mlsanityData to 14 Oct 2026

Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Models

arXiv 2210.13103 ↗First posted 24 Oct 2022cs.LG stat.MLcited by 7

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Abstract (arXiv)

The combination of deep neural nets and theory-driven models, which we call deep grey-box modeling, can be inherently interpretable to some extent thanks to the theory backbone. Deep grey-box models are usually learned with a regularized risk minimization to prevent a theory-driven part from being overwritten and ignored by a deep neural net. However, an estimation of the theory-driven part obtained by uncritically optimizing a regularizer can hardly be trustworthy when we are not sure what regularizer is suitable for the given data, which may harm the interpretability. Toward a trustworthy estimation of the theory-driven part, we should analyze regularizers' behavior to compare different candidates and to justify a specific choice. In this paper, we present a framework that enables us to analyze a regularizer's behavior empirically with a slight change in the neural net's architecture and the training objective.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 16 of its 30 references that are in the map. First posted on arXiv 24 Oct 2022.

Builds on

16 of 30 references.

References · 16

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  2. 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 205
  3. 2013Learning by Transductioncited by 121
  4. 2020Augmenting Physical Models with Deep Networks for Complex Dynamics Forecastingcited by 95
  5. 2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
  6. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
  7. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
  8. 2020Interpretable Sequence Learning for COVID-19 Forecastingcited by 22
  9. 2020Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Predictioncited by 18
  10. 2022Robust Hybrid Learning With Expert Augmentationcited by 17
  11. 2021Controlling Neural Networks with Rule Representationscited by 16
  12. 2020Tailoring: encoding inductive biases by optimizing unsupervised objectives at prediction timecited by 13
4 more
  1. 2020Integrating Machine Learning with Physics-Based Modelingcited by 8
  2. 2020Incorporating Physical Knowledge into Machine Learning for Planetary Space Physicscited by 3
  3. 2022Half-Inverse Gradients for Physical Deep Learningcited by 3
  4. 2022Unifying Model-Based and Neural Network Feedforward: Physics-Guided Neural Networks with Linear Autoregressive Dynamicscited by 2

Built on by

Cited by year (2026 to 14 Oct)

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

7 papers.

  1. 2026Variational Grey-Box Dynamics Matchingcited by 2
  2. 2024PILA: Physics-Informed Low Rank Augmentation for Interpretable Earth Observationcited by 1
  3. 2025Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transportcited by 1
  4. 2024A Data-to-Product Multimodal Conceptual Framework to Achieve Automated Software Evolution for Context-rich Intelligent Applicationscited by 0
  5. 2025Gray-Box Computed Torque Control for Differential-Drive Mobile Robot Trackingcited by 0
  6. 2026Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimationcited by 0
  7. 2026Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processescited by 0