Speaker
Description
Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Parameter dependence is typically explored through repeating simulations with resampled parameters, a forward-only approach that becomes prohibitively expensive for the high parameter dimension of modern machine learning potentials.
In this talk, I will present an analytical scheme to forward- and back-propagate potential parameter variation through energy minimization. This is achieved via the implicit derivative of an implicit function defined at a fixed point, such as an energy minimum. The implicit derivative gives an analytic expansion of minimum energy and structure as functions of potential parameters, used for high-throughput uncertainty quantification in forward propagation and solution of challenging inverse problems in backpropagation.
I will discuss how the implicit derivative can be efficiently evaluated for large atomic systems, in particular, using a sparse operator approach to compute the implicit derivative implemented in both automatic differentiation (AD) and non-AD frameworks. Our implementation in the LAMMPS code has minimal memory usage and excellent scalability, allowing implicit derivative evaluation for systems of arbitrary size[1].
I will show how the implicit derivative can be used to expand the scope of atomic simulation methods. In forward propagation, the implicit expansion has sufficient accuracy to replace thousands of energy minimizations with a single calculation. This enables high-throughput uncertainty quantification and exploration of model phenomenology that is not possible with existing methods. In backpropagation, the implicit derivative allows us to ‘fine-tune’ interatomic potentials and target subtle solute-induced defect reconstruction, a key feature in understanding plasticity and irradiation damage in bcc metals.
[1] I. Maliyov, P. Grigorev, T.D. Swinburne, arXiv:2407.02414, 2024
