Neural Networks
Neural networks compose many simple weighted units into flexible function approximators trained by gradient descent.
Layers of simple units
A neural network is built from units that each compute a weighted sum of their inputs and pass it through a nonlinear function. Stacking these units in layers lets the network represent complex relationships that a single linear model cannot.
Training by gradients
Training adjusts the weights to reduce a loss — a measure of prediction error. The backpropagation algorithm computes how the loss changes with each weight, and gradient descent nudges the weights in the improving direction, repeated over many passes through the data.
Why nonlinearity matters
Without the nonlinear activation functions between layers, stacking layers would collapse to a single linear map. Nonlinearity is what gives deep networks their expressive power — the ability to approximate a very wide class of functions given enough units and data.
Strengths and cautions
- Strong at high-dimensional pattern recognition and flexible approximation.
- Data-hungry, and opaque about why they predict what they do.
- Unreliable outside the distribution they were trained on.
Disciplined use
In a fusion context, neural networks are useful as fast surrogates for expensive physics and as estimators of hard-to-measure quantities. Their opacity means they inform rather than command: outputs are bounded, checked, and reproducible, and the network’s training data and weights are recorded so any prediction can be regenerated and audited.