Symbolic regression in materials science
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Artificial Intelligence Prospective
Symbolic regression in materials science Yiqun Wang†, Nicholas Wagner†, and James M. Rondinelli Evanston, IL 60208, USA
, Department of Materials Science and Engineering, Northwestern University,
Address all correspondence to James M. Rondinelli at [email protected] (Received 13 January 2019; accepted 11 June 2019)
Abstract The authors showcase the potential of symbolic regression as an analytic method for use in materials research. First, the authors briefly describe the current state-of-the-art method, genetic programming-based symbolic regression (GPSR), and recent advances in symbolic regression techniques. Next, the authors discuss industrial applications of symbolic regression and its potential applications in materials science. The authors then present two GPSR use-cases: formulating a transformation kinetics law and showing the learning scheme discovers the well-known Johnson–Mehl–Avrami–Kolmogorov form, and learning the Landau free energy functional form for the displacive tilt transition in perovskite LaNiO3. Finally, the authors propose that symbolic regression techniques should be considered by materials scientists as an alternative to other machine learning-based regression models for learning from data.
Motivation Era of big data in materials science Modern scientists perpetuate the scientific process embodied by the works of Tyco Brahe, Johannes Kepler, and Isaac Newton in the heliocentric revolution. Brahe was the observationalist. He took extensive, precise measurements of the position of planets over time. Kepler was the phenomenologist. From Brahe’s measurements, he derived concise analytic expressions that describe the motion of the solar system in a succinct manner. Last, Newton was the theorist. He realized that the mechanism behind the apple falling from the tree is the same as that underlying planets traveling around the sun, which could be formulated into a universal law (Newtonian gravitational law). All three scientific modalities are vital in making scientific discoveries: data acquisition (Brahe), data analysis (Kepler), and derivation from first principles (Newton). With recent advances in computer science, theoretical modeling, and experimental instrumentation, materials scientists have, in many ways, created a “mechanical Brahe” and marched into a new era of big data. Datasets of materials information, obtained from advanced characterization techniques,[1–3] combinatorial experiments,[4–6] high-throughput first-principle simulations,[7,8] literature mining,[9,10] and other techniques, are created at a faster rate every day with less and less human labor. All of this data enables new opportunities to construct novel laws of phenomenological behavior for systems that previously lacked them. Inspired by the Materials Genome Initiative,[11] the materials community is working collaboratively towards making digital
†
These authors contributed equally to this work.
materials data accessible to others. Multiple materials databases, such as Mater
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