We investigate the mean-field limit of large networks of interacting biological neurons. The neurons are represented by the so-called integrate and fire models that follow the membrane potential of each neuron and captures individual spikes. However we do not assume any structure on the graph of interactions but consider instead any connection weights between neurons that obey a generic mean-field scaling. We are able to extend the concept of extended graphons, introduced in Jabin-Poyato-Soler, by introducing a novel notion of discrete observables in the system. This is a joint work with D. Zhou.[-]

We investigate the mean-field limit of large networks of interacting biological neurons. The neurons are represented by the so-called integrate and fire models that follow the membrane potential of each neuron and captures individual spikes. However we do not assume any structure on the graph of interactions but consider instead any connection weights between neurons that obey a generic mean-field scaling. We are able to extend the concept of extended graphons, introduced in Jabin-Poyato-Soler, by introducing a novel notion of discrete observables in the system. This is a joint work with D. Zhou.[-]

Leveraging the existence of a hidden low-rank structure hinted by the diffusive limit, in this work, we design and test an angular space reduced order model for the linear radiative transfer equation based on reduced basis methods (RBMs). Our algorithm is built upon a high-fidelity solver employing the discrete ordinates method in the angular space, an upwind discontinuous Galerkin method for the physical space, with an efficient synthetic accelerated source iteration for the resulting linear system. Strategies are particularly proposed to tackle the challenges associated with the scattering operator within the RBM framework.
This is a joint work with Z.Peng, Y. Chen, and Y. Cheng.[-]