Filtered Neural Galerkin model reduction schemes for efficient propagation of initial condition uncertainties in digital twins
This work addresses efficiency challenges in digital twins for applications requiring real-time control and data assimilation, though it is incremental as it builds on existing Neural Galerkin schemes.
The paper tackles the high computational cost of ensemble-based uncertainty quantification in digital twins by introducing a reduced modeling approach that propagates only the mean and covariance of the solution distribution, eliminating the need for costly ensembles. Numerical experiments show this method achieves more than one order of magnitude speedup compared to ensemble-based approaches.
Uncertainty quantification in digital twins is critical to enable reliable and credible predictions beyond available data. A key challenge is that ensemble-based approaches can become prohibitively expensive when embedded in control and data assimilation loops in digital twins, even when reduced models are used. We introduce a reduced modeling approach that advances in time the mean and covariance of the reduced solution distribution induced by the initial condition uncertainties, which eliminates the need to maintain and propagate a costly ensemble of reduced solutions. The mean and covariance dynamics are obtained as a moment closure from Neural Galerkin schemes on pre-trained neural networks, which can be interpreted as filtered Neural Galerkin dynamics analogous to Gaussian filtering and the extended Kalman filter. Numerical experiments demonstrate that filtered Neural Galerkin schemes achieve more than one order of magnitude speedup compared to ensemble-based uncertainty propagation.