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SchNet: A continuous-filter convolutional neural network for modeling quantum interactions

Kristof T. Schütt, Pieter-Jan Kindermans, Huziel E. Sauceda, Stefan Chmiela, Alexandre Tkatchenko, Klaus-Robert Müller

TL;DR

The paper tackles the challenge of predicting molecular energies and forces across chemical and configurational variations. It introduces continuous-filter convolutions and the SchNet architecture, which yields rotation-invariant energies and energy-conserving, differentiable force fields by training on both energies and forces. It demonstrates state-of-the-art QM9 performance and strong MD17 results, and introduces ISO17 as a new benchmark to test generalization across chemical space. The work enables fast, differentiable PES modeling suitable for geometry optimization and molecular dynamics, advancing ML-driven quantum chemistry.

Abstract

Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential physical information, that would get lost if discretized. Thus, we propose to use continuous-filter convolutional layers to be able to model local correlations without requiring the data to lie on a grid. We apply those layers in SchNet: a novel deep learning architecture modeling quantum interactions in molecules. We obtain a joint model for the total energy and interatomic forces that follows fundamental quantum-chemical principles. This includes rotationally invariant energy predictions and a smooth, differentiable potential energy surface. Our architecture achieves state-of-the-art performance for benchmarks of equilibrium molecules and molecular dynamics trajectories. Finally, we introduce a more challenging benchmark with chemical and structural variations that suggests the path for further work.

SchNet: A continuous-filter convolutional neural network for modeling quantum interactions

TL;DR

The paper tackles the challenge of predicting molecular energies and forces across chemical and configurational variations. It introduces continuous-filter convolutions and the SchNet architecture, which yields rotation-invariant energies and energy-conserving, differentiable force fields by training on both energies and forces. It demonstrates state-of-the-art QM9 performance and strong MD17 results, and introduces ISO17 as a new benchmark to test generalization across chemical space. The work enables fast, differentiable PES modeling suitable for geometry optimization and molecular dynamics, advancing ML-driven quantum chemistry.

Abstract

Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential physical information, that would get lost if discretized. Thus, we propose to use continuous-filter convolutional layers to be able to model local correlations without requiring the data to lie on a grid. We apply those layers in SchNet: a novel deep learning architecture modeling quantum interactions in molecules. We obtain a joint model for the total energy and interatomic forces that follows fundamental quantum-chemical principles. This includes rotationally invariant energy predictions and a smooth, differentiable potential energy surface. Our architecture achieves state-of-the-art performance for benchmarks of equilibrium molecules and molecular dynamics trajectories. Finally, we introduce a more challenging benchmark with chemical and structural variations that suggests the path for further work.

Paper Structure

This paper contains 15 sections, 10 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Continuous-filter convolutions
  4. SchNet
  5. Architecture
  6. Molecular representation
  7. Atom-wise layers
  8. Interaction
  9. Filter-generating networks
  10. Training with energies and forces
  11. Experiments and results
  12. QM9 -- chemical degrees of freedom
  13. MD17 -- conformational degrees of freedom
  14. ISO17 -- chemical and conformational degrees of freedom
  15. Conclusions

Figures (3)

  • Figure 1: The discrete filter (left) is not able to capture the subtle positional changes of the atoms resulting in discontinuous energy predictions $\hat{E}$ (bottom left). The continuous filter captures these changes and yields smooth energy predictions (bottom right).
  • Figure 2: Illustration of SchNet with an architectural overview (left), the interaction block (middle) and the continuous-filter convolution with filter-generating network (right). The shifted softplus is defined as $\text{ssp}(x) = \ln(0.5e^x + 0.5)$.
  • Figure 3: 10x10 Å cuts through all 64 radial, three-dimensional filters in each interaction block of SchNet trained on molecular dynamics of ethanol. Negative values are blue, positive values are red.