EAGER: Real-Time: Ultrasonic Reconstruction and Localization with Deep Helmholtz Networks

利用深层亥姆霍兹网络进行超声重建和定位本项目研究基于物理信息的神经网络，以表征和监测超声材料和工程系统。研究超声波是因为它是一种无线、高分辨率、医疗安全和固有安全的技术，正在推动可穿戴设备、医疗植入物、安全/加密通信系统和成像的创新。该项目的神经网络算法可以从微观层面（如微电子机械系统）到宏观层面（如管道、飞机或铁路线）表征材料和工程系统。神经网络通过从模拟数据、物理约束和测量数据中学习超声波的一般行为来表征材料。然后将学习到的行为与真实的测量行为进行比较。为了实现我们的目标，研究了将神经网络（以及机器学习）应用于许多工程系统的三个重大挑战：(1)实验训练数据通常稀缺或不可用，(2)数据多样性和可变性通常很高，(3)纯数据驱动的方法提供的工程保证很少。数据稀缺性是通过用模拟而不是实验数据来训练神经网络来解决的。利用迁移学习理论将模拟数据中的广义知识迁移到实验数据的分析中，解决了数据的多样性和可变性问题。通过将基于物理的约束纳入神经网络，工程保证得到了改善。由此产生的神经网络被称为亥姆霍兹网络，以与时间无关的波动方程命名。该项目的目标是为亥姆霍兹网络奠定基础，亥姆霍兹网络是一种深度、生成式、物理信息丰富的神经网络，用于重建超声波传播并定位超声波源。亥姆霍兹网络是基于这样一个事实，即波的每个频率都可以表示为稀疏数量的空间模式的总和。这些模式受到亥姆霍兹方程的约束，这种物理约束确保了机器学习算法对于系统关键型工程系统（例如，飞机的健康监测）是值得信赖的。这种基于物理的机器学习是将先进的计算工具集成到实时工程系统中的一个重要主题（尽管没有被广泛研究）。本提案的研究重点是启动和探索三种新型神经网络的基础：(1)生成式亥姆霍兹网络，用于学习波的模态表示并重建波场；(2)定位网络，用于定位不确定条件下的超声波源；(3)定位亥姆霍兹网络，用于从学习到的模态表示中定位源。推力1探索生成模型（即生成亥姆霍兹网络）的创建，从模拟中学习介质的空间模态特征。这些生成模型然后从欠采样测试数据重建波场。Thrust 2研究在速度、延迟和/或振幅不确定性等模拟不确定性条件下定位超声源的定位网络。推力3研究使用迁移学习将推力1和推力2结合起来，并使用学习模式在几何复杂的介质中定位源。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Ultrasonic Reconstruction and Localization with Deep Helmholtz NetworksThis project studies physics-informed neural networks to characterize and monitor materials and engineered systems with ultrasound. Ultrasound is studied because it is a wireless, high resolution, medically safe, and inherently secure technology that is driving innovations in wearables, medical implants, secure / encrypted communication systems, and imaging. The project's neural network algorithms can characterize materials and engineered systems from the micro-level (e.g., micro-electrical-mechanical systems) to the macro-level (e.g., pipelines, airplanes, or rail lines). The neural networks characterize the materials by learning the general behavior of ultrasound from simulated data, physical constraints, and measured data. That learned behavior is then compared with the true measured behavior. To achieve our goal, three significant challenges of applying neural networks (and machine learning generally) to many engineered systems are studied: (1) experimental training data is often scarce or unavailable, (2) data diversity and variability is typically high, and (3) purely data-driven approaches offer few engineering assurances. Data scarcity is addressed by training neural networks with simulations rather than experimental data. Data diversity and variability is addressed by using transfer learning theory to transfer generalized knowledge from the simulation data into the analysis of the experimental data. Engineering assurances are improved by incorporating physics-based constraints into the neural networks. The resulting neural networks are referred to as Helmholtz networks, named for the time-independent wave equation.The objective of the project is to establish the foundation for Helmholtz networks, which are deep, generative, physics-informed neural networks that reconstruct ultrasonic wave propagation and locate ultrasonic sources. The Helmholtz networks are based on the fact that each frequency of a wave can be represented as the sum of a sparse number of spatial modes. The modes are constrained by the Helmholtz equation and this physical constraint ensures that the machine learning algorithm is trustworthy for system-critical engineered systems (e.g., health monitoring of an aircraft). Such physics-informed machine learning is an important (albeit not widely studied) topic for integrating advanced computation tools into real-time engineered systems. The research thrusts of this proposal are to initiate and explore the foundations for three new types of neural networks: (1) generative Helmholtz networks to learn modal representations of waves and reconstruct wavefields, (2) localization networks to locate ultrasonic sources under uncertainties, and (3) localization Helmholtz networks to locate sources from learned modal representations. Thrust 1 explores the creation of generative models (i.e., generative Helmholtz networks) that learn the spatial modal characteristics of a medium from simulations. These generative models then reconstruct wavefields from undersampled test data. Thrust 2 studies localization networks to locate ultrasonic sources under simulated uncertainties, such as velocity, delay, and/or amplitude uncertainty. Thrust 3 investigates the use of transfer learning to combine Thrust 1 and Thrust 2 and use the learned modes to locate sources in geometrically complex media.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.