Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information, and additional domain knowledge. Simple classical models are useful but sensitive to inaccuracies and may lead to poor performance when real systems display complex or dynamic behavior. On the other hand, purely data-driven approaches that are model-agnostic are becoming increasingly popular as datasets become abundant and the power of modern deep learning pipelines increases. Deep neural networks (DNNs) use generic architectures that learn to operate from data and demonstrate excellent performance, especially for supervised problems. However, DNNs typically require massive amounts of data and immense computational resources, limiting their applicability for some scenarios. In this article, we present the leading approaches for studying and designing model-based deep learning systems. These are methods that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches. Such model-based deep learning methods exploit both partial domain knowledge, via mathematical structures designed for specific problems, and learning from limited data. Among the applications detailed in our examples for model-based deep learning are compressed sensing, digital communications, and tracking in state-space models. Our aim is to facilitate the design and study of future systems at the intersection of signal processing and machine learning that incorporate the advantages of both domains.

中文翻译：

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基于模型的深度学习

信号处理、通信和控制传统上依赖于经典的统计建模技术。这种基于模型的方法利用表示基础物理学、先验信息和其他领域知识的数学公式。简单的经典模型很有用，但对不准确性很敏感，并且当真实系统显示复杂或动态行为时可能会导致性能不佳。另一方面，随着数据集变得丰富和现代深度学习管道的能力增强，与模型无关的纯数据驱动方法正变得越来越流行。深度神经网络 (DNN) 使用通用架构来学习如何根据数据进行操作并表现出出色的性能，尤其是对于受监督的问题。然而，DNN 通常需要大量数据和巨大的计算资源，限制了它们在某些场景中的适用性。在本文中，我们介绍了研究和设计基于模型的深度学习系统的主要方法。这些方法将原理性数学模型与数据驱动系统相结合，以受益于这两种方法的优势。这种基于模型的深度学习方法通​​过为特定问题设计的数学结构利用部分领域知识，并从有限的数据中学习。我们在基于模型的深度学习示例中详述的应用包括压缩传感、数字通信和状态空间模型中的跟踪。