Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization
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Abstract (arXiv)
Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable optimization. More recently, deep learning approaches that use highly parametric architectures tuned from data without relying on mathematical models, are becoming increasingly popular. Model-based optimization and data-centric deep learning are often considered to be distinct disciplines. Here, we characterize them as edges of a continuous spectrum varying in specificity and parameterization, and provide a tutorial-style presentation to the methodologies lying in the middle ground of this spectrum, referred to as model-based deep learning. We accompany our presentation with running examples in super-resolution and stochastic control, and show how they are expressed using the provided characterization and specialized in each of the detailed methodologies. The gains of combining model-based optimization and deep learning are demonstrated using experimental results in various applications, ranging from biomedical imaging to digital communications.
Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). Builds on 31 of its 58 references that are in the map. First posted on arXiv 5 May 2022.
Builds on
31 of 58 references.
References · 31
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- 2015Gradient-based Hyperparameter Optimization through Reversible Learningcited by 357
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- 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
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- 2020Model-Based Deep Learningcited by 136
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- 2019Combining Generative and Discriminative Models for Hybrid Inferencecited by 34
- 2019Learning Convex Optimization Control Policiescited by 31
- 2021Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Futurecited by 18
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- 2018Neural Network Detection of Data Sequences in Communication Systemscited by 15
- 2020Learned SPARCOM: Unfolded Deep Super-Resolution Microscopycited by 11
- 2019Neumann Networks for Inverse Problems in Imagingcited by 9
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- 2020Learned Factor Graphs for Inference from Stationary Time Sequencescited by 8
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- 2021LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receiverscited by 7
- 2021Learned super resolution ultrasound for improved breast lesion characterizationcited by 7
- 2021Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Modelscited by 6
- 2021Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problemscited by 6
- 2020ADMM-Net for Communication Interference Removal in Stepped-Frequency Radarcited by 2
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Citing papers per year: 2022: 9; 2023: 14; 2024: 15; 2025: 8; 2026: 4.
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- 2026Time-varying rPPG signal separation via block-sparse signal model21 May 2026
- 2026When Descent Is Too Stable: Event-Triggered Hamiltonian Learning to Optimize7 May 2026
- 2025Deep Unfolding: Recent Developments, Theory, and Design Guidelines3 Dec 2025
- 2025Unsupervised Unfolded rPCA (U2-rPCA): Deep Interpretable Clutter Filtering for Ultrasound Microvascular Imaging1 Oct 2025
- 2025Motion Estimation for Multi-Object Tracking using KalmanNet with Semantic-Independent Encoding14 Sep 2025
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