A Kronecker product accelerated efficient sparse Gaussian Process (E-SGP) for flow emulation
This work addresses computational bottlenecks in Bayesian machine learning for fluid mechanics applications, offering a more efficient alternative for surrogate modeling.
The paper tackles the computational inefficiency of Gaussian Process models for fluid mechanics surrogate modeling by introducing an Efficient Sparse Gaussian Process (E-SGP) that uses Kronecker products and optimized inducing points, achieving improved scalability and model quality with more accurate predictions and better uncertainty estimates compared to existing methods.
In this paper, we introduce an efficient sparse Gaussian process (E-SGP) for the surrogate modelling of fluid mechanics. This novel Bayesian machine learning algorithm allows efficient model training using databases of different structures. It is a further development of the approximated sparse GP algorithm, combining the concept of efficient GP (E-GP) and variational energy free sparse Gaussian process (VEF-SGP). The developed E-SGP approach exploits the arbitrariness of inducing points and the monotonically increasing nature of the objective function with respect to the number of inducing points in VEF-SGP. By specifying the inducing points on the orthogonal grid/input subspace and using the Kronecker product, E-SGP significantly improves computational efficiency without imposing any constraints on the covariance matrix or increasing the number of parameters that need to be optimised during training. The E-SGP algorithm developed in this paper outperforms E-GP not only in scalability but also in model quality in terms of mean standardized logarithmic loss (MSLL). The computational complexity of E-GP suffers from the cubic growth regarding the growing structured training database. However, E-SGP maintains computational efficiency whilst the resolution of the model, (i.e., the number of inducing points) remains fixed. The examples show that E-SGP produces more accurate predictions in comparison with E-GP when the model resolutions are similar in both. E-GP benefits from more training data but comes with higher computational demands, while E-SGP achieves a comparable level of accuracy but is more computationally efficient, making E-SGP a potentially preferable choice for fluid mechanic problems. Furthermore, E-SGP can produce more reasonable estimates of model uncertainty, whilst E-GP is more likely to produce over-confident predictions.