Wang, Tong; Le Maitre, Olivier; Hoteit, Ibrahim; Knio, Omar(2016-01-06)[Poster]
An ensemble-based approach is developed to conduct time-optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where a set deterministic predictions is used to model and quantify uncertainty in the predictions. In the operational setting, much about dynamics, topography and forcing of the ocean environment is uncertain, and as a result a single path produced by a model simulation has limited utility. To overcome this limitation, we rely on a finitesize ensemble of deterministic forecasts to quantify the impact of variability in the dynamics. The uncertainty of flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each the resulting realizations of the uncertain current field, we predict the optimal path by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of sampling strategy, and develop insight into extensions dealing with regional or general circulation models. In particular, the ensemble method enables us to perform a statistical analysis of travel times, and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.
We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.
We present recent developments in crowd dynamics models (e.g. pedestrian flow problems). Our formulation is given by a mean-field game (MFG) with congestion. We start by reviewing earlier models and results. Next, we develop our model. We establish new a priori estimates that give partial regularity of the solutions. Finally, we discuss numerical results.
The extensive scaling and integration within electronic systems have set the standards for what is addressed to as stochastic electronics. The individual components are increasingly diverting away from their reliable behavior and producing un-deterministic outputs. This stochastic operation highly mimics the biological medium within the brain. Hence, building on the inherent variability, particularly within novel non-volatile memory technologies, paves the way for unconventional neuromorphic designs. Neuro-inspired networks with brain-like structures of neurons and synapses allow for computations and levels of learning for diverse recognition tasks and applications.
We provide an indirect inference method to estimate the parameters of timehomogeneous scalar diffusion and jump diffusion processes. We obtain a system of ODEs that approximate the time evolution of the first two moments of the process by the approximation of the stochastic model applying a second order Taylor expansion of the SDE s infinitesimal generator in the Dynkin s formula. This method allows a simple and efficient procedure to infer the parameters of such stochastic processes given the data by the maximization of the likelihood of an approximating Gaussian process described by the two moments equations. Finally, we perform numerical experiments for two datasets arising from organic and inorganic fouling deposition phenomena.
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