Speaker: Abhishek Balakrishna
Title: Data Assimilation and Determining Functionals for Three-Dimensional Fluids
Abstract: Data assimilation is a technique that combines observational data with a given model to improve the model’s accuracy. We first discuss the idea and motivation behind a particular data assimilation technique (AOT algorithms) and apply this method to the 3-D Boussinesq equation (3D BE). We then describe how the data assimilated solution asymptotically approximates the true solution. The key point to note being that the data assimilation is performed using “finitely observed” data. Then we observe that the data assimilated solution is, in fact, regular (i.e., a strong solution) when the observed data satisfies a condition we present for only a finite collection of data. This result suggests a connection between our condition and regularity. Leveraging on the proximity of the 3D Navier-Stokes equation (3D NSE) to the 3D BE, we conclude by presenting a regularity criterion for the 3D NSE purely in terms of finitely observed data.
Speaker: Mingkai Yu
Title: State and parameter estimation from partial state observations in stochastic reaction networks
Abstract: We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species. We describe new Monte Carlo methods for the accurate and efficient estimation of unobserved states and parameters of a stochastic reaction network based on exact partial state observations in continuous time. We present evolution equations for the conditional distribution, provide particle filter algorithms, and demonstrate our approach with numerical examples. Time permitting, we will also cover scenarios in which observations are made in snapshots of time.