Stability (learning theory)

Physics

Interatomic potential

Mathematics

Politics

Operating system

Statistical physics

Statistics

Quadratic equation

Machine learning

Pseudopotential

Logit

Political science

Dislocation

Composite material

Materials science

Geometry

Condensed matter physics

Representation (politics)

Space (punctuation)

Computer science

Flexibility (engineering)

Molecular dynamics

Transferability

Quantum mechanics

Observable

Physical Review Materials

Data-driven, or machine learning (ML), approaches have become viable alternatives to semiempirical methods to construct interatomic potentials, due to their capacity to accurately interpolate and extrapolate from first-principles simulations if the training database and descriptor representation of atomic structures are carefully chosen. Here, we present highly accurate interatomic potentials suitable for the study of dislocations, point defects, and their clusters in bcc iron and tungsten, constructed using a linear or quadratic input-output mapping from descriptor space. The proposed quadratic formulation, called quadratic noise ML, differs from previous approaches, being strongly preconditioned by the linear solution. The developed potentials are compared to a wide range of existing ML and semiempirical potentials, and are shown to have sufficient accuracy to distinguish changes in the exchange-correlation functional or pseudopotential in the underlying reference data, while retaining excellent transferability. The flexibility of the underlying approach is able to target properties almost unattainable by traditional methods, such as the negative divacancy binding energy in W or the shape and the magnitude of the Peierls barrier of the $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ screw dislocation in both metals. We also show how the developed potentials can be used to target important observables that require large time-and-space scales unattainable with first-principles methods, though we emphasize the importance of thoughtful database design and degrees of nonlinearity of the descriptor space to achieve the appropriate passage of information to large-scale calculations. As a demonstration, we perform direct atomistic calculations of the relative stability of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ dislocations loops and three-dimensional C15 clusters in Fe and find the crossover between the formation energies of the two classes of interstitial defects occurs at around 40 self-interstitial atoms. We also compute the kink-pair formation energy of the $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ screw dislocation in Fe and W, finding good agreement with density functional theory informed line tension models that indirectly measure those quantities. Finally, we exploit the excellent finite-temperature properties to compute vacancy formation free energies with full anharmonicity in thermal vibrations. The presented potentials thus open up many avenues for systematic investigation of free-energy landscape of defects with ab initio accuracy.

Efficient and transferable machine learning potentials for the simulation of crystal defects in bcc Fe and W