Primer

The setting, in plain words. Log entries refer back to this page.

Where the plasma sits

A tokamak holds a gas of charged particles, hotter than the centre of the Sun, inside a doughnut-shaped magnetic cage. The field lines wind around the doughnut and form nested surfaces, like the layers of an onion wrapped into a ring. Particles and heat move easily along a surface and only slowly across them, which is the basis of magnetic confinement.

Because the plasma is nearly the same everywhere on one surface, most of the physics can be described by how things change from the centre (the core) to the edge. The log uses one number for “how far out”: ρ (rho), which is 0 at the centre and 1 at the edge.

The magnetic cage is shaped by coils outside the plasma, and by currents flowing in the plasma itself. Working out the shape the plasma settles into is the equilibrium problem. The machines named in this log are ITER, the large international device under construction in France, whose published scenarios are used as a benchmark, and MAST-U, a compact spherical tokamak in the UK, shaped more like a cored apple than a doughnut.

How heat and particles move

Heating systems pour power into the core. It leaks out across the surfaces, mostly through small-scale turbulence. How fast it leaks decides how hot the core gets, and that decides how much fusion power the plasma makes.

Transport is the name for that leakage. It is stiff: below a critical temperature gradient the turbulence is quiet, above it the turbulence switches on hard and the leak jumps. The plasma tends to sit right at that threshold, which makes it numerically awkward: small changes in the profile cause large changes in the leak, which change the profile, and so on.

Why these pieces have to be solved together

Integrated modelling couples the separate pieces of physics:

piece	what it answers	example code used here
equilibrium	what shape is the plasma, given the coil currents?	FreeGSNKE
transport	how fast do heat and particles leak across the surfaces?	TORAX with QLKNN
sources	where does the heating power go?	a Gaussian model now; ASCOT5 next
events	sudden internal collapses (“sawteeth”) and edge transitions	TORAX’s models

Each depends on the others, and each is solved at every time step of a simulation that covers seconds to minutes of plasma. The accurate versions of these codes take hours to days, which is the problem this project attacks.

What a surrogate is, and why it can’t simply be trusted

A surrogate is a neural network trained to reproduce a slow physics code. Once trained, it answers in microseconds. The catch is that a network will return a confident-looking number for any input, including plasma conditions it never saw in training, where its answer can be arbitrarily wrong.

In this project every surrogate sits behind a guard. At every radius and every time step the guard checks three things:

1. Is the input inside the region the network was trained on? (its domain)
2. Do several independently trained copies of the network agree? (an ensemble; if they disagree, nobody knows the answer)
3. Is the output physically possible? (finite, positive where it must be, within bounds)

If any check fails at a point, a trusted, slower physics model (the fallback) is used at that point instead, and the substitution is recorded. The fraction of points served by the fallback is reported for every run: a surrogate that is used rarely is not saving anything, and a rising fallback rate means the surrogate is being asked about conditions it doesn’t know.

What “guarantees” means here

Three kinds, each covering what the others can’t:

• Formal: proved mathematically for a whole box of inputs, e.g. “the predicted heat flux never decreases when the temperature gradient increases”. Proofs cover the network itself, not the physics it imitates.
• Statistical: calibrated error bars (conformal prediction) that contain the true answer at a stated rate, on data like the training data.
• Closed-loop: a whole simulation run with the surrogate compared with the same run using the physics model, because small errors at each step can grow or cancel over thousands of steps.

Open and gated codes

The toolkit is built so that everything it ships depends only on open-source codes that anyone can download (called Tier A in this log). Some of the most accurate fusion codes are available only through the UK Atomic Energy Authority (Tier B). Those may be used to generate training data or reference runs, but never as something the finished toolkit needs in order to run. The test suite is run a second time with every gated code switched off to prove it.

Why JAX

The simulation is written in JAX, a numerical library that compiles a whole calculation into one program for a GPU and can differentiate through it. That gives two things this project needs: speed, so thousands of runs are affordable, and exact derivatives of any output with respect to any input, which make uncertainty propagation, sensitivity analysis and optimisation practical. It also imposes discipline, described in the technical internals.