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We present machine learning models for fast estimating atomic forces. In our method, the total energy of a system is approximated as the summation of atomic energy which is the interaction energy with its surrounding chemical environment within a certain cutoff radius. Atomic energy is decomposed into two-body terms which are expressed as a linear combination of basis functions. For the force exerted on an atom, we employ a linear combination of a set of basis functions for representing pairwise force. We use least-square linear regression regularized by the l2-norm, known as Ridge regression, to estimate model parameters. We demonstrate that our model can accurately reproduce atomic forces and energies from density-functional-theory (DFT) calculations for crystalline and amorphous silicon. The machine learning force model is then applied to calculate the phonon dispersion of crystalline silicon. The result shows reasonable agreement with DFT calculations.
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