KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics

Revach, Guy; Shlezinger, Nir; Ni, Xiaoyong; Escoriza, Adria Lopez; Sloun, Ruud J. G. van; Eldar, Yonina C.

doi:10.1109/tsp.2022.3158588

Cited by 203 publications

(66 citation statements)

References 66 publications

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“…We compare this model-based deep learning mapping with several model-based tracking algorithms designed for such settings -the extended Kalman filter (EKF); unscented Kalman filter (UKF); and particle filter (PF) -as well as to a black-box RNN trained end-to-end. The results, reproduced from (31) are summarized in Table 1, and a representative reconstruction is visualized in Fig. 10.…”

Section: Resultsmentioning

confidence: 99%

“…Examples: The straight-forward application of DNNaided optimization replaces an internal computation of a model-based solver with a dedicated DNN, converting it into a trainable model-based deep learning system. An example of how this is done, based on (31), is detailed next. Example 13, where a Kalman filter is designed without knowing the distribution of the noise signals in Eq.…”

Section: Example 17mentioning

confidence: 99%

“…Example 18 was shown in (31) to overcome non-linearities and mismatches in the state-space model, outperforming the classical Kalman filter while retaining its data efficiency and interpretability. It is emphasized though that Example 18 represents one approach to combine Kalman filtering with DNN-aided optimization methodology.…”

Section: Example 18 Consider Again the Setting Ofmentioning

confidence: 99%

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Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization

Shlezinger¹,

Eldar²,

Boyd³

2022

Preprint

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Example 17mentioning

confidence: 99%

Section: Example 18 Consider Again the Setting Ofmentioning

confidence: 99%

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Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization

Shlezinger¹,

Eldar²,

Boyd³

2022

Preprint

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“…could provide significant benefit to this continually developing research area. We also highlight the topic of deep learning for coding and communication [47], [70], [113], [114], [101], which similarly poses a variety of specialized inverse problems whose study has largely relied on empirical evaluation.…”

Section: Other Topics On Deep Learning Methods In Inverse Problemsmentioning

confidence: 99%

Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Scarlett¹,

Heckel²,

Rodrigues³

et al. 2022

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In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms. In addition to summarizing existing results in these topics, we highlight several ongoing challenges and open problems.

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“…The latter provides distributions of states and in particular uncertainty estimation. While the classic KF is limited to linear dynamics, many non-linear extensions have been suggested [Krishnan et al, 2015, Coskun et al, 2017, Ullah et al, 2019, Revach et al, 2021. However, such models are typically limited to a constant prediction horizon (time-step).…”

Section: Related Workmentioning

confidence: 99%

Continuous Forecasting via Neural Eigen Decomposition

Belogolovsky¹,

Greenberg²,

Eitan³

et al. 2022

Preprint

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Motivated by a real-world problem of blood coagulation control in Heparin-treated patients, we use Stochastic Differential Equations (SDEs) to formulate a new class of sequential prediction problems -with an unknown latent space, unknown non-linear dynamics, and irregular sparse observations. We introduce the Neural Eigen-SDE (NESDE) algorithm for sequential prediction with sparse observations and adaptive dynamics. NESDE applies eigen-decomposition to the dynamics model to allow efficient frequent predictions given sparse observations. In addition, NESDE uses a learning mechanism for adaptive dynamics model, which handles changes in the dynamics both between sequences and within sequences. We demonstrate the accuracy and efficacy of NESDE for both synthetic problems and real-world data. In particular, to the best of our knowledge, we are the first to provide a patient-adapted prediction for blood coagulation following Heparin dosing in the MIMIC-IV dataset. Finally, we publish a simulated gym environment based on our prediction model, for experimentation in algorithms for blood coagulation control.

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KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics

Cited by 203 publications

References 66 publications

Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization

Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization

Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Continuous Forecasting via Neural Eigen Decomposition

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