# Operator Autoencoders: Learning Physical Operations on Encoded Molecular Graphs

arXiv: https://arxiv.org/abs/2105.12295 · HTML: https://mlsanity.com/paper/2105.12295/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 61 references that are in the map.
- First posted on arXiv 26 May 2021.

## Builds on (most cited first, 30 of 36)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Attribute2Image: Conditional Image Generation from Visual Attributes](https://mlsanity.com/paper/1512.00570/) (2015)
- [Learning Multimodal Graph-to-Graph Translation for Molecular Optimization](https://mlsanity.com/paper/1812.01070/) (2018)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders](https://mlsanity.com/paper/1809.02630/) (2018)
- [NeVAE: A Deep Generative Model for Molecular Graphs](https://mlsanity.com/paper/1802.05283/) (2018)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems](https://mlsanity.com/paper/2101.07206/) (2020)
- [Adversarial Feature Matching for Text Generation](https://mlsanity.com/paper/1706.03850/) (2017)
- [Molecular Hypergraph Grammar with its Application to Molecular Optimization](https://mlsanity.com/paper/1809.02745/) (2018)
- [Dirichlet Graph Variational Autoencoder](https://mlsanity.com/paper/2010.04408/) (2020)
- [A Model to Search for Synthesizable Molecules](https://mlsanity.com/paper/1906.05221/) (2019)
- [Deep Graph Generators: A Survey](https://mlsanity.com/paper/2012.15544/) (2020)

## Built on by (most cited first, 1 of 1)

- [Learning Dynamic Scene Reconstruction with Sinusoidal Geometric Priors](https://mlsanity.com/paper/2512.22295/) (2025)

## Abstract (arXiv)

Molecular dynamics simulations produce data with complex nonlinear dynamics. If the timestep behavior of such a dynamic system can be represented by a linear operator, future states can be inferred directly without expensive simulations. The use of an autoencoder in combination with a physical timestep operator allows both the relevant structural characteristics of the molecular graphs and the underlying physics of the system to be isolated during the training process. In this work, we develop a pipeline for establishing graph-structured representations of time-series volumetric data from molecular dynamics simulations. We then train an autoencoder to find nonlinear mappings to a latent space where future timesteps can be predicted through application of a linear operator trained in tandem with the autoencoder. Increasing the dimensionality of the autoencoder output is shown to improve the accuracy of the physical timestep operator.