Yuanqing Wang, Kenichiro Takaba, Michael S. Chen et al.
A force field as accurate as quantum mechanics (QM) and as fast as molecular mechanics (MM), with which one can simulate a biomolecular system efficiently enough and meaningfully enough to get quantitative insights, is among the most ardent dreams of biophysicists -- a dream, nevertheless, not to be fulfilled any time soon. Machine learning force fields (MLFFs) represent a meaningful endeavor towards this direction, where differentiable neural functions are parametrized to fit ab initio energies, and furthermore forces through automatic differentiation. We argue that, as of now, the utility of the MLFF models is no longer bottlenecked by accuracy but primarily by their speed (as well as stability and generalizability), as many recent variants, on limited chemical spaces, have long surpassed the chemical accuracy of $1$ kcal/mol -- the empirical threshold beyond which realistic chemical predictions are possible -- though still magnitudes slower than MM. Hoping to kindle explorations and designs of faster, albeit perhaps slightly less accurate MLFFs, in this review, we focus our attention on the design space (the speed-accuracy tradeoff) between MM and ML force fields. After a brief review of the building blocks of force fields of either kind, we discuss the desired properties and challenges now faced by the force field development community, survey the efforts to make MM force fields more accurate and ML force fields faster, envision what the next generation of MLFF might look like.
Pedro O. Pinheiro, Joshua Rackers, Joseph Kleinhenz et al.
We propose a new score-based approach to generate 3D molecules represented as atomic densities on regular grids. First, we train a denoising neural network that learns to map from a smooth distribution of noisy molecules to the distribution of real molecules. Then, we follow the neural empirical Bayes framework (Saremi and Hyvarinen, 19) and generate molecules in two steps: (i) sample noisy density grids from a smooth distribution via underdamped Langevin Markov chain Monte Carlo, and (ii) recover the "clean" molecule by denoising the noisy grid with a single step. Our method, VoxMol, generates molecules in a fundamentally different way than the current state of the art (ie, diffusion models applied to atom point clouds). It differs in terms of the data representation, the noise model, the network architecture and the generative modeling algorithm. Our experiments show that VoxMol captures the distribution of drug-like molecules better than state of the art, while being faster to generate samples.
Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large advances in accuracy and data efficiency for a range of applications in the physical sciences. An outstanding question for equivariant models is why they achieve such larger-than-expected advances in these applications. To probe this question, we examine the role of higher order (non-scalar) features in Euclidean Neural Networks (\texttt{e3nn}). We focus on the previously studied application of \texttt{e3nn} to the problem of electron density prediction, which allows for a variety of non-scalar outputs, and examine whether the nature of the output (scalar $l=0$, vector $l=1$, or higher order $l>1$) is relevant to the effectiveness of non-scalar hidden features in the network. Further, we examine the behavior of non-scalar features throughout training, finding a natural hierarchy of features by $l$, reminiscent of a multipole expansion. We aim for our work to ultimately inform design principles and choices of domain applications for {\tt e3nn} networks.
Ameya Daigavane, Bodhi P. Vani, Darcy Davidson et al.
Conformational ensembles of protein structures are immensely important both for understanding protein function and drug discovery in novel modalities such as cryptic pockets. Current techniques for sampling ensembles such as molecular dynamics (MD) are computationally inefficient, while many recent machine learning methods do not transfer to systems outside their training data. We propose JAMUN which performs MD in a smoothed, noised space of all-atom 3D conformations of molecules by utilizing the framework of walk-jump sampling. JAMUN enables ensemble generation for small peptides at rates of an order of magnitude faster than traditional molecular dynamics. The physical priors in JAMUN enables transferability to systems outside of its training data, even to peptides that are longer than those originally trained on. Our model, code and weights are available at https://github.com/prescient-design/jamun.
Patricia Suriana, Joshua A. Rackers, Ewa M. Nowara et al.
Machine learning models for 3D molecular property prediction typically rely on atom-based representations, which may overlook subtle physical information. Electron density maps -- the direct output of X-ray crystallography and cryo-electron microscopy -- offer a continuous, physically grounded alternative. We compare three voxel-based input types for 3D convolutional neural networks (CNNs): atom types, raw electron density, and density gradient magnitude, across two molecular tasks -- protein-ligand binding affinity prediction (PDBbind) and quantum property prediction (QM9). We focus on voxel-based CNNs because electron density is inherently volumetric, and voxel grids provide the most natural representation for both experimental and computed densities. On PDBbind, all representations perform similarly with full data, but in low-data regimes, density-based inputs outperform atom types, while a shape-based baseline performs comparably -- suggesting that spatial occupancy dominates this task. On QM9, where labels are derived from Density Functional Theory (DFT) but input densities from a lower-level method (XTB), density-based inputs still outperform atom-based ones at scale, reflecting the rich structural and electronic information encoded in density. Overall, these results highlight the task- and regime-dependent strengths of density-derived inputs, improving data efficiency in affinity prediction and accuracy in quantum property modeling.
Ewa M. Nowara, Joshua Rackers, Patricia Suriana et al.
Deep generative models are increasingly used for molecular discovery, with most recent approaches relying on equivariant graph neural networks (GNNs) under the assumption that explicit equivariance is essential for generating high-quality 3D molecules. However, these models are complex, difficult to train, and scale poorly. We investigate whether non-equivariant convolutional neural networks (CNNs) trained with rotation augmentations can learn equivariance and match the performance of equivariant models. We derive a loss decomposition that separates prediction error from equivariance error, and evaluate how model size, dataset size, and training duration affect performance across denoising, molecule generation, and property prediction. To our knowledge, this is the first study to analyze learned equivariance in generative tasks.