Tackling a costly bottleneck in automotive design

Automobile designers are experts at solving complex problems, finding the balance between improving future vehicle performance and ensuring the safety of their passengers. This is how the global automotive industry has delivered rising fuel efficiency and decreasing road fatality rates over many decades.

As an example case, consider vehicle frame design. Stronger frames improve safety, but the typical approaches to strengthen frames increase material and hence weight, negatively impacting fuel efficiency and emissions. To find the right balance, engineers rely on highly complex, exact calculations to evaluate structural strength across different variations of frame designs. These calculations are computationally expensive, and typically require thousands of iterations, resulting in a costly, time-consuming computational design process. Advanced computing tools have enabled huge strides in this area, but are now hitting limits in their return-on-investment.

Mazda has been a pioneer in the application of emerging tools in machine learning to this challenge, seeking to overcome the limits of conventional numerical design approaches. In recent work, the Mazda team tackled this challenge by combining simulation, optimization, and statistical analysis to better understand how the shape of a car’s frame affects its performance. By using genetic algorithms and data-driven methods, they were able to extract interpretable design guidelines that help engineers focus on the most important features when designing strong, lightweight frames [1].

Now the team at Mazda has partnered with Q-CTRL, collaboratively investigating how quantum computers can help accelerate design timelines at reduced cost by minimizing the number of calculations required in the design process. Through this investigation, Quantum Machine Learning is being put to the test in a real-world application.

Surrogate models: a faster way to optimize designs

To address this challenge, we explored a framework which utilizes quantum computing to augment an established machine learning approach: surrogate models. 

Surrogate models are fast, data-driven approximations of expensive calculations, simulations or experiments. They learn from a set of existing calculations and can be used to quickly approximate the performance of new designs. This approach can make it possible to explore a much larger set of design options in a short amount of time, allowing for the rapid discovery of designs with superior characteristics.

Our surrogate models were built to estimate a vehicle frame’s structural strength based on its geometric shape. By learning from the performance of previously calculated frame designs – which were conducted using costly computational techniques –the models were able to identify patterns and make reliable predictions of structural strength for new shapes. These “trained” surrogate models can then be used by engineers as a design tool, enabling rapid exploration of lighter and stronger frame designs.

Can quantum models help when data is limited?

We evaluated both classical and quantum machine learning (QML) models as surrogates. We were especially interested in the potential of QML models in practical, data-limited scenarios, due to the high-cost associated with generating the data. Remember, unlike circumstances where machine learning is applied to the simple observation of correlations e.g. customer purchasing decisions, here the relevant data must first be generated by expensive and time-consuming calculations. There are promising signals that quantum models will offer an advantage in such data-limited scenarios by capturing complex relationships in the data using the high-dimensional representation space of quantum computation.

What did we find? When using the full set of available training data, classical models – especially neural networks – delivered the strongest performance. But as we reduced the amount of training data available, the performance gap between classical and quantum models shrank until quantum models based on quantum support vector machines (QSVM) even outperformed their classical counterparts.

This scale, where the training data set was reduced by five times from its original, accurately reflects the scenarios Mazda and other engineering teams often face: small datasets, complex design spaces, and high costs for generating new simulations. Quantum models showed their ability to perform well in these critical low-data regimes, even though they didn’t show a universal advantage, making them an exciting candidate tool in automotive engineering.

Stronger frame designs with less computation

We also showed how to fully integrate these new quantum models into the design process for vehicle frames. With quantum models that could reliably estimate a car frame’s structural strength in hand, we integrated them into a full optimization workflow to guide the search for better designs. In this setup, the quantum models acted as fast surrogate predictors, replacing costly simulations and allowing the optimizer to evaluate many frame candidates in less time.

