Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model achieves speedups of over three orders of magnitude compared to ab initio methods and reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art.

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model achieves speedups of over three orders of magnitude compared to ab initio methods and reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art.

Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our representation satisfies all structural, geometric, efficiency, and generalizability constraints. Afterward, we provide a general algorithm to encode any atomistic system. Finally, we report performance comparable to state-of-the-art methods on numerous tasks.

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art and makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner.

We present a novel learning framework that consistently embeds underlying physics while bypassing a significant drawback of most modern, data-driven coarse-grained approaches in the context of molecular dynamics (MD), i.e., the availability of big data. The generation of a sufficiently large training dataset poses a computationally demanding task, while complete coverage of the atomistic configuration space is not guaranteed. As a result, the explorative capabilities of data-driven coarse-grained models are limited and may yield biased "predictive" tools. We propose a novel objective based on reverse Kullback-Leibler divergence that fully incorporates the available physics in the form of the atomistic force field. Rather than separating model learning from the data-generation procedure - the latter relies on simulating atomistic motions governed by force fields - we query the atomistic force field at sample configurations proposed by the predictive coarse-grained model. Thus, learning relies on the evaluation of the force field but does not require any MD simulation. The resulting generative coarse-grained model serves as an efficient surrogate model for predicting atomistic configurations and estimating relevant observables. Beyond obtaining a predictive coarse-grained model, we demonstrate that in the discovered lower-dimensional representation, the collective variables (CVs) are related to physicochemical properties, which are essential for gaining understanding of unexplored complex systems. We demonstrate the algorithmic advances in terms of predictive ability and the physical meaning of the revealed CVs for a bimodal potential energy function and the alanine dipeptide.

Extending spatio-temporal scale limitations of models for complex atomistic systems considered in biochemistry and materials science necessitates the development of enhanced sampling methods. The potential acceleration in exploring the configurational space by enhanced sampling methods depends on the choice of collective variables (CVs). In this work, we formulate the discovery of CVs as a Bayesian inference problem and consider the CVs as hidden generators of the full-atomistic trajectory. The ability to generate samples of the fine-scale atomistic configurations using limited training data allows us to compute estimates of observables as well as our probabilistic confidence on them. The methodology is based on emerging methodological advances in machine learning and variational inference. The discovered CVs are related to physicochemical properties which are essential for understanding mechanisms especially in unexplored complex systems. We provide a quantitative assessment of the CVs in terms of their predictive ability for alanine dipeptide (ALA-2) and ALA-15 peptide.