Deep-Learning Surrogates

Neural networks learn complex, high-dimensional input-output maps from simulation data, serving as fast surrogates where classical methods struggle.

Why neural surrogates

Classical surrogates - polynomials, Gaussian processes, RBFs - handle smooth responses in modest dimensions well but strain when inputs number in the hundreds, outputs are whole fields, or the response is sharply nonlinear. Deep neural networks are universal approximators that scale to such regimes, learning the map f: x to y directly from a large set of simulation samples.

Architectures by output type

Kronos motion — classical

Fully connected networks for scalar or low-dimensional outputs
Convolutional networks for outputs on regular grids, such as field snapshots
Graph neural networks for outputs on unstructured meshes
Recurrent and transformer models for time-series and sequence outputs
Autoencoders to compress fields into a latent space before regression

Training

The network minimizes a loss - typically mean-squared error - over the training set by stochastic gradient descent with backpropagation. Because simulation data is expensive, neural surrogates are hungry for samples, so techniques like data augmentation, transfer learning from cheaper models, and physics-based regularization are used to make the most of limited runs.

Getting uncertainty

A plain network gives a point prediction with no error bar. Uncertainty is added by deep ensembles (train several networks and use their spread), Monte Carlo dropout (sample networks at test time), Bayesian neural networks (distributions over weights), or by predicting a mean and variance jointly. Any deployment for decision-making needs one of these to avoid overconfident predictions.

The extrapolation trap

Neural surrogates interpolate well but extrapolate poorly and unpredictably outside their training distribution, often with high confidence. They can also violate physical constraints - conservation, symmetry, monotonicity - unless those are enforced by architecture or loss. This makes validation on held-out and out-of-distribution data essential.

In fusion engineering

Deep surrogates are attractive for emulating expensive transport, equilibrium, and disruption models across wide operating spaces. In Kronos studies they are trained on full-fidelity simulation data of the machines, always paired with uncertainty estimates and checked against physics-based baselines before informing design choices; nothing they produce substitutes for a hardware result.