Data-driven electrostatic heat flux closures with sparse regression

Licentiate thesis, 2026

Developing models which are both accurate and computationally efficient is a
long-standing goal in plasma physics. For systems where small-scale kinetic
phenomena significantly influence global dynamics, this can be challenging, as
global kinetic simulation – though highly accurate – is often computationally
intractable. Fluid models often provide a viable alternative, but their accuracy
depends on how well the utilised closure captures the neglected kinetic physics.

For collisional plasmas, closures can be constructed rigorously through
perturbative expansion around thermal equilibrium. However, no similarly
general framework exists in the collisionless case, prompting the development
of a variety of collisionless closures with limited ranges of validity. Examples
include the Chew-Goldberger-Low closure, valid in the strongly magnetised
limit, and Hammett-Perkins-like closures for linear Landau damping. Many
problems of interest lie outside these regimes, however, often necessitating
ad-hoc or theoretically poorly justified closures.

This motivates the exploration of alternative approaches to closure construc-
tion. In this thesis, we use a data-driven approach, employing machine learning
methods to systematically construct closures from first-principles kinetic simu-
lation data. Initially restricting ourselves to one-dimensional setups, we develop
a two-step sparse regression procedure based on the SINDy framework and
use it to discover a new six-term closure for electrostatic phenomena. The
closure accurately captures both linear and nonlinear regimes of the electron
two-stream instability, as well as Landau damping of Langmuir waves. Addi-
tionally, the closure generalises naturally to multi-species modelling, relevant
for streaming instabilities.

Having identified the closure form in the first step of the procedure, we
further show how its free parameters can be dynamically estimated from
fluid quantities. For this, we illustrate how both neural networks and more
interpretable methods can be leveraged – in the latter case through a newly
developed framework for nonlinear sparse regression.