Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. Consequently, extensive research has focused on analysing turbulent flows from a data-driven perspective. However, due to the complex and chaotic nature of these systems, traditional models often become unstable. To overcome these limitations, we propose a purely stochastic approach that separately addresses the evolution of large-scale coherent structures and the closure of high-fidelity statistical data. To this end, the dynamics of the filtered data are learnt using an autoregressive model. This combines a variational-autoencoder (VAE) and Transformer architecture. The VAE projection is probabilistic, ensuring consistency between the model’s stochasticity and the flow’s statistical properties. The mean realisation of stochastically sampled trajectories from our model shows relative $ {L}_1 $ and $ {L}_2 $ distances of 6% and 10%, respectively. Moreover, our framework enables the construction of meaningful confidence intervals, achieving a prediction interval coverage probability of 80% with minimal interval width. To recover high-fidelity velocity fields from the filtered space, Gaussian Process (GP) regression is employed. This strategy has been tested in the context of a Kolmogorov flow exhibiting chaotic behavior. We compare the performance of our model with state-of-the-art probabilistic baselines, including a VAE and a diffusion model. We demonstrate that our Gaussian process-based closure outperforms these baselines in capturing first and second moment statistics in this particular test bed, providing robust and adaptive confidence intervals.

Modeling detailed chemical kinetics is a primary challenge in combustion simulations. We present a novel framework to enforce physical constraints, specifically total mass and elemental conservation, during the reaction of ML models’ training for the reduced composition space chemical kinetics of large chemical mechanisms in combustion. In these models, the transport equations for a subset of representative species are solved with the ML approaches, while the remaining nonrepresentative species are “recovered” with a separate artificial neural network trained on data. Given the strong correlation between full and reduced solution vectors, our method utilizes a small neural network to establish an accurate and physically consistent mapping. By leveraging this mapping, we enforce physical constraints in the training process of the ML model for reduced composition space chemical kinetics. The framework is demonstrated here for methane, CH4, and oxidation. The resulting solution vectors from our deep operator networks (DeepONet)-based approach are accurate and align more consistently with physical laws.

Transfer learning has been highlighted as a promising framework to increase the accuracy of the data-driven model in the case of data sparsity, specifically by leveraging pretrained knowledge to the training of the target model. The objective of this study is to evaluate whether the number of requisite training samples can be reduced with the use of various transfer learning models for predicting, for example, the chemical source terms of the data-driven reduced-order modeling (ROM) that represents the homogeneous ignition of a hydrogen/air mixture. Principal component analysis is applied to reduce the dimensionality of the hydrogen/air mixture in composition space. Artificial neural networks (ANNs) are used to regress the reaction rates of principal components, and subsequently, a system of ordinary differential equations is solved. As the number of training samples decreases in the target task, the ROM fails to predict the ignition evolution of a hydrogen/air mixture. Three transfer learning strategies are then applied to the training of the ANN model with a sparse dataset. The performance of the ROM with a sparse dataset is remarkably enhanced if the training of the ANN model is restricted by a regularization term that controls the degree of knowledge transfer from source to target tasks. To this end, a novel transfer learning method is introduced, Parameter control via Partial Initialization and Regularization (PaPIR), whereby the amount of knowledge transferred is systemically adjusted in terms of the initialization and regularization schemes of the ANN model in the target task.

In this paper, a surrogate model approach for non-linear aerodynamics is presented in order to reduce the computational effort of coupled aeroelastic analyses. The usability of the approach is demonstrated in static as well as transient aeroelastic analyses of the HIRENASD wing-fuselage configuration. Furthermore, it is shown that the surrogate model approach is able to cover variations of flow conditions at a fixed Mach and Reynolds number.