Discovering knowledge from data is a quantum jump from quantity to quality, which is the characteristic and the spirit of the development of science. Symbolic regression (SR) is playing a greater role in the discovery of knowledge from data, specifically in this era of exponential data growth, because SRs are able to discover mathematical formulas from data. These formulas may provide scientifically meaningful models, especially when combined with domain knowledge. This article provides an overview of SR applications in the field of materials science and engineering. Integrating domain knowledge with SR is the key and a crucial approach, which allows gaining knowledge from data quickly, accurately, and scientifically. In the data-driven paradigm, SR allows for uncovering the underlying mechanisms of materials behavior, properties, and functions, in a wide range of areas from basic academic research to industrial applications, including experiments and computations, by providing explicit interpretable models from data, in comparison with other machine-learning “black-box” models. SR will be a powerful tool for rational and automatic materials development.

Continued progress in artificial intelligence (AI) and associated demonstrations of superhuman performance have raised the expectation that AI can revolutionize scientific discovery in general and materials science specifically. We illustrate the success of machine learning (ML) algorithms in tasks ranging from machine vision to game playing and describe how existing algorithms can also be impactful in materials science, while noting key limitations for accelerating materials discovery. Issues of data scarcity and the combinatorial nature of materials spaces, which limit application of ML techniques in materials science, can be overcome by exploiting the rich scientific knowledge from physics and chemistry using additional AI techniques such as reasoning, planning, and knowledge representation. The integration of these techniques in materials-intelligent systems will enable AI governance of the scientific method and autonomous scientific discovery.

The authors developed a Behler–Parrinello-type neural network (NN) to improve the density-functional tight-binding (DFTB) energy and force prediction. The Δ-machine learning approach was adopted and the NN was designed to predict the energy differences between the density functional theory (DFT) quantum chemical potential and DFTB for a given molecular structure. Most notably, the DFTB-NN method is capable of improving the energetics of intramolecular hydrogen bonds and torsional potentials without modifying the framework of DFTB itself. This improvement enables considerably larger simulations of complex chemical systems that currently could not easily been accomplished using DFT or higher level ab initio quantum chemistry methods alone.

We report on the structural evolution of diamond-like carbon (DLC) films by the nanosecond pulsed laser annealing process. DLC film is coated on cemented carbide (WC-Co) by cathodic arc ion plating, which is then annealed by ArF laser (193 nm, 20 ns) at different laser fluences (0.9–1.7 J/cm2). Upon laser annealing, Raman spectra divulge higher sp3 fractions accompanied by a blue shift in the G-peak position, which indicates the changes of sp2 sites from rings to chains. At higher fluence (>1.2 J/cm2), the film converts into reduced graphene oxide confirmed by its Raman-active vibrational modes: D, G, and 2D.

The authors prepared a micro-structured, thermosensitive hydrogel with N-isopropylacrylamide microgels with a lower critical solution temperature (LCST) of 32 °C dispersed on a matrix of N-isopropylacrylamide-co-dimethylacrylamide with an LCST at 40 °C. Incubation of the hydrogel at 33 °C in a solution of fluorescein-albumin induced loading of the protein. The protein was not loaded at a temperature below the LCST of the microgels (4 °C), suggesting that the shrinkage of the microgels followed by the formation of micropores within the hydrogel matrix is a prerequisite for protein loading. A sustained and complete release of the loaded protein was obtained at 37 °C.

Herein, we present the fabrication and characterization of Gd:PbI2 thin films from low-cost material using a cost-effective spin-coating technique by taking the Gd content as 1.0, 2.0, and 3.0 wt% in PbI2. Single-phase and good crystallinity films oriented along the c-axis were confirmed by X-ray diffraction and FT-Raman spectroscopy. Size of crystallites increased with Gd concentration and was estimated to be in the range of 16–32 nm. Determination of morphology and size of grains (50–103 nm), and elemental confirmation were carried out by SEM/EDX analysis. Optical transparency of fabricated films was found to be in the range of 72–92%. The energy gap is reduced from 2.31 to 2.05 eV; this makes Gd:PbI2 films highly applicable in solar cells. The stable value of refractive index is estimated to be in the range of 1.85–2.3. Dielectric constant was observed to be reduced with doping and in the range of 2.5–35, and ac conductivity was also reduced by doping; however, both were enhanced with frequency. The values of χ(1), χ(3), and n(2) are found to be in the range of 0.15 to 2.5, 8 × 10−14 to 6.5 × 10−9, and 5 × 10−12 to 4 × 10−8, respectively.

Using general-purpose photovoltaic device model, we have simulated the operation and functionality of a working Sn perovskite/Cu2O hole transport layer (HTL)/Cu back-contact device versus a standard Pb perovskite/Spiro HTL/Ag back-contact device. The results are extremely promising in that they showcase comparable cell efficiencies, with the Sn perovskite/Cu2O HTL/Cu back-contact device showing a highest 22.9% efficiency [Jsc of 353.4 A/m2, Voc of 0.84 V, fill factor (FF) of 0.77] at 427 nm active layer thickness compared with 24.6% of the standard Pb perovskite/Spiro HTL/Ag back-contact device (Jsc of 356.8 A/m2, Voc of 0.82 V, FF of 0.84) at the same active layer thickness. Jsc, Voc, and FF kinetics reveal that the Sn perovskite/Cu2O HTL/Cu back-contact device can perform better by reducing the recombination centers both within each layer matrix and in the interfacial contacts.

Magnetic nanoparticles have many potential applications in therapeutics and drug delivery. Heating by magnetic nanoparticles for hyperthermia application has gained tremendous popularity as a non-invasive treatment for tumor ablation. The heating effect of magnetic nanoparticles at different concentrations (1–10 wt%) in the fluid is investigated by varying the alternating magnetic field (60–260 Oe). The observed temperature rise (ΔT) shows an unusual increase with applied field in a higher nanoparticle concentration. In contrast to the previous model, the present study shows that temperature rise is more rapid in the higher particle concentration (~10 wt%) and low applied field (<125 Oe), and ΔT varies as H3/2 instead of H2.

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.