PDEs | Victor Boussange

Forward and inverse modelling of eco-evolutionary dynamics in ecological and economic systems

Ecological and economic systems are complex adaptive systems, composed of multiple entities which interact and undergo evolutionary processes. The complexity of these systems present a crucial challenge for underpinning their general organizational principles. This thesis develops innovative modelling techniques and advances our comprehension of the eco-evolutionary processes and feedbacks that shape these systems.

Victor Boussange

Forward and inverse modelling of eco-evolutionary dynamics in ecological and economic systems

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In this article we propose two numerical methods based on machine learning and on Picard iterations, respectively, to approximately solve non-local nonlinear PDEs. Our work extends recently developed methods to overcome the curse of dimensionality in solving PDEs.

Victor Boussange, Sebastian Becker, Arnulf Jentzen, Benno Kuckuck, Loïc Pellissier

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Machine learning to solve highly dimensional non-local nonlinear PDEs

Partial Differential Equations (PDEs) are equations that arise in a variety of models in physics, engineering, finance and biology. I develop numerical schemes based on machine learning techniques to solve for a special class of PDEs (cf below) in high dimension.