mlsanityData to 14 Oct 2026

Hybrid Modeling Design Patterns

arXiv 2401.00033 ↗First posted 29 Dec 2023cs.AI cs.LGcited by 2

Not on the map. Why?

Abstract (arXiv)

Design patterns provide a systematic way to convey solutions to recurring modeling challenges. This paper introduces design patterns for hybrid modeling, an approach that combines modeling based on first principles with data-driven modeling techniques. While both approaches have complementary advantages there are often multiple ways to combine them into a hybrid model, and the appropriate solution will depend on the problem at hand. In this paper, we provide four base patterns that can serve as blueprints for combining data-driven components with domain knowledge into a hybrid approach. In addition, we also present two composition patterns that govern the combination of the base patterns into more complex hybrid models. Each design pattern is illustrated by typical use cases from application areas such as climate modeling, engineering, and physics.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 37 of its 98 references that are in the map. First posted on arXiv 29 Dec 2023.

Builds on

37 of 98 references.

References · 37

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,367
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  5. 2019Hamiltonian Neural Networkscited by 712
  6. 2016CNN Architectures for Large-Scale Audio Classificationcited by 704
  7. 2019The frontier of simulation-based inferencecited by 502
  8. 2015Deep Kernel Learningcited by 445
  9. 2020Lagrangian Neural Networkscited by 398
  10. 2017PDE-Net: Learning PDEs from Datacited by 311
  11. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  12. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 210
25 more
  1. 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 205
  2. 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 171
  3. 2020Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systemscited by 164
  4. 2019Hamiltonian Generative Networkscited by 137
  5. 2021Exact imposition of boundary conditions with distance functions in physics-informed deep neural networkscited by 137
  6. 2017Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modelingcited by 131
  7. 2021Modeling Irregular Time Series with Continuous Recurrent Unitscited by 103
  8. 2021Neural Transformation Learning for Deep Anomaly Detection Beyond Imagescited by 99
  9. 2017Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledgecited by 96
  10. 2020Augmenting Physical Models with Deep Networks for Complex Dynamics Forecastingcited by 95
  11. 2023A Mathematical Guide to Operator Learningcited by 76
  12. 2016Label-Free Supervision of Neural Networks with Physics and Domain Knowledgecited by 74
  13. 2017Convolutional Gaussian Processescited by 44
  14. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 38
  15. 2019Achieving Conservation of Energy in Neural Network Emulators for Climate Modelingcited by 28
  16. 2018HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systemscited by 21
  17. 2022Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficientscited by 17
  18. 2020Learning Partially Known Stochastic Dynamics with Empirical PAC Bayescited by 16
  19. 2020Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systemscited by 14
  20. 2022WaveY-Net: Physics-augmented deep learning for high-speed electromagnetic simulation and optimizationcited by 8
  21. 2022Learning Interacting Dynamical Systems with Latent Gaussian Process ODEscited by 5
  22. 2022Performance Analysis of Electrical Machines Using a Hybrid Data- and Physics-Driven Modelcited by 2
  23. 2023Combining Slow and Fast: Complementary Filtering for Dynamics Learningcited by 2
  24. 2020Magnetic Field Simulation with Data-Driven Material Modelingcited by 1
  25. 2020Data-Driven Solvers for Strongly Nonlinear Material Responsecited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 1.

2 papers.

  1. 2024Learnable & Interpretable Model Combination in Dynamical Systems Modelingcited by 1
  2. 2026Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimationcited by 0