mlsanityData to 7 Oct 2026

Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction

arXiv 2303.12534 ↗First posted 22 Mar 2023physics.comp-ph stat.MLcited by 9

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Abstract (arXiv)

Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition operator are useful for visualization, and they can provide an efficient basis for computing statistics such as the likelihood and average time of events (predictions). Here we develop inexact iterative linear algebra methods for computing these eigenfunctions (spectral estimation) and making predictions from a data set of short trajectories sampled at finite intervals. We demonstrate the methods on a low-dimensional model that facilitates visualization and a high-dimensional model of a biomolecular system. Implications for the prediction problem in reinforcement learning are discussed.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 11 of its 72 references that are in the map. First posted on arXiv 22 Mar 2023.

Builds on

11 of 72 references.

References · 11

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  3. 2017VAMPnets: Deep learning of molecular kineticscited by 135
  4. 2017Time-lagged autoencoders: Deep learning of slow collective variables for molecular kineticscited by 64
  5. 2018Solving for high dimensional committor functions using artificial neural networkscited by 34
  6. 2019Analog forecasting of extreme-causing weather patterns using deep learningcited by 33
  7. 2019Computing Committor Functions for the Study of Rare Events Using Deep Learningcited by 29
  8. 2020Batch Stationary Distribution Estimationcited by 19
  9. 2019Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnetscited by 14
  10. 2022Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of datacited by 7
  11. 2022Krylov-Bellman boosting: Super-linear policy evaluation in general state spacescited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 3; 2026: 1.

9 papers.

  1. 2023A Comprehensive Survey on Rare Event Predictioncited by 18
  2. 2024The surprising efficiency of temporal difference learning for rare event predictioncited by 7
  3. 2024Using pretrained graph neural networks with token mixers as geometric featurizers for conformational dynamicscited by 5
  4. 2024Pushing the Limits of All-Atom Geometric Graph Neural Networks: Pre-Training, Scaling and Zero-Shot Transfercited by 3
  5. 2025Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Pathscited by 3
  6. 2023Probing reaction channels via reinforcement learningcited by 1
  7. 2025An exact multiple-time-step variational formulation for the committor and the transition ratecited by 1
  8. 2025Hierarchical geometric deep learning enables scalable analysis of molecular dynamicscited by 1
  9. 2026Machine learning kinetics from molecular dynamics datacited by 0