Neural Network Surrogates

Neural networks approximate expensive physics across large, high-dimensional datasets, trading interpretability for speed and scale.

Learning the physics response

A neural network surrogate learns the mapping from a physics code's inputs to its outputs by training on many examples. Once trained, it evaluates in milliseconds, regardless of how long the original code took. Networks handle large, high-dimensional, strongly nonlinear relationships that reduced-order models and Gaussian processes struggle with, which makes them attractive for the hardest parts of a twin.

Architectures for physical fields

Kronos motion — pid vs model

Fully connected networks for scalar inputs mapping to scalar or small vector outputs
Convolutional networks for spatial field data such as flux or temperature maps
Operator-learning networks that map whole input functions to output functions across resolutions

Physics-informed training

Purely data-driven networks can violate conservation laws between training points. Physics-informed training adds the governing equations as penalties, so the network is rewarded for respecting the physics as well as fitting the data. This improves accuracy where data is sparse and reduces unphysical predictions, an important safeguard in a twin.

The extrapolation hazard

Neural networks can be confidently wrong outside their training region, and unlike a Gaussian process a plain network does not report its own uncertainty. Twins address this by pairing networks with uncertainty methods, such as ensembles of networks or Bayesian layers, and by detecting when an input lies outside the trained domain and deferring to full physics. A surrogate that cannot say it does not know has no place in a safety-relevant loop.

Role in the Kronos twins

Network surrogates carry the large, nonlinear jobs: fast plasma-equilibrium reconstruction for the Hyperion breeder inside the control cycle, and rapid response surfaces for the burner's tandem-mirror plug behavior. They are trained today on validated simulations and will be re-trained on real data after first tritium near 2030, with their uncertainty always reported. See surrogate models and twin-in-the-loop control.