Neural Operators for Field Surrogates

Neural operators learn the mapping from parameters to entire physical fields, giving Kronos fast, resolution-flexible surrogates for transport and thermal solves.

Learning operators, not points

Many twin quantities are not single numbers but whole fields: the neutron flux over the blanket, the temperature over the divertor, the strain over a magnet. A neural operator learns the solution operator, the mapping from input functions (source profile, boundary conditions, material properties) to the output field, rather than a point-to-point regression. This lets one trained model return the field for a range of inputs and, for the Fourier-operator family, at flexible resolution.

Where Kronos applies them

• Neutronics: source and geometry -> flux and spectrum field (distilling Monte Carlo)
• Thermomechanics: heat sources and boundaries -> temperature and strain fields
• Divertor/expander: upstream conditions -> heat-flux footprint
• Burner DEC: end-loss distribution -> conversion-stage loading

Neural operators are attractive for these because they are mesh-flexible and generalize across the parametric operating space, so the twin can query a new operating point without a fresh Monte Carlo or FEM run. They pair naturally with reduced-order representations, the operator can output modal coefficients rather than a dense field, cutting cost further.

Physics and validation

Kronos regularizes operator surrogates with conservation constraints where they apply (energy and particle balance), so the learned field respects the physics it approximates rather than merely fitting samples. Each operator is validated against its reference solver across held-out parameters, with special attention to conservation error and to extrapolation, an operator asked outside its training envelope must degrade gracefully and lower its confidence, not return a confident wrong field.

As with all surrogates, the offline reference (Monte Carlo transport, FEM thermomechanics) remains the ground truth and the fallback; the neural operator is the fast online stand-in that keeps the coupled twin step inside the shadow's latency budget.