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Hybrid Modeling: the best of both worlds

We work on a wide variety of cutting-edge AI research topics along with real-world applications ensuring the successful transfer into Bosch business.

Woman stands in server room and works on hybrid modeling with her laptop

Imagine you're a traveler embarking on a journey to a new and unfamiliar destination. You have a map that provides a general overview of the route, highlighting major landmarks and roads. However, you also have a local guide who knows the hidden gems, shortcuts, and insider knowledge that the map may not reveal. Individually, the map and the guide can help you navigate, but when you combine them, your journey becomes enriched and more fulfilling. The map gives you a big-picture understanding, while the guide adds depth and context. This symbolic relation between the map and the guide fits well to hybrid modeling.

What are Hybrid Models?

Just as in the introductory example hybrid models draw on the merging of two contrasting perspectives. Hybrid models offer a powerful approach by combining data-driven models, derived from observation or simulation, with first-principle based models rooted in statistics, physics, or chemistry. This integration proves particularly valuable in situations where neither approach alone suffices. While first-principle based models delve deep into the underlying physics of a system, they may fall short in capturing all relevant details, resulting in inaccuracies. Conversely, data-driven models excel at accurately capturing complex relationships within extensive data sets, but they may lack the ability to shed light on how the system behaves under new conditions. By integrating the two into a joint architecture, hybrid modeling can combine the strengths of both approaches offering a way to enable more accurate, interpretable predictions while making the solutions more data efficient and easier to validate.

Hybrid modeling graphic
Hybrid models combine data-driven models with first-principle based models.

The moon landing and Hybrid Modeling

The historic moon landing in 1969 stands as a remarkable demonstration to the power of combining physics-based principles with data-driven approaches. Precise navigation was a critical hurdle during the mission, as the spacecraft had to reach the target region with an accuracy of 500 meters after traveling 400,000 kilometers. By way of comparison, this is like throwing a ball 400 m and hitting the target with a precision of half a millimeter. Planning the flight trajectory relied on the laws of physics, but due to modeling errors and idealized assumptions, exact planning was not possible, especially when neglecting other celestial objects. To overcome this challenge, the spacecraft's position was regularly measured and compared to physics-based values. However, measurements have their limitations, including inherent inaccuracies and noise. Taking on this task, a pioneering hybrid modeling approach called the Kálmán filter was used. The Kálmán filter combines predictions on Newton’s Laws with onboard measurements to improve the accuracy of determining the actual position of the spacecraft. In this context, hybrid modeling has been an integral part of our scientific endeavors since the 1960s.

Graphic of the moon landing in 1969
The moon landing in 1969.

How does the technology work?

To understand the inner workings of this technology, hybrid modeling design patterns are used which effectively combine first principles-based (P) models with data-driven (D) models. These design patterns provide blue-prints for typical solutions to recurring modeling challenges and distill useful solution approaches that generalize across applications.

Hybrid Modeling Design Patterns
The design patterns can be communicated via block diagrams. Block diagrams consist of rectangular boxes representing computational blocks and of directed arrows, which indicate the flow of inputs and outputs between boxes.

The delta model is a foundational design pattern within hybrid modeling and serves as a powerful method for synergizing the strengths of first-principles-based and data-driven models. This design pattern proves particularly valuable when the first-principles-based model captures the underlying physical processes but may fall short in terms of precision or comprehensiveness for specific applications. By including a data-driven component that accounts for discrepancies or unmodeled phenomena, the delta model significantly improves the overall accuracy and predictive capabilities of the hybrid model. The Advantages: The delta model offers a number of compelling advantages that underscores its utility in hybrid modeling. One of its key strengths lies in its ability to facilitate rapid prototyping. With the availability of a first-principles-based model (P), modeling efforts can be initiated quickly. As more data becomes accessible or the need for greater precision arises, the data-driven component (D) can be introduced incrementally to refine the model without the need for a complete overhaul.

Physics-based preprocessing stands as another vital design pattern in hybrid modeling that leverages domain knowledge to optimize the performance of data-driven models. By incorporating transformations derived from physical laws or other domain-specific knowledge, this design pattern preprocesses the input data before feeding it into a data-driven model. The preprocessing step introduces valuable inductive biases, reduces data dimensionality, and enhances the overall efficiency and interpretability of the resulting model. The Advantages: Using the transformation model (P) allows the model to directly compute features, reducing the learning burden on the data-driven model (D). Particularly when P involves dimensionality reduction, the lower-dimensional representation often exhibits reduced complexity as noise is eliminated and redundant information is discarded. This simplification enables the learning algorithm to extract meaningful patterns more effectively and strike a better balance between performance and training dataset size, ultimately improving data efficiency.

Further examples of hybrid modeling design patterns include:

  • Feature learning
  • Physical constraints
  • Composition patterns

How is Hybrid Modeling relevant for Bosch?

Hybrid modeling holds significant relevance for Bosch in the realm of Industrial AI, offering an ideal balance between accuracy and resource efficiency in numerous areas. Bosch has already made notable strides in developing a diverse array of successful hybrid models spanning various domains like engineering or manufacturing. While many of these models were initially designed for specific projects, the underlying principles can be applied more broadly. As a result, Bosch is actively accelerating the implementation and adoption of hybrid modeling technology throughout the company, recognizing its potential to drive innovation and optimize performance across a wide range of applications.

Our Bosch Experts in Hybrid Modeling

Bosch experts in hybrid modeling
From left to right Barbara Rakitsch, Stefan Kurz, Maja Rudolph

At Bosch Research, a dedicated team of experts is working on introducing hybrid modeling methods into the various research areas and successively into the business units at Bosch.


Rudolph, M., Kurz, S., Rakitsch, B. (2023) Hybrid Modeling Design Patterns. [PDF]