6 papers
Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
Aaron Pim, Tristan Pryer
We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define…
Surrogate Modelling of Proton Dose with Monte Carlo Dropout Uncertainty Quantification
Aaron Pim, Tristan Pryer
Accurate proton dose calculation using Monte Carlo (MC) is computationally demanding in workflows like robust optimisation, adaptive replanning, and probabilistic inference, which…
A Unified Framework from Boltzmann Transport to Proton Treatment Planning
Andreas E. Kyprianou, Aaron Pim, Tristan Pryer
This work develops a rigorous mathematical formulation of proton transport by integrating both deterministic and stochastic perspectives. The deterministic framework is based on th…
Deep Uzawa for Kinetic Transport with Lagrange-Enforced Boundaries
Charalambos Makridakis, Aaron Pim, Tristan Pryer +1
We propose a neural network framework for solving stationary linear transport equations with inflow boundary conditions. The method represents the solution using a neural network a…
Optimal control of a kinetic equation
Aaron Pim, Tristan Pryer, Alex Trenam
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-pos…
Efficient Proton Transport Modelling for Proton Beam Therapy and Biological Quantification
Ben S. Ashby, Veronika Chronholm, Daniel K. Hajnal +4
In this work, we present a fundamental mathematical model for proton transport, tailored to capture the key physical processes underpinning Proton Beam Therapy (PBT). The model pro…