Accelerating shape optimization by deep neural networks with on-the-fly determined architecture

TL;DR

The paper tackles the computational bottleneck of CFD-driven multi-objective shape optimization by introducing CFDNNetAdapt, an adaptive surrogate-assisted MOEA that on-the-fly discovers suitable DNN architectures and replaces CFD in the search once accuracy is achieved. The method blends NSGA-II with multiple MLP surrogates, selecting the best architecture via IGD-based similarity to CFD-predicted Pareto sets and verifies promising solutions with CFD. Benchmark results on ZDT/LZ problems show CFDNNetAdapt often matches or surpasses state-of-the-art SAOAs while offering significant speedups, though performance depends on problem topology; a real-life ejector optimization demonstrates substantial CPU-time savings and experimental validation of selected designs. Overall, the approach provides a flexible, scalable framework for accelerating expensive CFD-based multi-objective optimization and is open-source for broader application to shape optimization problems.

Abstract

In component shape optimization, the component properties are often evaluated by computationally expensive simulations. Such optimization becomes unfeasible when it is focused on a global search requiring thousands of simulations to be evaluated. Here, we present a viable global shape optimization methodology based on multi-objective evolutionary algorithms accelerated by deep neural networks (DNNs). Our methodology alternates between evaluating simulations and utilizing the generated data to train DNNs with various architectures. When a suitable DNN architecture is identified, the DNN replaces the simulation in the rest of the global search. Our methodology was tested on five ZDT benchmark functions, showing itself at the level of and sometimes more flexible than other state-of-the-art acceleration approaches. Then, it was applied to a real-life optimization problem, namely the shape optimization of a single-phase ejector. Compared with a non-accelerated methodology, ours was able to save weeks of CPU time in solving this problem. To experimentally confirm the performance of the optimized ejector shapes, four of them were 3D printed and tested on the lab scale confirming the predicted performance. This suggests that our methodology could be used for acceleration of other real-life shape optimization problems.

Figures (21)

• Figure 1: Schematic of the baseline optimization framework. The vectors $\bm{p}$ and $\bm{o}$ contain the parameters and objectives, respectively. Furthermore, $\bm{f}_\mathrm{cost}$ is the cost function, $\mathcal{P}^*$ the Pareto-optimal set and $\mathcal{O}^*$ the Pareto-optimal front.
• Figure 1: Sketch of the experimental setup. P1,P2 - centrifugal pumps; E1 - heat exchanger; V1-V4 - valves; red lines - primary (driving) fluid; blue lines - secondary (entrained) fluid; magenta lines - mixed stream.
• Figure 1: Ejector geometry and qualitative view of the computational mesh. The overall mesh structure is shown in the top part of the figure, details of specific positions along the ejector are shown on the figure bottom.
• Figure 1: Comparison of simulation and experimental data, namely the scaled pressure drop $(\Delta_\mathrm{s} p)$ and the secondary-to-primary flow rate ratio $(r_Q)$ are depicted for different primary fluid flow rates $\dot{Q}_\mathrm{inlet}$. Colors correspond to ejector designs displayed in Figure \ref{['fig:exppof']}.
• Figure 1: Histogram for the number of neurons in each hidden layer of the MLPs proposed by CFDNNetAdapt for optimization of the ejector shape. Data for 25 algorithm runs are shown.