Time-dependent stochastic basis adaptation for uncertainty quantification

Understand

We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters.

• Stochastic basis adaptation allows the determination of a low dimensional stochastic basis representation of a quantity of interest (QoI).
• Extending basis adaptation to time-dependent problems is challenging because small errors introduced in the previous time steps of the low dimensional approximate solution accumulate over time and cause divergence from the true solution.
• To address this issue we have introduced an approach where the basis adaptation varies at every time step so that the low dimensional basis is adapted to the QoI at that time step.