The optimization algorithm starts from the initial geometries (Geo init ) and the initial force field (F F init ) then the force field is iteratively improved. For each iteration of the training loop shown in Algorithm 3, two different local optimizations are performed, one being local geometry optimization using the steepest descent method and the main one being minimization of the fitness error on the energy minimized geometries by updating the force field parameters using various local optimization method such as L-BFGS-B and SLSQP. Both of these methods are classified as quasi-Newton methods where the Hessian matrix is approximated by successive gradient calculations . Error minimization step uses the Geo min and the optimized force field (F F cur ) from the last iteration and after applying the selected gradient-based algorithm, F F cur gets updated with the newly trained force field. This step uses the surrogate model where the error is calculated with only the single step calculations. After that the geometry optimization step starts from Geo init and yields optimized geometries (Geo min ) using F F cur . The true error is calculated right after the geometry optimization, if there are any geometries that require it. After each iteration, the true error (E cur ) for F F cur on the training data is calculated. If E cur is lower than the lowest error so far (E best ), F F cur is saved as the best force field (F F best ). The error on the surrogate gets closer to the true error as parameters converge because changes in parameters become minimal. One disadvantage of separating the energy minimization from the local optimization is that the fitness score for the geometry items will be be ignored by the local optimization since the atom positions will not change. This introduces a discrepancy between the true error and the surrogate one. However, if the training data has multiple items related to the geometry based items as a result of potential energy surface scans (PES), the discrepancy could be minimized. As it is demonstrated through numerical experiments, the surrogate approach works well in practice for a variety of training tasks which have geometry based items.