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 quantifi...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 highdimensional 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.展开更多
基金support from an Emergence@INP grant from the CNRS.T.D.Sthanks the Institute for Pure and Applied Mathematics at the University of California,Los Angeles(supported by NSF grant DMS-1925919)for their hospitality.T.D.S+1 种基金P.G.gratefully acknowledge support from ANR grants ANR-19-CE46-0006-1 and ANR-23-CE46-0006-1,IDRIS allocationA0120913455EuratomGrantNo.633053.
文摘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 highdimensional 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.
