Bayesian Methods and Optimization
Gradient-free optimization of chaotic acoustics with reservoir computing
Gradient-based optimization of chaotic acoustics is challenging for a threefold reason:
- first-order perturbations grow exponentially in time
- the statistics of the solution may have a slow convergence
- the time-averaged acoustic energy may physically have discontinuous variations, which means that the gradient does not exist for some design parameters.
We develop a versatile optimization method, which finds the design parameters that minimize time-averaged acoustic cost functionals, and overcomes the three aforementioned challenges. The method is gradient-free, model-informed, and data-driven with reservoir computing based on echo state networks.
First, we analyze the predictive capabilities of echo state networks in thermoacoustics both in the short- and long-time prediction of the dynamics. We find that both fully data-driven and model-informed architectures are able to learn the chaotic acoustic dynamics, both time-accurately and statistically. Informing the training with a physical reduced-order model with one acoustic mode markedly improves the accuracy and robustness of the echo state networks, while keeping the computational cost low. Echo state networks offer accurate predictions of the long-time dynamics, which would be otherwise expensive by integrating the governing equations to evaluate the time-averaged quantity to optimize.
Second, we couple echo state networks with a Bayesian technique to explore the design thermoacoustic parameter space. The computational method is minimally intrusive because it requires only the initialization of the physical and hyperparameter optimizers.
Third, we find the set of flame parameters that minimize the time-averaged acoustic energy of chaotic oscillations, which are caused by the positive feedback with a heat source, such as a flame in gas turbines or rocket motors. These oscillations are known as thermoacoustic oscillations. The optimal set of flame parameters is found with the same accuracy as brute-force grid search but with a convergence rate that is more than one order of magnitude faster. This work opens up new possibilities for nonintrusive (“hands-off”) optimization of chaotic systems, in which the cost of generating data, for example, from high-fidelity simulations and experiments, is high.
For further details:
- Huhn, F., & Magri, L. (2022). Gradient-free optimization of chaotic acoustics with reservoir computing. Physical Review Fluids, 7(1), 014402.
Minimization of skin-friction drag of a turbulent boundary-layer flow:
A Bayesian optimization framework is developed to optimize low-amplitude wall-normal blowing control of a turbulent boundary-layer flow. The Bayesian optimization framework determines the optimum blowing amplitude and blowing coverage to achieve up to a 5% net-power saving solution within 20 optimization iterations, requiring 20 direct numerical simulations (DNS).
The power input required to generate the low-amplitude wall-normal blowing is measured experimentally for two different types of blowing device and is used in the simulations to assess control performance. Wall-normal blowing with amplitudes of less than 1% of the free-stream velocity generate a skin-friction drag reduction of up to 76% over the control region, with a drag reduction which persists for up to 650δ0 downstream of actuation (where δ0 is the boundary-layer thickness at the start of the simulation domain).
It is shown that it is the slow spatial recovery of the turbulent boundary-layer flow downstream of control which generates the net-power savings in this study. The downstream recovery of the skin-friction drag force is decomposed using the Fukagata-Iwamoto-Kasagi (FIK) identity, which shows that the generation of the net-power savings is due to changes in contributions to both the convection and streamwise development terms of the turbulent boundary-layer flow.
For further details
- Mahfoze, O. A., Moody, A., Wynn, A., Whalley, R. D., & Laizet, S. (2019). Reducing the skin-friction drag of a turbulent boundary-layer flow with low-amplitude wall-normal blowing within a Bayesian optimization framework. Physical Review Fluids, 4(9), 094601.