k-Wave: An open-source toolbox for the time-domain simulation of acoustic wave fields

计算机模拟有时被描述为科学的“第三支柱”，与实验和理论并列。计算机模拟也已成为辅助工业设计和开发的重要工具。在声学方面，计算机模拟被广泛应用于各种各样的应用，如对尚未建成的音乐厅或演讲厅的声音进行建模，解释地震的录音，预测新铁路线或高速公路的噪音，改善乐器的声音，超声治疗中的治疗计划，以及增强医学超声诊断中的图像。对于大多数基于声波方程（描述所有波效应的数学表达式）的计算机模型，有必要表示每个波长上几个点的声场变化。想想在方格纸上画出沙滩上的起伏；每个波动需要几个方格来捕捉沙子上升和下降的事实。当要模拟的域（音乐厅、海洋、人类头部等）的大小通常是数百个声波波长时，计算需求就变得非常大。继续这个类比，这意味着绘图纸——计算机内存——必须非常大。因此，在许多应用中，有必要依靠近似模型，而近似模型忽略了重要的波现象，如衍射。k-Wave是一个开源的（免费提供的）声学建模工具箱，它最初是为了满足对生物组织中声学（超声波）传播的快速有效的全波模型的需求而编写的，并且对于不是计算专家的人来说易于使用。这种结合被证明是非常成功的，k-Wave现在在世界各地拥有成千上万的用户。有从事生物医学超声和光声学工作的用户，但也有许多其他领域的用户发现k-Wave对他们的特定应用很有用。这个提议的目的是重新设计和改进k-Wave。更新后的代码将使用自k-Wave首次发布以来开发的新的编程功能和软件工程最佳实践。我们将添加令人兴奋的新功能，例如将声学和热模型耦合在一起的能力，当声源只有很小的频率范围时进行快速预测，以及准确地表示复杂的边界，例如在音乐厅中遇到的边界。一个主要的进步将是能够自动找到求解器相对于波动方程中参数的梯度。这将允许k-Wave直接用于机器学习（深度学习，人工智能）的应用程序。作为项目的一部分，我们还将开发新的培训材料，开设培训课程，并与声学各个领域的新用户社区合作。对k-Wave提出的修改不仅将支持和改进现有的模拟活动，而且将激励研究人员以新颖的方式和在新颖的情况下测试新想法和开发新功能。经典模拟和深度学习相结合所带来的可能性尤其令人兴奋。潜在的应用包括规划癌症和神经系统疾病的突破性超声治疗，提供对海洋环境的更深入了解，以及改进声学空间的设计，包括歌剧院和城市环境。

Computer simulation is sometimes described as the 'third pillar' of science, alongside experiment and theory. Computer simulations have also become essential tools to aid design and development in industry. In acoustics, computer simulations are used very widely, in such diverse applications as modelling the sound of yet-to-be-built concert halls or lecture theatres, interpreting recordings from earthquakes, predicting the noise from new train lines or motorways, improving the sound of musical instruments, treatment planning in ultrasound therapy, and enhancing images in diagnostic medical ultrasound.For most computer models based on the acoustic wave equation (a mathematical expression that describes all wave effects), it is necessary to represent the variations in the acoustic field at several points per wavelength. Think of drawing the undulations in beach sand by colouring squares on graph paper; several squares are required per undulation to capture the fact the sand rises and falls. When the domain to be simulated (concert hall, ocean, human head, etc) is many hundreds of acoustic wavelengths in size, which is often the case, the computational demands become significant. To continue the analogy, this means the graph paper - the computer memory - must be very large. In many applications, therefore it has been necessary to fall back on approximate models, which neglect important wave phenomena, such as diffraction.k-Wave is an open-source (freely available) acoustic modelling toolbox that was first written to satisfy the demand for a fast and efficient full-wave model of acoustic (ultrasonic) propagation in biological tissue, and one that is easy-to-use for people who are not computational specialists. This combination has proved highly successful, and k-Wave now has many thousands of users around the world. There are users working in biomedical ultrasound and photoacoustics, but there are also many users in other fields who have found k-Wave to be useful for their particular applications.The aim of this proposal is to re-engineer and improve k-Wave. The updated code will use new programming features and software-engineering best-practices that have developed since k-Wave was first released. We will add exciting new features, such as the ability to couple acoustic and thermal models together, to make rapid predictions when the acoustic source has only a small range of frequencies, and to accurately represent complex boundaries such as those encountered in a concert hall. One major advancement will be the ability to automatically find the gradient of the solver with respect to the parameters in the wave equation. This will allow k-Wave to be directly used for applications in machine learning (deep learning, artificial intelligence). As part of the project, we will also develop new training materials, run training courses, and work with new user communities across all areas of acoustics. The proposed changes to k-Wave will not only support and improve existing simulation activities, but will spur researchers to test new ideas and exploit the new functionality in novel ways and in novel situations. The possibilities opened up by the combination of classical simulation and deep learning is particularly exciting. Potential applications include planning for ground-breaking ultrasound treatments for cancer and neurological disorders, providing a greater understanding of our ocean environments, and improving the design of acoustic spaces including opera houses and urban environments.