High dimensional linear inverse modelling

TL;DR

This paper presents two linear inverse modelling methods for high-dimensional stochastic systems that are accurate regardless of system size, avoiding state space truncation and maintaining computational efficiency.

Contribution

It introduces novel linear inverse modelling techniques that scale efficiently with system size and do not require truncation of the state space.

Findings

Methods are accurate regardless of dimensionality

Computational time and memory scale linearly with system size

No state space truncation needed

Abstract

We introduce and demonstrate two linear inverse modelling methods for systems of stochastic ODE's with accuracy that is independent of the dimensionality (number of elements) of the state vector representing the system in question. Truncation of the state space is not required. Instead we rely on the principle that perturbations decay with distance or the fact that for many systems, the state of each data point is only determined at an instant by itself and its neighbours. We further show that all necessary calculations, as well as numerical integration of the resulting linear stochastic system, require computational time and memory proportional to the dimensionality of the state vector.