Learning Gradient Fields for Molecular Conformation Generation

Abstract

We study a fundamental problem in computational chemistry known as molecular conformation generation, trying to predict stable 3D structures from 2D molecular graphs. Existing machine learning approaches usually first predict distances between atoms and then generate a 3D structure satisfying the distances, where noise in predicted distances may induce extra errors during 3D coordinate generation. Inspired by the traditional force field methods for molecular dynamics simulation, in this paper, we propose a novel approach called ConfGF by directly estimating the gradient fields of the log density of atomic coordinates. The estimated gradient fields allow directly generating stable conformations via Langevin dynamics. However, the problem is very challenging as the gradient fields are rototranslation equivariant. We notice that estimating the gradient fields of atomic coordinates can be translated to estimating the gradient fields of interatomic distances, and hence develop a novel algorithm based on recent score-based generative models to effectively estimate these gradients. Experimental results across multiple tasks show that ConfGF outperforms previous state-of-the-art baselines by a significant margin.

SE(3) Equivariant Graph Neural Networks with Complete Local Frames

“…To generate molecular conformations (i.e. equilibrium state) with a single stage, (Shi et al, 2021) define "gradient filed" to serve as pseudo-forces acting on each particle. By evolving the particles following the direction of the gradient field, the nonequilibrium system will finally converge to an equilibrium state.…”

“…Learning Framework. Following (Shi et al, 2021), for this first-order statistical ensemble system, we leverage a score-based generative modeling framework to estimate the gradient field of atomic positions (See more details about score-based networks in (Shi et al, 2021; or Appendix A.2.3, A.3.2). The optimization objective of EVFN Φ can be summarized as:…”

“…Modeling many-body systems has been a long-standing challenge in scientific fields from classical and quantum physics (Carleo & Troyer, 2017;Zhang et al, 2018;Satorras et al, 2021b) to structural biology (Senior et al, 2020;Shi et al, 2021), due to its high numerical complexity and complicated evolving mechanism. Graph neural network (GNN), which is superior to model the high-dimensional structured data with permutation equivariance, brings a new opportunity to model the many-body systems in an end-to-end manner.…”

“…This drawback may become serious when modeling complex dynamical scenarios such as molecular simulation, where geometric information (e.g., angular potentials and rotatable bonds) plays an important role in inducing conformation changes (Klicpera et al (2020); ). To mitigate this issue, we propose a new model called Equivariant Vector Field Network (EVFN) to fit the gradient vector fields (Song & Ermon, 2019;Shi et al, 2021) of many-body systems. With a scalarization block and a vectorization block, EVFN is able to represent tensor information losslessly in the original space and outputs equivariant vector fields with no restriction on the direction.…”

Towards Conditional Generation of Minimal Action Potential Pathways for Molecular Dynamics

“…Another approach is to use a deep model to generate a new frame given a set of history frames using, by using temporal dynamical models such as LSTMs [18,8]. Other works have used Langevin dynamics to find stable conformations [17]. However, in this case, we want to generalize the model to predict outside the stable conformation, such that we can hopefully generate non-equilibrium trajectories.…”