machine learning tasks

regression, classification, clustering, ...

think in terms of machine learning tasks
(regression, classification, ...)
rather than specific algorithms
(neural networks, Gaussian processes, ...)

regression: matching inputs and continuous outputs

classification: matching inputs and discrete outputs

dim. reduction: finding low-dim. representations

clustering: grouping similar data points

reinforcement learning: sequential decision making (control) under uncertainty

machine learning algorithms are essential to solve these tasks in higher dimensions

many problems need to be broken up into multiple tasks

reduced-order modeling

1. dimensionality reduction
   maps high- to low-dim. inputs/outputs
2. regression or classification
   low-dimensional input-output mappings
3. back-projection (optional)
   inverts step 1. for new predictions

outlier detection (extreme events)

1. dimensionality reduction
   maps high- to low-dim. representations
2. clustering or classification
   low similarity or class probabilities

formulating sensible tasks requires
domain knowledge

optimizing settings

with Bayesian optimization

GAMG - generalized geometric algebraic multigrid

full GAMG entry in fvSolution

						p
{
	solver                    GAMG;
	smoother                  DICGaussSeidel;
	tolerance                 1e-06;
	relTol                    0.01;
	cacheAgglomeration        yes;
	nCellsInCoarsestLevel     10;
	processorAgglomerator     none;
	nPreSweeps                0;
	preSweepsLevelMultiplier  1;
	maxPreSweeps              10;
	nPostSweeps               2;
	postSweepsLevelMultiplier 1;
	maxPostSweeps             10;
	nFinestSweeps             2;
	interpolateCorrection     no;
	scaleCorrection           yes;
	directSolveCoarsest       no;
	coarsestLevelCorr
	{
		solver          PCG;
		preconditioner  DIC;
		tolerance       1e-06;
		relTol          0.01;
	}
}
						
					

optimal settings depend on

$\rightarrow$ high-dim. search space with uncertainty

~15% runtime reduction

references & examples (GitHub)

• tuning GAMG solver settings
• tuning turbulence model parameters

understanding turbulent flows

with modal decomposition

flow past a cylinder: $|\mathbf{u}|$ at $Re=dU_\mathrm{in}/\nu=100$

data $=$ spatial patterns $\times$ temporal patterns

$|\mathbf{u}|$ at $Re=dU_\mathrm{in}/\nu=3700$; DNS setup based on
O. Lehmkuhl et al. (2013)

PSD of force coefficients (p-Welch, 4 segments)
$St=fT_\mathrm{conv}$ and $T_\mathrm{conv}=d/U_\mathrm{in}$

adaptive sin-taper spectral POD
refer to B. C. Y. Yeung, O. T. Schmidt (2024)

vortex shedding mode
$St\approx 0.22$, streamwise component

Airbus XRF-1 shock buffet mode ($Re_\infty = 3.3\times 10^6$, $Ma_\infty =0.84$, $\alpha=-4^\circ$); DDES by S. Spinner (DLR)

references & examples

• flowTorch (flow analysis)
• sparse spatial sampling (visualization)
• Airbus XRF-1 modal analysis

closed-loop flow control

with model-based deep reinforcement learning

closed-loop control benchmark, $Re=100$

instantaneous reward $R_n$

$$ R_n = 3 - (c_{x,n} + 0.1 |c_{y,n}|) $$

$c_{i, n}$ - force coefficients at step $n$

evaluation of optimal policy (control law)

evaluation of optimal policy (control law)

drag reduction by approx. $25\%$

references

• A. Weiner, J. Geise (2024)
• source code (GitHub)