# Items filtered by date: Monday, 01 February 2021

## Aggregation with intrinsic interactions on Riemannian manifolds

#### Speaker: Razvan Fetecau (Simon Fraser University)

We consider a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions, defined via optimal mass transport, on several specific manifolds (sphere, hypercylinder, rotation group \(SO(3)\)), and investigate the mean-field particle approximation. We study the long-time behaviour of solutions, where the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. The analytical results are illustrated with numerical experiments that exhibit various asymptotic patterns.

Time: February 12, 2021 3:30pm-4:30pm

Location: Virtually via Zoom

Host: Changhui Tan

## Numerical methods for solving nonlinear differential equations from homotopy methods to machine learning

#### Speaker: Wenrui Hao (Pennsylvania State University)

Many systems of nonlinear differential equations are arising from engineering and biology and have attracted research scientists to study the multiple solution structure such as pattern formation. In this talk, I will present several methods to compute the multiple solutions of nonlinear differential equations. First, I will introduce the homotopy continuation technique to compute the multiple steady states of nonlinear differential equations and also to explore the relationship between the number of steady-states and parameters. Then I will use the machine learning techniques to solve nonlinear differential equations and learn the multiple solutions by developing a randomized Newton's method for the neural network discretization. Several benchmark problems will be used to illustrate these ideas.

Time: February 19, 2021 3:30pm-4:30pm

Location: Virtually via Zoom

Host: Qi Wang