Modeling the Kinetics of Austenite Decomposition for Arbitrary Cooling Conditions Using Symbolic Regression

Bernhard Bloder; Gabriel Kronberger; Thomas Antretter; Peter Raninger

doi:10.1007/s11661-026-08211-1

Modeling the Kinetics of Austenite Decomposition for Arbitrary Cooling Conditions Using Symbolic Regression

Bernhard Bloder^*
, Gabriel Kronberger
, Thomas Antretter
, Peter Raninger

^*Corresponding author for this work

Research Center Hagenberg

Research output: Contribution to journal › Article › peer-review

Abstract

Symbolic regression searches for mathematical expressions that best fit a given set of data points. In this work we use this regression method to describe phase transformations from austenite to product phases for different isothermal and non-isothermal cooling conditions with a single analytical equation. Besides the data processing steps, we describe the underlying mathematical algorithm and present an expression for the employed data set. The resulting equation describes the phase transformation rate and can be used to describe the phase transformation kinetics for arbitrary cooling paths. The result is validated on four additional measurements with different heat treatment and final microstructures. The application of the method to a wider range of chemical compositions is discussed.

Original language	English
Pages (from-to)	3398-3410
Number of pages	13
Journal	Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science
Volume	57
Issue number	7
DOIs	https://doi.org/10.1007/s11661-026-08211-1
Publication status	Published - Jul 2026

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10.1007/s11661-026-08211-1

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title = "Modeling the Kinetics of Austenite Decomposition for Arbitrary Cooling Conditions Using Symbolic Regression",

abstract = "Symbolic regression searches for mathematical expressions that best fit a given set of data points. In this work we use this regression method to describe phase transformations from austenite to product phases for different isothermal and non-isothermal cooling conditions with a single analytical equation. Besides the data processing steps, we describe the underlying mathematical algorithm and present an expression for the employed data set. The resulting equation describes the phase transformation rate and can be used to describe the phase transformation kinetics for arbitrary cooling paths. The result is validated on four additional measurements with different heat treatment and final microstructures. The application of the method to a wider range of chemical compositions is discussed.",

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language = "English",

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Modeling the Kinetics of Austenite Decomposition for Arbitrary Cooling Conditions Using Symbolic Regression. / Bloder, Bernhard; Kronberger, Gabriel; Antretter, Thomas et al.
In: Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, Vol. 57, No. 7, 07.2026, p. 3398-3410.

Research output: Contribution to journal › Article › peer-review

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T1 - Modeling the Kinetics of Austenite Decomposition for Arbitrary Cooling Conditions Using Symbolic Regression

AU - Bloder, Bernhard

AU - Kronberger, Gabriel

AU - Antretter, Thomas

AU - Raninger, Peter

PY - 2026/7

Y1 - 2026/7

N2 - Symbolic regression searches for mathematical expressions that best fit a given set of data points. In this work we use this regression method to describe phase transformations from austenite to product phases for different isothermal and non-isothermal cooling conditions with a single analytical equation. Besides the data processing steps, we describe the underlying mathematical algorithm and present an expression for the employed data set. The resulting equation describes the phase transformation rate and can be used to describe the phase transformation kinetics for arbitrary cooling paths. The result is validated on four additional measurements with different heat treatment and final microstructures. The application of the method to a wider range of chemical compositions is discussed.

AB - Symbolic regression searches for mathematical expressions that best fit a given set of data points. In this work we use this regression method to describe phase transformations from austenite to product phases for different isothermal and non-isothermal cooling conditions with a single analytical equation. Besides the data processing steps, we describe the underlying mathematical algorithm and present an expression for the employed data set. The resulting equation describes the phase transformation rate and can be used to describe the phase transformation kinetics for arbitrary cooling paths. The result is validated on four additional measurements with different heat treatment and final microstructures. The application of the method to a wider range of chemical compositions is discussed.

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JF - Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science

IS - 7

ER -

Modeling the Kinetics of Austenite Decomposition for Arbitrary Cooling Conditions Using Symbolic Regression

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