Model Order Reduction with Dynamically Transformed Modes for Electrophysiological Simulations

Abstract

The numerical simulation of neuromuscular processes in skeletal muscles typically imposes high computational costs, resulting in the need for techniques to reduce these costs. One submodel in these types of multiphysics multiscale simulations is the electrophysiological model, describing the propagation of an action potential (AP) in a muscle fiber. Involved in the simulation of the propagation are two traveling waves, resulting in difficulties for classical model order reduction (MOR) techniques based on linear subspaces.

Instead, we apply the nonlinear MOR method shifted Proper Orthogonal Decomposition (sPOD) to construct dynamically transformed reduced basis functions depending on time-dependent paths spanning the adaptive reduced ansatz space.

Our numerical experiments demonstrate that the constructed reduced ansatz space can accurately capture the dynamics of two fully separated wavefronts and reduce the degrees of freedom of the whole simulation. However, it cannot represent the activation of the AP in the center of the fiber and overlapping wave parts. The constructed reduced order model outperforms the high-dimensional full order model in terms of the computational costs while the accuracy is maintained and reaches speedup factors between 2 and 73 depending on the time discretization.