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Within the Josef Ressel Centre for Symbolic Regression we work on new algorithms for symbolic regression and develop a methodological and technical framework for incremental model adaptation for handling concept drift with symbolic regression models.

## Facts

- Lead: Gabriel Kronberger, University of Applied Sciences Upper Austria (FH OÖ)
- Duration: 2 years initial phase, 3 years extension after successful evaluation
- Total budget: 1.140.000 Euro.
- 2 PhD Students, 2 Postdocs, Masterstudents
- Partner: FH OÖ, AVL List, Miba Frictec, Christian Doppler Research Association

## Partner

The Josef Ressel Centre is a cooperation of three companies. It is led by University of Applied Sciences Upper Austria, Hagenberg Campus (FH OÖ). The two company partners are AVL List GmbH and Miba Frictec GmbH. They provide relevant business cases and expert knowledge as well as infrastructure (testing benches) and data. The company partners also provide 50% of the financial funding for the project. The other 50% are funded by the BMDW through the Christian Doppler Research Association.

## Publications

The project has been started in January 2018. There are publications so far.

## Research

Symbolic regression is a data-based modelling method where the goal is to find a formula that describes given data. Similarly to other regression methods, a goal is to create a model that allows to predict one or multiple variables given known values for the variables used as input to the model. However, in symbolic regression one does not merely fit parameters to a fixed model structure. Instead, the goal is to identify the necessary model structure as well as optimal model parameters for the given dataset.

*Symbolic regression means to find a simple symbolic expression (formula) that fits a given dataset. It is a supervised learning technique.*

The term symbolic regression stems from earlier work by John Koza on genetic programming. In later developments different algorithm variants for symbolic regression have been proposed many of which are based on evolutionary algorithms.

When using genetic programming the users specifies which operators and basic functions are allowed to be used in the symbolic regression model. The algorithm starts with a set of random expressions and through selection and recombination evolves a well-fitting symbolic regression model.

The resulting symbolic regression model might look like the following:

*A symbolic regression model produced with genetic programming.*

A drawback of evolutionary algorithms is that they are non-deterministic. For industrial applications we need deterministic and efficient parameter-less solvers for symbolic regression problems. In the Josef Ressel Centre we develop and implement such algorithms.

We take up the idea of “Prioritized Grammar Enumeration” (Worm and Chiu, 2013) which uses dynamic programming to create symbolic regression models. The algorithm uses a formal grammar as input which describes the structure of the symbolic regression models and is then able to produce all models for this structure up to a certain maximum size. The approach has potentially exponential asymptotic runtime for increasing formula sizes or number of variables. Therefore, heuristics are necessary to guide the search process to potentially more interesting parts of the search tree.

*Prioritized grammar enumeration is a non-evolutionary solution methods for symbolic regression. Formulas are generated from a formal grammar, identical functions are detected via dynamic programming.*

## Applications

Symbolic regression is a general technique that can be used for modelling technical systems. In the Josef Ressel Centre we use it for modelling components of powertrains.

*An example for a hybrid power train with engine, electric motor with battery, transmission and differential drive. Modern powertrains are made up from many complex components and there are many possible design variants. Models are necessary for simulation of powertrains in a virtual design process. We plan to use symbolic regression e.g. for modelling engine performance, or, friction performance, or battery load state.*

For this we use data from testing benches as operated by our company partners AVL and Miba.

*Testing bench for friction plates as operated by Miba Frictec in Roitham. Foto: © Bernhard Plank (http://imBilde.at)*

Two company partners participate in the proposed JRC. AVL List GmbH (AVL) is the largest independent company for development, simulation and testing technology of powertrains. AVL uses various methods for regression modelling for powertrain development and develops a commercial software product for powertrain calibration (AVL CAMEO ™). AVL plans to integrate the developed symbolic regression algorithms into the AVL CAMEO Software. Furthermore, we investigate whether symbolic regression models can be implemented successfully on engine or transmission control units for optimized control of powertrain components.

Miba Frictec GmbH (Miba) produces friction materials and components for friction systems as used for instance in clutch and automatic transmission systems and provides services for the design and dimensioning of friction systems. Miba currently uses symbolic regression models for the prediction of key characteristics of friction plates for virtual design and dimensioning of friction systems. These models are trained on data gathered from multiple test‐benches for friction systems that are operated in Roitham. Miba plans to integrate the results of the JRC into their in‐house software‐tools so that Miba engineers are able to easily create and validate symbolic regression models for friction systems.

## HeuristicLab

We plan to integrate the methods developed in thr JRC into our open-source software framework HeuristicLab.

HeuristicLab is used by academics and practitioners all over the world for teaching and industrial projects.

## Team

*Michael Kommenda, Gabriel Kronberger (Lead), Lukas Kammerer, Florian Bachinger, Bogdan Burlacu, Eva-Maria Holzleitner (© Petra Wiesinger, FH OÖ)*

## Further Information

Project description on the CDG website:

http://www.cdg.ac.at/forschungseinheiten/labor/symbolische-regression/?tx_cdglabors_labors%5Baction%5D=show&tx_cdglabors_labors%5Bcontroller%5D=Labor