3 papers
math.NA2026
On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation
Minh-Hieu Do, François Madiot, Karim Ammar +1
Physics-Based Loss Scaling (PBLS) is introduced for Mixed-Formulation PINNs (MF-PINNs) applied to the neutron diffusion equation. In particular, we propose a new \textit{scaled} lo…
math.NA2026
A posteriori error estimates for mixed finite element discretization of the multigroup Neutron Simplified Transport equations with Robin boundary condition
Patrick Ciarlet, Minh-Hieu Do, Mario Gervais +1
We analyse a posteriori error estimates for the discretization with mixed finite elements on simplicial or Cartesian meshes of the multigroup neutron simplified transport (SPN ) eq…
math.NA2025
Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations
Patrick Ciarlet, Minh-Hieu Do, François Madiot
The multigroup neutron diffusion equations are often used to model the neutron density at the nuclear reactor core scale. Classically, these equations can be recast in a mixed vari…