Fraunhofer Institute for Mechanics of Materials IWMMachine learning only reaches its full potential when expert knowledge is specifically integrated. This is exactly what gray-box models do: they combine data-driven AI methods with physical and process-specific domain knowledge. The project has demonstrated how materials parameters can be identified, production processes modeled, and microstructures automatically classified.
Grey-Box Models – Integrating Application Knowledge into Learning Processes
Completed research project
Project description
Market needs and challenges
Industrial production processes are becoming increasingly complex, while available process data is often sparse and incomplete. Purely data-driven black-box models frequently fail due to a lack of interpretability and generalizability. At the same time, physics-based white-box models are computationally intensive and not flexible enough for use in real-time process control. Industry and SMEs need models that combine both efficiency and comprehensibility.
Project approach
Grey-box models specifically integrate domain and expert knowledge into machine learning methods. The project developed methods that combine simulation data, physical relationships, and statistical learning methods. Specific approaches include adaptive sampling algorithms for efficient parameter exploration, surrogate models for forming processes, gray-box approaches for materials parameter identification, and causality-based structure recognition in production facilities - always with the goal of making models more interpretable and robust.
Contribution to addressing challenges
The methods developed make it possible to create reliable process models with significantly less data and computational effort. Automated classification of microstructures replaces subjective manual evaluations. Adaptive sampling methods significantly reduce the simulation effort. Causality analyses help identify the causes of errors in plants at an early stage. In this way, gray-box models make a concrete contribution to quality assurance, process optimization, and digitalization in the manufacturing industry.
Fraunhofer IWM’s work packages in the project:
Focus area 1: Materials parameter identification
Fraunhofer IWM developed gray-box approaches for identifying materials parameters from experimental data. A “mixture of experts” model and neural networks with a physically informed custom loss function were used. Result: reproducible stress-strain curves based on identified materials parameters.
Focus area 2: Surrogate modeling for forming processes
Using cup drawing as an example, knowledge-based and data-driven feature extraction methods (feature engineering vs. feature learning) were compared. Result: a surrogate model with uncertainty quantification (Gaussian processes) that reliably predicts process results from a small amount of simulation data.
Focus area 3: Automatic classification of microstructures
Fracture surfaces from SEM images were automatically classified using gray-box approaches (Haralick texture features, random forests, SVMs). Result: the first validated methodology for objective, reproducible damage analysis as an alternative to manual evaluation.
Based on the project results, Fraunhofer IWM can offer industrial companies the following research and development services:
1. Materials parameter identification using gray-box methods
Fraunhofer IWM identifies materials model parameters from experimental data by combining machine learning with physical domain knowledge. Mixture-of-Experts models and neural networks with physically informed loss functions are used. Industrial companies benefit from faster, more objective, and reproducible calibration of their materials models.
2. Surrogate modeling for forming processes
Fraunhofer IWM develops data-efficient surrogate models for forming simulations that require relatively few simulation runs. Using cup drawing as an example, the institute demonstrated how probabilistic models (Gaussian processes) reliably predict process results while simultaneously quantifying uncertainties. For companies, this means a significant reduction in computational and time requirements during process design.
3. Automated classification of microstructures and fracture surfaces
Grey-box approaches are used to automatically detect and classify fracture surfaces and microstructures in high-resolution SEM images. This involves combining Haralick texture features with classical ML methods such as random forests and support vector machines. This provides industrial companies with an objective, reproducible alternative to time-consuming manual damage analysis, with the potential to accelerate and standardize quality assurance processes.
4. Knowledge-based feature extraction for process and simulation data
Fraunhofer IWM develops customized methods for extracting relevant features from high-dimensional simulation and measurement data. Both knowledge-based (feature engineering) and data-driven approaches (feature learning) are compared to identify the most suitable strategy for the specific application. The results are compact, interpretable data representations that serve as the basis for process control and quality assessment.
5. Adaptive sampling strategies for simulation spaces
In cooperation with partners, Fraunhofer IWM applies adaptive, data-driven sampling methods to explore the parameter space of simulations in a targeted and efficient manner. Through the intelligent selection of new simulation points, the information gain per simulation run is maximized. This enables companies to reduce the effort required for time-consuming parameter studies in process and product development and to improve the data foundation for downstream ML models.
6. Gray-Box models for process modeling with uncertainty quantification
Fraunhofer IWM creates process models that specifically combine physical expert knowledge with statistical learning methods while explicitly identifying prediction uncertainties. This approach is particularly well-suited for use cases where only limited process data is available. In addition to precise process predictions, companies receive reliable information about the certainty of these predictions.
