Maths PhD student at the University of Bath, supervised by Federico Cornalba and Tony Shardlow. Previously, MMathPhys in Maths and Physics at the University of Warwick.
I study problems at the interface between interacting particle systems and stochastic PDEs using tools from numerical and stochastic analysis.
Preprint · 2026
We introduce, analyse and simulate a class of reduced SPDE models for stochastic Cucker-Smale dynamics.Our models are a computationally cheaper alternative that preserve the flocking behaviour of the underlying particle system.
Kamran Arora, Federico Cornalba, Ana Djurdjevac
Preprint · 2026
We introduce a spatial dG approximation of the Dean-Kawasaki equation. The key ingredient is a general procedure for discretising multiplicative, divergence-form noise on finite element spaces whilst preserving its cross-variation structure.
Kamran Arora, Federico Cornalba and Tony Shardlow
Software · 2026+
A lightweight JAX + Equinox library of composable spatial discretisations and operators for solving SPDEs with Diffrax. End-to-end differentiable and compatible with jit, grad, vmap.
Kamran Arora
Preprint · 2025
An algebraically reversible formulation of Deep Equilibrium Models that allows for exact gradient computation with constant memory complexity.
Sam McCallum, Kamran Arora and James Foster