mlsanityData to 14 Oct 2026

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

arXiv 2410.06074 ↗First posted 8 Oct 2024cs.LG cs.NA math.NAcited by 5

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Abstract (arXiv)

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 20 of its 33 references that are in the map. First posted on arXiv 8 Oct 2024.

Builds on

20 of 33 references.

References · 20

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  4. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
  5. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  6. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  7. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  8. 2020Weakly-Supervised Disentanglement Without Compromisescited by 239
  9. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 221
  10. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 216
  11. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  12. 2024ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEscited by 82
8 more
  1. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 77
  2. 2023A Mathematical Guide to Operator Learningcited by 76
  3. 2020On Second Order Behaviour in Augmented Neural ODEscited by 68
  4. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 62
  5. 2020"Hey, that's not an ODE": Faster ODE Adjoints via Seminormscited by 35
  6. 2021Discovering Sparse Interpretable Dynamics from Partial Observationscited by 25
  7. 2024Marrying Causal Representation Learning with Dynamical Systems for Sciencecited by 23
  8. 2024Mechanistic Neural Networks for Scientific Machine Learningcited by 16

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 1.

5 papers.

  1. 2025Discovering Physics Laws of Dynamical Systems via Invariant Function Learningcited by 5
  2. 2025Adaptive Physics-informed Neural Networks: A Surveycited by 5
  3. 2025Mechanistic PDE Networks for Discovery of Governing Equationscited by 4
  4. 2025Learning Explicit Single-Cell Dynamics Using ODE Representationscited by 1
  5. 2026Identifying ODEs from Unstructured Data with Causal Representation Learningcited by 0