Surrogate Models Inside the MPC Loop

MPC needs to roll the plant model forward many times per cycle, so Kronos uses fast differentiable surrogates as the prediction model.

The rollout cost problem

Every MPC solve rolls the dynamics forward over the horizon, many times, as the optimizer searches. If each rollout required a mesh-based physics solve, MPC could not run in real time. Kronos uses the L3 surrogates, the equilibrium and stability PINNs for the breeder, the ambipolar-potential PINN for the burner, as the prediction model f_twin, so each rollout is a sequence of fast forward passes.

Differentiability buys gradients

Because the surrogates are neural networks, they are differentiable end to end. MPC gets gradients of the predicted trajectory with respect to the actuator sequence for free via automatic differentiation, turning the optimization into a smooth gradient-based problem rather than a derivative-free search. This is a major reason Kronos chose PINN surrogates over black-box lookup: the sensitivity information is intrinsic.

# gradient-based MPC step using a differentiable surrogate
x = rollout(f_surrogate, x0, u_seq)     # forward passes over horizon
J = cost(x, u_seq)
grad = autodiff(J, u_seq)                # d cost / d actuators
u_seq = project_to_constraints(u_seq - step * grad)   # one RTI step

The surrogate must be accurate over the horizon, not just at one point, so Kronos trains and validates the surrogates specifically on rollout accuracy, penalizing accumulated multi-step error, not only single-step error. A surrogate that is pointwise accurate but drifts over a rollout would give MPC a confidently wrong forecast.

Uncertainty into the loop

The surrogate reports predictive uncertainty, and MPC uses it: higher uncertainty tightens the effective constraints (via the envelope shrinking) so the controller is more cautious where the model is less trustworthy. This closes the loop between surrogate fidelity and control conservatism, ensuring MPC never bets more on the model than the model's validated accuracy justifies.