The animation below shows the optimization process using a QSVM surrogate trained with 250 data points, and run on a simulated quantum computer. The optimization starts with seven arbitrary points defining the vehicle frame’s cross-section, with their locations updated after each optimization step. As the process proceeds, the points evolve until they converge to the frame design with the highest strength-to-weight ratio. In this example the resulting optimized strength-to-weight ratio surpassed the best value in the training data by 8%, and we could preserve this performance in other examples using only half of the number of training points.

Executing QML methods on real hardware 

Our collaboration took critical first steps towards the execution of quantum-enabled vehicle design on real quantum computing hardware. We focused on studying the efficacy of the quantum kernel itself, the object used to identify the key—and potentially hidden—relationships in the data.

The quantum kernel is constructed by defining a quantum circuit that maps each data point into a quantum state. The quantum computer then estimates the similarity between two data points by preparing both states and measuring the probability of a specific outcome that reflects how much the states overlap. These similarity values are used to build a QSVM model, which then learns to predict the desired output. 

In our demonstrations, we computed these similarity measurements using IBM's superconducting quantum devices. To improve the reliability and accuracy of these computations, Fire Opal, Q-CTRL’s error-suppressing performance-management software, was used to reduce the impact of hardware noise and optimize circuit execution. The results closely matched ideal simulations, suggesting that current hardware, when paired with performance-management tools like Fire Opal, can already support key components of quantum machine learning.

Leveraging classical methods to do more with even less data 

In order to push these techniques further into the low-data regime, we explored new reinforcement-learning strategies that dynamically guide data collection. Instead of training the model in advance using the available data points, as in the previous case, we embedded the training process into our optimization loop. In this way, an initial crude model is dynamically updated directly from data points that are explored by the optimization engine. 

This iterative procedure helped the learning process focus on regions in parameter space capable of delivering strong designs, leading to a reduced number of calls to the costly simulations. We tested this learning strategy using a classical neural network surrogate with as few as 100 evaluations, resulting in a 28% improvement over the best value in the existing data set. 

The next step is to test this approach using quantum surrogates. Kernel-based models like QSVMs are particularly well-suited to this process because they can be efficiently updated without retraining from scratch. By computing kernel values between the new design and the existing data, the model can be quickly extended. This is an exciting new direction to continue refining our results so far.

Towards practical quantum-enhanced design

Our collaboration with Mazda has demonstrated that quantum machine learning can be meaningfully applied to real engineering workflows. By integrating quantum surrogate models into a structural design optimization loop, we showed that these models can support the search for stronger and lighter frame designs, providing an alternative with potential to give advantages over classical approaches in data-limited settings. Functionality in the low-data regime is crucial not only because generating new data is resource intensive in this case, but also because the number of quantum circuits that must be executed grows with the size of the training data, quickly becoming a limiting factor for practical implementation on quantum devices. 

Fortunately, device size is not a constraint for this problem as the required number of qubits coincides with the number of features in the QML model. In fact, our tests on real quantum hardware, supported by Fire Opal, confirmed that current devices can already handle the key kernel calculation component of the workflow. 

"Working with Q-CTRL gave us a chance to explore a new and fast moving area of technology in a way that was grounded in our real design challenges. The team brought a strong mix of technical expertise and practical focus, helping us understand how quantum machine learning might fit into our workflow. It was a productive and insightful collaboration."Shimoda Wataru (霜田 航), Mazda Motor Corporation

Together, these results suggest that quantum machine learning, combined with targeted data strategies and the right software tools, can already support parts of real design workflows today. As hardware and methods continue to improve, we anticipate these techniques may become a practical option for engineering teams working under real-world constraints.

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_{[1] Masanori Honda, Chikara Kawamura, Isamu Kizaki, Yoichi Miyajima, Akihiro Takezawa, Mitsuru Kitamura, “Construction of Design Guidelines for Optimal Automotive Frame Shape Based on Statistical Approach and Mechanical Analysis”, CMES - Computer Modeling in Engineering and Sciences, Volume 128, Issue 2,2021, Pages 731-742.}