Discovering causal relations and equations from data

G Camps-Valls, A Gerhardus, U Ninad, G Varando… - Physics Reports, 2023 - Elsevier
Physics is a field of science that has traditionally used the scientific method to answer
questions about why natural phenomena occur and to make testable models that explain the …

Artificial intelligence in physical sciences: Symbolic regression trends and perspectives

D Angelis, F Sofos, TE Karakasidis - Archives of Computational Methods …, 2023 - Springer
Symbolic regression (SR) is a machine learning-based regression method based on genetic
programming principles that integrates techniques and processes from heterogeneous …

A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge

LS Keren, A Liberzon, T Lazebnik - Scientific Reports, 2023 - nature.com
Discovering a meaningful symbolic expression that explains experimental data is a
fundamental challenge in many scientific fields. We present a novel, open-source …

[HTML][HTML] Shape-constrained multi-objective genetic programming for symbolic regression

C Haider, FO de Franca, B Burlacu, G Kronberger - Applied Soft Computing, 2023 - Elsevier
We describe and analyze algorithms for shape-constrained symbolic regression, which
allow the inclusion of prior knowledge about the shape of the regression function. This is …

Theory-inspired machine learning—towards a synergy between knowledge and data

JG Hoffer, AB Ofner, FM Rohrhofer, M Lovrić, R Kern… - Welding in the …, 2022 - Springer
Most engineering domains abound with models derived from first principles that have
beenproven to be effective for decades. These models are not only a valuable source of …

Controllable neural symbolic regression

T Bendinelli, L Biggio… - … Conference on Machine …, 2023 - proceedings.mlr.press
In symbolic regression, the objective is to find an analytical expression that accurately fits
experimental data with the minimal use of mathematical symbols such as operators …

Complementing a continuum thermodynamic approach to constitutive modeling with symbolic regression

K Garbrecht, D Birky, B Lester, J Emery… - Journal of the Mechanics …, 2023 - Elsevier
An interpretable machine learning method, physics-informed genetic programming-based
symbolic regression (P-GPSR), is integrated into a continuum thermodynamic approach to …

Toward physically plausible data-driven models: a novel neural network approach to symbolic regression

J Kubalík, E Derner, R Babuška - IEEE Access, 2023 - ieeexplore.ieee.org
Many real-world systems can be described by mathematical models that are human-
comprehensible, easy to analyze and help explain the system's behavior. Symbolic …

Interpretability in symbolic regression: a benchmark of explanatory methods using the Feynman data set

GSI Aldeia, FO de Franca - Genetic Programming and Evolvable …, 2022 - Springer
In some situations, the interpretability of the machine learning models plays a role as
important as the model accuracy. Interpretability comes from the need to trust the prediction …

Comparing optimistic and pessimistic constraint evaluation in shape-constrained symbolic regression

C Haider, FO de França, G Kronberger… - Proceedings of the …, 2022 - dl.acm.org
Shape-constrained Symbolic Regression integrates prior knowledge about the function
shape into the symbolic regression model. This can be used to enforce that the model has …