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Solving for high dimensional committor functions using artificial neural networks

arXiv 1802.10275 ↗First posted 28 Feb 2018cs.LG cs.NA math.NAcited by 34

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Abstract (arXiv)

In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of transition path theory, which satisfies a high-dimensional Fokker-Planck equation. By working with the variational formulation of such partial differential equation and parameterizing the committor function in terms of a neural network, approximations can be obtained via optimizing the neural network weights using stochastic algorithms. The numerical examples show that moderate accuracy can be achieved for high-dimensional problems.

Key facts. Cited by 34 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Feb 2018.

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Citing papers per year: 2021: 10; 2022: 5; 2023: 7; 2024: 5; 2025: 3; 2026: 4.

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  1. 2022Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equationscited by 56
  2. 2021Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNscited by 38
  3. 2021On the Representation of Solutions to Elliptic PDEs in Barron Spacescited by 25
  4. 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problemscited by 21
  5. 2023GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEscited by 20
  6. 2021A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schr"odinger Eigenvalue Problemscited by 19
  7. 2021A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equationscited by 18
  8. 2023Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networkscited by 18
  9. 2021Reinforcement learning of rare diffusive dynamicscited by 15
  10. 2022Minimax Optimal Kernel Operator Learning via Multilevel Trainingcited by 13
  11. 2023Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemescited by 10
  12. 2023Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event predictioncited by 9
22 more
  1. 2023A Finite Expression Method for Solving High-Dimensional Committor Problemscited by 9
  2. 2022Approximation of Functionals by Neural Network without Curse of Dimensionalitycited by 8
  3. 2023Diffusion Methods for Generating Transition Pathscited by 8
  4. 2021Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEscited by 5
  5. 2021Supervised Learning and the Finite-Temperature String Method for Computing Committor Functions and Reaction Ratescited by 5
  6. 2024Deep Learning Method for Computing Committor Functions with Adaptive Samplingcited by 5
  7. 2024The fast committor machine: Interpretable prediction with kernelscited by 5
  8. 2021A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networkscited by 4
  9. 2021Computing the Invariant Distribution of Randomly Perturbed Dynamical Systems Using Deep Learningcited by 4
  10. 2025Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Pathscited by 4
  11. 2022Computing non-equilibrium trajectories by a deep learning approachcited by 3
  12. 2022The Mori-Zwanzig formulation of deep learningcited by 2
  13. 2024Accelerated Sampling of Rare Events using a Neural Network Bias Potentialcited by 2
  14. 2023Probing reaction channels via reinforcement learningcited by 1
  15. 2024Error Bounds for Physics-Informed Neural Networks in Fokker-Planck PDEscited by 1
  16. 2025An exact multiple-time-step variational formulation for the committor and the transition ratecited by 1
  17. 2026Conditional Tropical Cyclogenesis Rates via Rare-Event Sampling in a Neural Weather Emulatorcited by 1
  18. 2024Computing Transition Pathways for the Study of Rare Events Using Deep Reinforcement Learningcited by 0
  19. 2025Nonparametric Reaction Coordinate Optimization with Histories: A Framework for Rare Event Dynamicscited by 0
  20. 2026A Priori Sampling of Transition States with Guided Diffusioncited by 0
  21. 2026Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Eventscited by 0
  22. 2026Machine learning kinetics from molecular dynamics datacited by 0