Updating DMD Operators for Changes in Domain Properties

TL;DR

This paper introduces efficient update strategies for Dynamic Mode Decomposition models that adapt to changes in reservoir properties without retraining, enabling fast and accurate surrogate modeling for geological carbon storage.

Contribution

The work presents novel lightweight update methods for DMD models that handle permeability and spatial property changes without new data or retraining.

Findings

Updates recover plume migration within 3% of full retraining

Models execute hundreds of times faster than retraining

Enables real-time optimization in carbon storage workflows

Abstract

Fast and reliable surrogate models are critical for optimization, control and uncertainty analysis in geological carbon-storage projects, yet high-fidelity multiphase simulators remain too expensive. Dynamic Mode Decomposition (DMD) offers an attractive data-driven reduction framework, but its operators are trained for a single set of reservoir properties. When permeability or well location changes, conventional practice is to regenerate snapshots and retrain the surrogate, erasing most of the speed advantage. This work presents a lightweight alternative that updates an existing DMD or DMD-with-control model without incorporating new simulation data or retraining. Two complementary update strategies are introduced. For cases where permeability changes uniformly across the domain, the proposed updates adjust the models internal dynamics and control response to match the new flow timescale. When permeability varies in space, the approach modifies the spatial representation so that high-permeability zones are given greater influence on the models reduced basis. Numerical experiments demonstrate that the proposed updates recover plume migration and pressure build-up within three percent of a freshly trained surrogate yet execute hundreds of times faster than full retraining. These methods therefore enable real-time optimization and rapid what-if studies while preserving the physical fidelity demanded by carbon-storage workflows.