An important problem in engineering is to estimate the evolution of a hidden (latent) variable, such as the trajectory of a rocket, from noisy observations. If the dynamics of the latent variable is known, and also the relationship between the latent variable and the observation, then Bayes filtering is a robust method for estimating the latent ... Read more 10 Apr 2026 - 4 minute read
In this follow-up to our post on basic concepts, we will explore the dynamics generated by models of linear vibrations. Linear models of vibrating structures have the form \[\begin{equation} M\ddot{x} + C\dot{x} + Kx = F, \label{eq:basic_vibrations} \end{equation}\] where $x(t) \in \R^N$ is a vector function representing the displacement from... Read more 18 Nov 2024 - 3 minute read
Vibrating mechanical systems are modelled by the equation \[\begin{equation} M\ddot{x} + C\dot{x} + Kx = F,\label{eq:basic_vibration} \end{equation}\] where $x(t) \in \R^N$ is a vector function representing the displacement from equilibrium, $F$ are external forces, $M$ is the mass, $C$ is the damping, and $K$ is the stiffness. The dimension $... Read more 06 Nov 2024 - 11 minute read
Flank milling is a manufacturing process in which material is removed from the workpiece using a cutter rotating at high speed. Since the cutter rotates much faster than the feed rate of the tool, the cutter can be thought of as a solid of revolution, and the envelope swept by this solid becomes the final surface of the workpiece. Numerous book... Read more 07 Oct 2023 - 8 minute read
A typical problem in machine learning is to fit a collection of labelled data points $(\bold{x}^1, y^1), \ldots, (\bold{x}^p, y^p)$ using some model function \[y = f(\bold{x}).\] Each point $\bold{x} = (x_1, \ldots, x_N)$ is a vector in $\R^N$, where $N$ could easily be about millions. For example, a black and white picture with a regular came... Read more 06 Apr 2023 - 3 minute read