We consider the efficient numerical approximation on nonlinear systems of initial value Ordinary Differential Equations (ODEs) on Banach state spaces $\mathcal{S}$ over $\mathbb{R}$ or $\mathbb{C}$. We assume the right hand side depends $in$ $affine$ $fashion$ on a vector $y =(y_j)_{j \geq 1}$ of possibly countably many parameters, normalized such that $|y_j| \leq 1$. Such affine parameter dependence of the ODE arises, among others, in ...

We present a novel, deterministic approach to inverse problems for identification of parameters in differential equations from noisy measurements. Based on the parametric deterministic formulation of Bayesian inverse problems with unknown input parameter from infinite dimensional, separable Banach spaces, we develop a practical computational algorithm for the efficient approximation of the infinite-dimensional integrals with respect to ...

We establish posterior sparsity in Bayesian inversion for systems with distributed parameter uncertainty subject to noisy data. We generalize the particular case of scalar diffusion problems with random coefficients in [29] to broad classes of operator equations. For countably parametric, deterministic representations of uncertainty in the forward problem which belongs to a certain sparsity class, we quantify analytic regularity of the ...