The left panelshows the energy profile for arotation around an O-C-C-C dihedral angle. In the right panel of Figure 4, we show energy predictions along a minimum energy path of an intramolecular hydrogen transfer reaction. A.2.2 3BPADataset The 3BPA dataset contains DFT train test splits of a flexible drug-like organic molecule sampled from different temperature molecular dynamics trajectories [33]. The first step of the algorithm is to contract the generalized Clebsch-Gordan coefficients with the weights of the product basis. Then, the last dimension of cν is contracted with theAi-features' last dimension resulting in the a-tensor with correlation orderν 1.

Recently, several equivariant message passing neural networks (MPNNs) have been shown to outperform models built using otherapproaches intermsofaccuracy.

In the paper, we propose a class of efficient mirror descent ascent methods to solve the nonsmooth nonconvex-strongly-concave minimax problems by using dynamic mirror functions, and introduce a convergence analysis framework to conduct rigorous theoretical analysis forourmirror descent ascent methods. For our stochastic algorithms, we first prove that the mini-batch stochastic mirror descent ascent (SMDA) method obtains agradient complexity ofO(κ3 4)for findingan -stationary point,whereκdenotes thecondition number.