5 papers
When does least-squares residual minimization solve a differential equation?
Carlos Esteve-Yagüe, Richard Tsai, Stanley Osher
Least-squares residual minimization approximates a differential equation through an optimization problem. This paper investigates the conditions required to transition from station…
Solving Hamilton-Jacobi equations by residual minimization of monotone finite-difference discretizations
Olivier Bokanowski, Carlos Esteve-Yagüe, Richard Tsai
We introduce a method for solving Hamilton--Jacobi equations, both inviscid and viscous, by minimizing the squared residuals of monotone finite-difference discretizations on grids…
FedMAP: Personalised Federated Learning for Real Large-Scale Healthcare Systems
Fan Zhang, Daniel Kreuter, Carlos Esteve-Yagüe +11
Federated learning (FL) promises to enable collaborative machine learning across healthcare sites whilst preserving data privacy. Practical deployment remains limited by statistica…
Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws
Carlos Esteve-Yagüe, Enrique Zuazua
We give a full characterization of the range of the operator which associates, to any initial condition, the viscosity solution at time of a Hamilton-Jacobi equation with conve…
Differentiability with respect to the initial condition for Hamilton-Jacobi equations
Carlos Esteve-Yagüe, Enrique Zuazua
We prove that the viscosity solution to a Hamilton-Jacobi equation with a smooth convex Hamiltonian of the form is differentiable with respect to the initial condition. Mo…