matrix math with a higher-precision master copy of the weights and a loss-scaling step to protect small gradients. This roughly doubles throughput and halves memory with no meaningful loss in the trained surrogate's fidelity, because the training objective is already statistical.

• Double precision: equilibrium, MHD, thermomechanics, coupled solves
• Mixed precision: PINN, GNN, surrogate, anomaly training
• Reduced precision at inference: compiled twin surrogates
• Higher-precision accumulation for reductions and dot products

Monte Carlo transport is an intermediate case. Per-history arithmetic tolerates single precision, but tallies accumulate over billions of histories, so their accumulators use higher-precision summation to avoid catastrophic cancellation. Precision is thus split within a single code: cheap per-history, careful per-tally.

At the far end, twin surrogates are quantized to reduced precision for fast inference in the 50 to 100 ms shadow. The chain runs from double-precision truth at the physics core, through mixed-precision training, to reduced-precision real-time evaluation, each step chosen so the final control decision stays inside its physics-validated envelope.