mlsanityData to 7 Oct 2026

Neural Flows: Efficient Alternative to Neural ODEs

arXiv 2110.13040 ↗First posted 25 Oct 2021cs.LG cs.NA math.NAcited by 99

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Abstract (arXiv)

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose an alternative by directly modeling the solution curves - the flow of an ODE - with a neural network. This immediately eliminates the need for expensive numerical solvers while still maintaining the modeling capability of neural ODEs. We propose several flow architectures suitable for different applications by establishing precise conditions on when a function defines a valid flow. Apart from computational efficiency, we also provide empirical evidence of favorable generalization performance via applications in time series modeling, forecasting, and density estimation.

Key facts. Cited by 99 papers in the map (data through 7 Oct 2026). Builds on 56 of its 87 references that are in the map. First posted on arXiv 25 Oct 2021.

Builds on

56 of 87 references.

References · 56

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Citing papers per year: 2022: 5; 2023: 15; 2024: 17; 2025: 30; 2026: 32.

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  25. 2025Symbolic Neural Ordinary Differential Equationscited by 2
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  27. 2025Simulation-Free Differential Dynamics through Neural Conservation Lawscited by 2
  28. 2025MTM: A Multi-Scale Token Mixing Transformer for Irregular Multivariate Time Series Classificationcited by 2
  29. 2025Neural non-canonical Hamiltonian dynamics for long-time simulationscited by 2
  30. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  31. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 2
  32. 2025FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classificationcited by 2
  33. 2026TiWeaver: Unified Temporal Dynamics Modeling via Contextual Patchingcited by 2
  34. 2022Deep Learning Aided Laplace Based Bayesian Inference for Epidemiological Systemscited by 1
  35. 2023Forecasting the 2016-2017 Central Apennines Earthquake Sequence with a Neural Point Processcited by 1
  36. 2023Forecasting Irregularly Sampled Time Series using Graphscited by 1
  37. 2024Probabilistic Forecasting of Irregular Time Series via Conditional Flowscited by 1
  38. 2024Pretext Training Algorithms for Event Sequence Datacited by 1

50 most cited of 99 All 99 (JSON)