68 citations · 231 across the 47 of their papers we have counts for
4 papers · 1 filter
Semilinear fractional elliptic PDEs with gradient nonlinearities on open balls: existence of solutions and probabilistic representation
Guillaume Penent, Nicolas Privault
We provide sufficient conditions for the existence of viscosity solutions of fractional semilinear elliptic PDEs of index with polynomial gradient nonlinearities on $d…
Numerical solution of the incompressible Navier-Stokes equation by a deep branching algorithm
Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault
We present an algorithm for the numerical solution of systems of fully nonlinear PDEs using stochastic coded branching trees. This approach covers functional nonlinearities involvi…
A deep branching solver for fully nonlinear partial differential equations
Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault
We present a multidimensional deep learning implementation of a stochastic branching algorithm for the numerical solution of fully nonlinear PDEs. This approach is designed to tack…
Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
Guillaume Penent, Nicolas Privault
We present an algorithm for the numerical solution of ordinary differential equations by random enumeration of the Butcher trees used in the implementation of the Runge-Kutta metho…