We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

In social dilemmas, a class of multi-agent games, agents' rationality-based strategic interactions to learn a payoff-maximizing strategy would result in diminishing returns. Such games include the prisoner's dilemma and public goods game where individually rational decision making reults in all decision-making agents receiving smallest rewards. In this presentation, I will explain a new decision-making model that elicits cooperative behavior in social dilemmas. The model enables the social interaction (reciprocity) between agents in their decision making, which allows cooperative behavior to emerge. We discuss how methods for feedback system design and analysis can be applied to explain the emergence of cooperative behavior and how we can tune such behavior.

KAUST Robotics, Intelligent Systems and Control Lab (RISC Lab) will host the KAUST Research Conference on Robotics and Autonomy 2022 (#RobotoKAUST) from February 28 until March 2, 2022. The conference will address the most recent trends of robotics application in a range of disciplines. To attend RobotoKAUST Gala, please, read more about the event and follow the event registration instructions.

Robot navigation typically comprises of decision making at two different levels - global planning to compute a viable trajectory to the robot's destination and strategic (local) interaction to elicit cooperation and resolve any conflicts with other robots/pedestrians that would arise while navigating along the trajectory. Robot navigation in crowded environments is particularly challenging as the robot needs to exhibit navigation behaviors that are conceived as socially compliant by human pedestrians or vehicles they maneuver at both of the levels. In this presentation, I will introduce some of relevant works from my research group.