Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

Bayesian Probabilistic Numerical Methods

The emergent field of probabilistic numerics has thus far lacked rigorous statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain Bayesian inverse problems, albeit problems that are non-standard. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well-defined, ...

Probabilistic Methods for State Estimation in Robotics

The eld of Arti cial Intelligence (AI) is currently undergoing a transition. While in the eighties, rule-based and logical representations were the representation of choice in the majority of AI systems, in recent years various researchers have explored alternative representational frameworks, which emphasis on frameworks that enable systems to represent and handle uncertainty. Out of those, pr...

Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of signif...

Bayesian Methods for Function Estimation

New numerical methods for solving the time-dependent Maxwell equations

We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to construct a family of unconditionally stable algorithms, the conventional Yee algorithm, and two new variants of the Yee algorithm that do not require the use of ...