Mathematical Foundations of the S.M.A.R.T. Generator
Every AI layer running Hyperion and Aegis/MetroVolt rests on a small set of equations: equilibrium PDEs, MHD eigenproblems, Bayesian inference, and constrained optimization.
Why the math is the product
Kronos does not apply generic machine learning to fusion. Each learned or optimizing component is a discretization, surrogate, or inverse of a governing equation for one of the two machines. The breeder (Hyperion) is a D-T spherical tokamak with Q_sci 3.076, 85.0 MW fusion power, 9.66 MA plasma current, 16.84 T peak field (8 T on-axis) and negative triangularity delta -0.30. The burner (Aegis / MetroVolt) is a D-3He tandem-mirror generator with a 26.49 T plug, 17 T throat and 5.44% neutron fraction feeding direct energy conversion. The AI stack exists to solve, estimate, control, and optimize these physics faster than a mesh solver can.
The five mathematical pillars
- Equilibrium PDEs: the Grad-Shafranov equation for the breeder, the ambipolar/paraxial force balance for the burner mirror.
- Stability spectra: linearized ideal and resistive MHD eigenproblems bounding the safe operating envelope.
- Function approximation with physics constraints: PINNs and neural operators that carry the PDE residual in their loss.
- State estimation and inference: Kalman-family filters and Bayesian posteriors that fuse the 60+ port diagnostic constellation.
- Optimization: constrained QPs for model-predictive control and Bayesian/trajectory optimization for scenario design.
One framework, two instantiations
The same abstract objects appear on both machines but with different operators. Equilibrium reconstruction is a Grad-Shafranov inverse problem on the breeder and an ambipolar-potential solve on the burner. Stability analysis is ballooning and vertical-mode spectra on the breeder, min-B interchange and mirror-gate analysis on the burner. This shared structure is why one AI-native architecture serves both plants.
These machines are design-and-simulation studies. Breeder construction begins Q2 2027 with first-of-a-kind first tritium targeted ~2030; no hardware net-gain is claimed before FOAK. The mathematics below is therefore validated against multi-physics simulation and legacy device data, with a defined path to plant synchronization once hardware exists.
The burner carries four honest design-and-simulation gates that the math surfaces rather than hides: the plug coil is overstressed ~3-3.9x at the design bore; its operating regime sits 166-830x beyond any built device, so it is not post-dictable today; a commercial unit's He-3 demand is ~400x current domestic supply; and simulated availability of 0.86-0.995 is 30-100x short of the 0.99982 a hyperscale Tier III facility expects. Every optimizer and estimator here treats those as hard facts.