  This paper explores the application of methods from information geometry to
the sequential Monte Carlo (SMC) sampler. In particular the Riemannian manifold
Metropolis-adjusted Langevin algorithm (mMALA) is adapted for the transition
kernels in SMC. Similar to its function in Markov chain Monte Carlo methods,
the mMALA is a fully adaptable kernel which allows for efficient sampling of
high-dimensional and highly correlated parameter spaces. We set up the
theoretical framework for its use in SMC with a focus on the application to the
problem of sequential Bayesian inference for dynamical systems as modelled by
sets of ordinary differential equations. In addition, we argue that defining
the sequence of distributions on geodesics optimises the effective sample sizes
in the SMC run. We illustrate the application of the methodology by inferring
the parameters of simulated Lotka-Volterra and Fitzhugh-Nagumo models. In
particular we demonstrate that compared to employing a standard adaptive random
walk kernel, the SMC sampler with an information geometric kernel design
attains a higher level of statistical robustness in the inferred parameters of
the dynamical systems.
