Integrating the O(N) sparse differentiation Hessian algorithm with long-range machine learning interatomic potentials (such as MACE-POLAR or LOREM) enables the calculation of exact analytic Hessians for defect structures in \text{SrTiO}_3 supercells containing over 10,000 atoms in less wall-clock time than standard numerical differentiation using a short-range baseline MACE model.
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Related patents (prior art)
This hypothesis overlaps subject matter covered by existing third-party patents. It is published as research, not as a patentable claim of ours.
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Supporting Research Papers
- Long-Range Machine Learning Interatomic Potentials for Defect Energetics in SrTiO₃
Machine learning interatomic potentials (MLIPs) have advanced rapidly in recent years, yet the majority of models remain semilocal in nature and neglect long-range electrostatic interactions. A growin...
- Colour me shocked: Exact Molecular Hessians from local MLIPs in O(N) time using sparse differentiation!
The Hessian of the energy with respect to the nuclear positions is indispensable in atomistic modelling. However, constructing this matrix requires O(N) Hessian vector products, traditionally limiting...
- Truncated automatic sparse differentiation for machine learning interatomic potentials
Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily ...
- Permutation invariant neural network prediction of vacancy formation under deformation and varying chemical environment in FCC high entropy alloys
Vacancy formation energies govern diffusion, irradiation damage, phase stability, and dynamic failure in high-entropy alloys (HEAs), yet their strong dependence on local chemical environments and mech...
- Machine learning predictions of the Hessian matrix for peptides chains and small proteins
Molecular Hessians have a key role in describing molecular vibrations, trajectories and optimization paths. An explicit calculation of them through standard quantum mechanical methods can be computati...
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