Design patterns provide a systematic way to convey solutions to recurring
modeling challenges. This paper introduces design patterns for hybrid modeling,
an approach that combines modeling based on first principles with data-driven
modeling techniques. While both approaches have complementary advantages there
are often multiple ways to combine them into a hybrid model, and the
appropriate solution will depend on the problem at hand. In this paper, we
provide four base patterns that can serve as blueprints for combining
data-driven components with domain knowledge into a hybrid approach. In
addition, we also present two composition patterns that govern the combination
of the base patterns into more complex hybrid models. Each design pattern is
illustrated by typical use cases from application areas such as climate
modeling, engineering, and physics.

Introduction to Hybrid Modeling

The concept of hybrid modeling combines the strengths of two different modeling approaches: modeling based on first principles and data-driven modeling techniques. First principles modeling involves using fundamental laws, equations, and rules to describe a system or phenomenon mathematically. Data-driven modeling, on the other hand, uses data and statistical techniques to build models that can capture patterns and relationships.

By combining these two approaches, hybrid modeling aims to leverage the accuracy and interpretability of first principles models with the flexibility and predictive power of data-driven models. This allows for a more comprehensive understanding of complex systems and enables better predictions and decision-making.

Design Patterns for Hybrid Modeling

In order to enable the application of hybrid modeling in various domains, this paper introduces design patterns that provide systematic solutions to the challenges of hybrid modeling. These design patterns act as blueprints for combining data-driven components with domain knowledge into a cohesive hybrid model.

Base Patterns

The paper presents four base patterns that form the foundation of hybrid modeling:

  1. Data Augmentation Pattern: This pattern involves augmenting first principles models with additional data to enhance their accuracy and improve predictions. By incorporating real-world data into the model, it becomes more robust and capable of capturing non-linear relationships that might be missed by purely theoretical models.
  2. Reduced Order Modeling Pattern: In this pattern, data-driven techniques are used to create simplified, low-dimensional models based on high-dimensional first principles models. These reduced order models are computationally efficient and can be used for real-time simulations or optimization.
  3. Uncertainty Quantification Pattern: Uncertainty is an inherent part of both first principles and data-driven models. This pattern focuses on quantifying and propagating uncertainties through a hybrid model, allowing for more reliable predictions and better decision-making in the presence of uncertainty.
  4. Calibration Pattern: Calibration involves adjusting the parameters of a first principles model using data-driven techniques in order to improve its fit to real-world observations. This pattern enables fine-tuning of the model to account for discrepancies between model predictions and experimental data.

Composition Patterns

In addition to the base patterns, the paper introduces two composition patterns that govern the combination of the base patterns into more complex hybrid models:

  1. Sequential Composition Pattern: This pattern involves sequentially applying different base patterns to sequentially refine and enhance the hybrid model. Each base pattern can be applied in a specific order, depending on the problem at hand, to build a more comprehensive model.
  2. Parallel Composition Pattern: In this pattern, multiple base patterns are combined in parallel to create a holistic hybrid model. Each base pattern focuses on a specific aspect of the system and contributes to the overall understanding and predictive power of the model.

Applications and Implications

The design patterns for hybrid modeling presented in this paper have wide-ranging applications across various domains. The examples provided in the paper highlight the use of these patterns in climate modeling, engineering, and physics. However, the multi-disciplinary nature of hybrid modeling means that these patterns can be adapted and applied to other fields as well.

By adopting these design patterns, practitioners can approach hybrid modeling in a structured and systematic manner. This allows for efficient collaboration between domain experts, data scientists, and modelers from different disciplines. The resulting hybrid models have the potential to revolutionize decision-making processes by providing more accurate, robust, and interpretable predictions.


The concept of hybrid modeling offers great promise in addressing complex modeling challenges by combining first principles and data-driven modeling techniques. Through the introduction of design patterns for hybrid modeling, this paper provides a framework for systematically integrating these approaches. The four base patterns and two composition patterns serve as blueprints for building hybrid models that leverage the strengths of both approaches. With applications in diverse fields, hybrid modeling has the potential to propel scientific and engineering advancements to new heights.

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