Viktor Martinek

Viktor Martinek, Ophelia Frotscher, Markus Richter et al.

Thermodynamic equations of state (EOS) are essential for many industries as well as in academia. Even leaving aside the expensive and extensive measurement campaigns required for the data acquisition, the development of EOS is an intensely time-consuming process, which does often still heavily rely on expert knowledge and iterative fine-tuning. To improve upon and accelerate the EOS development process, we introduce thermodynamics-informed symbolic regression (TiSR), a symbolic regression (SR) tool aimed at thermodynamic EOS modeling. TiSR is already a capable SR tool, which was used in the research of https://doi.org/10.1007/s10765-023-03197-z. It aims to combine an SR base with the extensions required to work with often strongly scattered experimental data, different residual pre- and post-processing options, and additional features required to consider thermodynamic EOS development. Although TiSR is not ready for end users yet, this paper is intended to report on its current state, showcase the progress, and discuss (distant and not so distant) future directions. TiSR is available at https://github.com/scoop-group/TiSR and can be cited as https://doi.org/10.5281/zenodo.8317547.

Viktor Martinek, Roland Herzog

Symbolic Regression aims to find symbolic expressions that describe datasets. Due to better interpretability, it is a machine learning paradigm particularly powerful for scientific discovery. In recent years, several works have expanded the concept to allow the description of similar phenomena using a single expression with varying sets of parameters, thereby introducing categorical variables. Some previous works allow only "non-shared" (category-value-specific) parameters, and others also incorporate "shared" (category-value-agnostic) parameters. We expand upon those efforts by considering multiple categorical variables, and introducing intermediate levels of parameter sharing. With two categorical variables, an intermediate level of parameter sharing emerges, i.e., parameters which are shared across either category but change across the other. The new approach potentially decreases the number of parameters, while revealing additional information about the problem. Using a synthetic, fitting-only example, we test the limits of this setup in terms of data requirement reduction and transfer learning. As a real-world symbolic regression example, we demonstrate the benefits of the proposed approach on an astrophysics dataset used in a previous study, which considered only one categorical variable. We achieve a similar fit quality but require significantly fewer individual parameters, and extract additional information about the problem.

Viktor Martinek

Symbolic regression (SR) uncovers mathematical models from data. Several benchmarks have been proposed to compare the performance of SR algorithms. However, existing ground-truth rediscovery benchmarks overemphasize the recovery of "the one" expression form or rely solely on computer algebra systems (such as SymPy) to assess success. Furthermore, existing benchmarks continue the expression search even after its discovery. We improve upon these issues by introducing curated lists of acceptable expressions, and a callback mechanism for early termination. As a starting point, we use the symbolic regression for scientific discovery (SRSD) benchmark problems proposed by Yoshitomo et al., and benchmark the two SR packages SymbolicRegression.jl and TiSR. The new benchmarking method increases the rediscovery rate of SymbolicRegression.jl from 26.7%, as reported by Yoshitomo et at., to 44.7%. Performing the benchmark takes 41.2% less computational expense. TiSR's rediscovery rate is 69.4%, while performing the benchmark saves 63% time.