In this talk, I will discuss a non-perturbative technique for QFT
called Similarity renormalisation group (SRG) where the Hamiltonian of a given
QFT is renormalised using continuous unitary transformations. This
transformation is achieved using an operator-valued differential equation called
the flow equation. I will show how the fixed points and their stability of the
operator flow equation is obtained using Lyapunov's direct method. In a chosen
basis, the operator flow equation reduces to non-linear coupled
integro-differential equations of the n-point vertex functions. I will discuss
the difficulties in solving such an equation and present a numerical framework
that can overcome the said difficulties. In particular, the numerical framework
comprises (1) Approximating the n-point vertex using statistical function
approximation - Gaussian process regression (GPR). (2) One-loop integration
using GPR stochastic quadrature. (3) Error propagation for the function
approximation and the integration. (4) Efficiently updating the Gaussian process
model for every ODE step. (5) Alleviating the stiffness of the ODE using
Exponential time difference (ETD) method. (6) Error propagation in the ODE by
interpreting it as a stochastic differential equation and using Ito calculus.
Lastly I will discuss the applications of SRG in non-perturbative QFT and
non-relativistic quantum many body problems in particular pairing in neutron matter.