The combination of CFD with ML has been already applied to several CFD configurations and is a promising research direction with the potential to enable the advancement of so far unsolved problems, thanks to the ability of deep models to learn in a hierarchical manner with little to no need for prior knowledge. However, this approach presents a paradigm shift to change the focus of CFD from time-consuming feature detection to in-depth examinations of relevant features, enabling deeper insight into the physics involved in complex natural processes.

Closed-loop flow control has a wide range of applications like gust mitigation for aircraft or process intensification of chemical plants. However, creating robust control laws that map potentially high-dimensional state spaces to suitable control actions is not straightforward. The core idea behind DRL is the optimization of neural-network-based control laws by trial-and-error learning. A so-called agent applies control actions to an environment, which then transitions to a new state, and returns a reward expressing its intrinsic objective.

The talk will start with reduced-order surrogate modeling using Gaussian process regression. In this scheme, the full-order solvers are used offline merely as a ‘black-box’ for data generation, whereas the online stage is entirely simulation-free, which guarantees reliable and efficient multi-query simulations of large-scale engineering assets. The second method is the Bayesian reduced-order operator inference, a non-intrusive, physics-informed approach that inherits the formulation structure of projection-based reduced-state governing equations yet without requiring access to the full-order solvers. The reduced-order operators are estimated using Bayesian inference. They probabilistically describe a low-dimensional dynamical system for the predominant latent states, and provide a naturally embedded Tikhonov regularization together with a quantification of modeling uncertainties. The third method employs deep kernel learning — a probabilistic deep learning tool that integrates neural networks into manifold Gaussian processes — for the data-driven discovery of low-dimensional latent dynamics from high-dimensional measurements given by noise-corrupted images.

The first part of the talk will focus on the development of an artificial neural network chemistry manifold to simulate a premixed methane-air flame undergoing side-wall quenching. Similar to the tabulation of a Quenching Flamelet-Generated Manifold, the neural network is trained on a one-dimensional head-on quenching flame database to learn the intrinsic chemistry manifold. A-posteiori investigations demonstrated that the chemical source terms must be corrected at the manifold boundaries to ensure the boundedness of the thermo-chemical state at all times. The ANN model is evaluated against widely-used approaches, such as the detailed chemistry and the flamelet-based manifold approximation, on a 2D side-wall quenching configuration. Recently, deep learning frameworks have demonstrated excellent performance in modeling nonlinear

To address these modeling and design challenges at the pace required by rapid climate change, data-driven models can work in tandem with physics-based approaches and enable faster results while maintaining accuracy and reliability.

The primary focus will be on supervised learning strategies, where a multivariate, non-linear function approximation of given data sets is found through a high-dimensional, non-convex optimization problem that is efficiently solved on modern GPUs. This approach can thus for example be employed in cases where current submodels in the discretization schemes currently rely on heuristic data. A prime of example of this is shock detection and shock capturing for high order methods, where essentially all known approaches require some expert user knowledge as guid- ing input. As an illustrative example, this talk will show how modern, multiscale neural network architectures originally designed for image segmentation can ameliorate this problem and provide parameter free and grid independent shock front detection on a subelement level. With this information, we can then inform a high order artificial viscosity operator for inner-element shock capturing.