Exploring parameter dependence of atomic minima with implicit differentiation
Abstract Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has found application for emerging invers...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | npj Computational Materials |
| Online Access: | https://doi.org/10.1038/s41524-024-01506-0 |
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| _version_ | 1832571485971021824 |
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| author | Ivan Maliyov Petr Grigorev Thomas D. Swinburne |
| author_facet | Ivan Maliyov Petr Grigorev Thomas D. Swinburne |
| author_sort | Ivan Maliyov |
| collection | DOAJ |
| description | Abstract Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has found application for emerging inverse problems such as fine-tuning or targeted design. Here, the implicit derivative of functions defined as a fixed point is used to Taylor-expand the energy and structure of atomic minima in potential parameters, evaluating terms via automatic differentiation, dense linear algebra or a sparse operator approach. The latter allows efficient forward and backpropagation through relaxed structures of arbitrarily large systems. The implicit expansion accurately predicts lattice distortion and defect formation energies and volumes with classical and machine-learning potentials, enabling high-dimensional uncertainty propagation without prohibitive overhead. We then show how the implicit derivative can be used to solve challenging inverse problems, minimizing an implicit loss to fine-tune potentials and stabilize solute-induced structural rearrangements at dislocations in tungsten. |
| format | Article |
| id | doaj-art-ed783071f8044725a8b17747f108da89 |
| institution | Kabale University |
| issn | 2057-3960 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Computational Materials |
| spelling | doaj-art-ed783071f8044725a8b17747f108da892025-02-02T12:33:48ZengNature Portfolionpj Computational Materials2057-39602025-01-011111810.1038/s41524-024-01506-0Exploring parameter dependence of atomic minima with implicit differentiationIvan Maliyov0Petr Grigorev1Thomas D. Swinburne2Aix-Marseille Université, CNRS, CINaM UMR 7325Aix-Marseille Université, CNRS, CINaM UMR 7325Aix-Marseille Université, CNRS, CINaM UMR 7325Abstract Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has found application for emerging inverse problems such as fine-tuning or targeted design. Here, the implicit derivative of functions defined as a fixed point is used to Taylor-expand the energy and structure of atomic minima in potential parameters, evaluating terms via automatic differentiation, dense linear algebra or a sparse operator approach. The latter allows efficient forward and backpropagation through relaxed structures of arbitrarily large systems. The implicit expansion accurately predicts lattice distortion and defect formation energies and volumes with classical and machine-learning potentials, enabling high-dimensional uncertainty propagation without prohibitive overhead. We then show how the implicit derivative can be used to solve challenging inverse problems, minimizing an implicit loss to fine-tune potentials and stabilize solute-induced structural rearrangements at dislocations in tungsten.https://doi.org/10.1038/s41524-024-01506-0 |
| spellingShingle | Ivan Maliyov Petr Grigorev Thomas D. Swinburne Exploring parameter dependence of atomic minima with implicit differentiation npj Computational Materials |
| title | Exploring parameter dependence of atomic minima with implicit differentiation |
| title_full | Exploring parameter dependence of atomic minima with implicit differentiation |
| title_fullStr | Exploring parameter dependence of atomic minima with implicit differentiation |
| title_full_unstemmed | Exploring parameter dependence of atomic minima with implicit differentiation |
| title_short | Exploring parameter dependence of atomic minima with implicit differentiation |
| title_sort | exploring parameter dependence of atomic minima with implicit differentiation |
| url | https://doi.org/10.1038/s41524-024-01506-0 |
| work_keys_str_mv | AT ivanmaliyov exploringparameterdependenceofatomicminimawithimplicitdifferentiation AT petrgrigorev exploringparameterdependenceofatomicminimawithimplicitdifferentiation AT thomasdswinburne exploringparameterdependenceofatomicminimawithimplicitdifferentiation |