Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

TL;DR

This paper introduces a real-time, low-rank approximation method for computing sensitivities in evolutionary systems, enabling efficient, accurate sensitivity analysis without the need for adjoint equations or extensive I/O.

Contribution

The paper presents a novel variational principle-based approach for sensitivity computation that is computationally efficient and suitable for real-time applications in complex systems.

Findings

Effective sensitivity computation demonstrated on chaotic and turbulent systems

Method reduces computational load compared to traditional adjoint methods

Applicable to high-dimensional and infinite-dimensional parameter spaces

Abstract

We present a new methodology for computing sensitivities in evolutionary systems using a model-driven low-rank approximation. To this end, we formulate a variational principle that seeks to minimize the distance between the time derivative of the reduced approximation and sensitivity dynamics. The first-order optimality condition of the variational principle leads to a system of closed-form evolution equations for an orthonormal basis and corresponding sensitivity coefficients. This approach allows for the computation of sensitivities with respect to a large number of parameters in an accurate and tractable manner by extracting correlations between different sensitivities on the fly. The presented method requires solving forward evolution equations, sidestepping the restrictions imposed by forward/backward workflow of adjoint sensitivities. For example, the presented method, unlike the adjoint equation, does not impose any I/O load and can be used in applications in which real time sensitivities are of interest. We demonstrate the utility of the method for three test cases: (1) computing sensitivity with respect to model parameters in the Rossler system (2) computing sensitivity with respect to an infinite-dimensional forcing parameter in the chaotic Kuramoto-Sivashinsky equation and (3) computing sensitivity with respect to reaction parameters for species transport in a turbulent reacting flow.