The identification of a nonlinear dynamic model is an open topic in control
theory, especially from sparse input-output measurements. A fundamental
challenge of this problem is that very few to zero prior knowledge is available
on both the state and the nonlinear system model. To cope with this challenge,
we investigate the effectiveness of deep learning in the modeling of dynamic
systems with nonlinear behavior by advocating an approach which relies on three
main ingredients: (i) we show that under some structural conditions on the
to-be-identified model, the state can be expressed in function of a sequence of
the past inputs and outputs; (ii) this relation which we call the state map can
be modelled by resorting to the well-documented approximation power of deep
neural networks; (iii) taking then advantage of existing learning schemes, a
state-space model can be finally identified. After the formulation and analysis
of the approach, we show its ability to identify three different nonlinear
systems. The performances are evaluated in terms of open-loop prediction on
test data generated in simulation as well as a real world data-set of unmanned
aerial vehicle flight measurements.

本文提出了一种依赖于稀疏测量数据的深度学习方法，可以对非线性系统动力学行为进行建模和状态估计，并在多个测试数据集上验证了其有效性。

学习降维非线性状态空间模型：一种基于输出误差的规范方法

Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach

An inverse elastic source problem with sparse measurements is of concern. A
generic mathematical framework is proposed which incorporates a low-
dimensional manifold regularization in the conventional source reconstruction
algorithms thereby enhancing their performance with sparse datasets. It is
rigorously established that the proposed framework is equivalent to the
so-called \emph{deep convolutional framelet expansion} in machine learning
literature for inverse problems. Apposite numerical examples are furnished to
substantiate the efficacy of the proposed framework.

本文针对具有稀疏测量的反弹性源问题，提出了一种泛化的数学框架，并在常规源重建算法中引入低维流形正则化，从而提高了它们对稀疏数据集的性能；并且已经严格证明了该提出的框架在机器学习文献中称为 “深度卷积框架展开” 的反问题等价。通过合适的数值示例，证明了所提出框架的功效。

弹性源成像中深度学习的数学框架

A Mathematical Framework for Deep Learning in Elastic Source Imaging

We present an information-theoretic framework for sequential adaptive
compressed sensing, Info-Greedy Sensing, where measurements are chosen to
maximize the extracted information conditioned on the previous measurements. We
show that the widely used bisection approach is Info-Greedy for a family of
$k$-sparse signals by connecting compressed sensing and blackbox complexity of
sequential query algorithms, and present Info-Greedy algorithms for Gaussian
and Gaussian Mixture Model (GMM) signals, as well as ways to design sparse
Info-Greedy measurements. Numerical examples demonstrate the good performance
of the proposed algorithms using simulated and real data: Info-Greedy Sensing
shows significant improvement over random projection for signals with sparse
and low-rank covariance matrices, and adaptivity brings robustness when there
is a mismatch between the assumed and the true distributions.

介绍了一种信息理论框架，用于顺序自适应压缩感知，并针对高斯混合模型信号和稀疏测量设计，提出了 Info-Greedy 算法，大大提高了稀疏和低秩信号的测量效果，增加了鲁棒性。