Active learning of potential-energy surfaces of weakly bound complexes with regression-tree ensembles.

Several pool-based active learning (AL) algorithms were employed to model potential-energy surfaces (PESs) with a minimum number of electronic structure calculations. Theoretical and empirical results suggest that superior strategies can be obtained by sampling molecular structures corresponding to large uncertainties in their predictions while at the same time not deviating much from the true distribution of the data. To model PESs in an AL framework, we propose to use a regression version of stochastic query by forest, a hybrid method that samples points corresponding to large uncertainties while avoiding collecting too many points from sparse regions of space. The algorithm is implemented with decision trees that come with relatively small computational costs. We empirically show that this algorithm requires around half the data to converge to the same accuracy in comparison to the uncertainty-based query-by-committee algorithm. Moreover, the algorithm is fully automatic and does not require any prior knowledge of the PES. Simulations on a 6D PES of pyrrole(H2O) show that <15 000 configurations are enough to build a PES with a generalization error of 16 cm-1, whereas the final model with around 50 000 configurations has a generalization error of 11 cm-1.

Filter calculation for x-ray tomosynthesis reconstruction.

Filtered backprojection reconstruction is an efficient image reconstruction method which is widely used in CT and 3D x-ray imaging. The way data have to be filtered depends on the acquisition geometry and the number of projections (views) which were acquired. For standard geometries like circle or helix it is known how to effectively filter the data. But there are acquisition geometries for which the application of standard filters yields poor results, e.g. in situations where the number of views is very small or for a limited angular range. In tomosynthesis, both conditions apply, i.e. the number of projections is typically very small and, moreover, the angular coverage is much less than 180°. This paper proposes a new method to design effective filters which are specific for the acquisition geometry. Examples from x-ray tomosynthesis are utilized to demonstrate the excellent performance of the proposed method.