Fast Adjoint-assisted Multilevel Multi delity Method for Uncertainty Quanti cation of the Aleatoric Kind

PhDIn this thesis an adjoint-based multilevel multi delity Monte Carlo (MLMF) method is proposed, analysed, and demonstrated using test problems. Firstly, a multifi delity framework using the approximate function evaluation [1] based on the adjoint error correction of Giles et al. [2] is employed as a low fidelity model. This multifi delity framework is analysed using the method proposed by Ng and Wilcox [3]. The computational cost reduction and accuracy is demonstrated using the viscous Burgers' equation subject to uncertain boundary condition. The multi fidelity framework is extended to include multilevel meshes using the MLMF of Geraci [4] called the FastUQ. Some insights on parameters affecting computational cost are shown. The implementation of FastUQ in Dakota toolkit is outlined. As a demonstration, FastUQ is used to quantify uncertainties in aerodynamic parameters due to surface variations caused by manufacturing process. A synthetic model for surface variations due to manufacturing process is proposed based on Gaussian process. The LS89 turbine cascade subject to this synthetic disturbance model at two o -design conditions is used as a test problem. Extraction of independent random modes and truncation using a goal-based principal component analysis is shown. The analysis includes truncation for problems involving multiple QoIs and test conditions. The results from FastUQ are compared to the state-of-art SMLMC method and the approximate function evaluation using adjoint error correction called the inexpensive Monte Carlo method (IMC). About 70% reduction in computational cost compared to SMLMC is achieved without any loss of accuracy. The approximate model based on the IMC has high deviations for non-linear and sensitive QoI, namely the total-pressure loss. FastUQ control variate effectively balances the low fi delity model errors and additional high fidelity evaluations to yield accurate results comparable to the high fidelity model.This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 642959

Seeding and adjoining zero-halo partitioned parallel scientific codes

Algorithmic differentiation tools can automate the adjoint transformation of parallel message passing codes [18] using the AMPI library. Nevertheless, a non-trivial and manual step post-differentiation is seed initialisation and retrieval of the output values from the differentiated code. In this work, we present the problems and ambiguities associated with seed initialisation and output retrieval for adjoint transformation of zero-halo partitioned MPI programs. Shared-node reduction is an important parallel primitive in the zero-halo context. We introduce a general framework to eliminate ambiguities in seeding and retrieval for a general class of shared-node reduction using a conceptual master-worker model. Corollaries from the model show the need for new MPI calls for retrieval and eliminate MPI calls for seed initialisation. Different possible implementations for seeding manually assembled adjoints were inferred from the model, namely, (i) partial and (ii) unique. We successfully demonstrate the seeding of the manually assembled adjoint FPI in a 3d zero-halo partitioned unstructured compressible flow solver. The different implementations, their merits and demerits are highlighted. Tapenade AD tool was used throughout this work. Keywords

HYBRID PARALLELISATION OF AN ALGORITHMICALLY DIFFERENTIATED ADJOINT SOLVER

This research has been supported by the European Commission under the HORIZON 2020 Marie Curie fellowship (grant no. 642959

An adjoint-assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

In this work we propose, analyze, and demonstrate an adjoint-based multilevel multifidelity Monte Carlo (MLMF) framework called FastUQ. The framework is based on the MLMF of Geraci et al. and uses the Inexpensive Monte Carlo (IMC) method of Ghate as low-fidelity surrogate. The setup cost of IMC-1 surrogate in FastUQ requires just the adjoint solution at the input mean whose computational cost is independent of the number of input uncertainties making it suitable for solving problems with a large number of uncertain parameters. We demonstrate the robustness of the method to quantify uncertainties in aerodynamic parameters due to surface variations caused by the manufacturing processes for a highly loaded turbine cascade. A stochastic model for surface variations on the cascade is proposed and optimal dimensionality reduction of model parameters is realised using goal-based principal component analysis using adjoint sensitivities of multiple quantities of interest. The proposed method achieves a 70% reduction in computational cost in predicting the mean quantities such as total-pressure loss and mass flow rate compared to the state-of-art MLMC method