Regularised atomic body-ordered permutation-invariant polynomials for the construction of interatomic potentials

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

“…Moreover, it was recently demonstrated in Ref. [22] that including liquid structures acts as regularization of the fitting solution, which improves the transferability and prediction power of ML potentials.…”

“…Most commonly, atomic descriptors encode the local geometry on neighboring atoms using the distances and/or angles between atoms [11,15,18], spectral analysis of local atomic environments [15,18] or a tensorial description of atomic coordinates [19,20]. A systematic basis that preserves the symmetry of the potential energy function with respect to rotations and permutations can also be developed by writing the total energy as a sum of atomic body-ordered terms giving atomic body-ordered permutation-invariant polynomials [21,22]. Some innovative descriptors, e.g., proposed by Mallat et al [23,24], are based on the scaling wavelets transformation.…”

Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport

“…In a ML potential, the site potential U i is not directly modeled as a function of the relative coordinates {r i j }, but as a function of a high-dimensional descriptor vector, whose components are invariant with respect to spatial translation, three-dimensional rotation and inversion, and permutation of atoms with the same species [30]. Many descriptors have been proposed, including, e.g., Behler's symmetry functions [31], the smooth overlap of atomic positions (SOAP) [30], the bispectrum [7], the Coulomb matrix [32], the moment tensor [17], the atomic cluster expansions [33], the embedded atom descriptor [34], the Gaussian moments [35], and the atomic permutationally invariant polynomials [36]. There are libraries implementing various descriptors [37][38][39].…”

Perspective on integrating machine learning into computational chemistry and materials science

“…249 MQCD, i.e., classical dynamics of nuclei coupled to the time-dependent quantum mechanical evolution of electrons, are commonly used to simulate light-induced nonadiabatic dynamics of molecules, [250][251][252] as well as coupled electron-nuclear dynamics in extended systems. 253 While on-the-fly MQCD simulations have become feasible in the last decade, the accessible time scale and the number of non-equilibrium trajectories that can realistically be simulated on-the-fly is too limited to enable comprehensive statistical analysis and ensemble averaging. ML shows great promise in nonadiabatic excitedstate simulations 20,21 as documented by recent works using NNs to construct excited-state energy landscapes to perform fewest-switches surface hopping MD at longer time scales or with more comprehensive ensemble averaging than would otherwise be possible with on-the-fly dynamics.…”

“…Recently, explicit atomic high body order expansions in permutationally invariant polynomials (e.g. aPIPs 273 , ACE 274 ) have emerged as appealing alternative to kernel and deep learning methods as they accurately This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.…”