# Deep Learning Based Inversion of Locally Anisotropic Weld Properties from Ultrasonic Array Data
## 1 Introduction  
Ultrasound is a popular method for carrying out non-destructive evaluation (NDE) of safety critical infrastructure, and it is frequently utilised across a variety of industries, including aerospace, automotive and energy. It entails the use of ultrasonic transducers to generate, transmit, and receive high-frequency mechanical waves, which propagate throughout the component to be inspected. The resulting scattered wave fields can then be post-processed to create images of the component's interior, highlighting the presence of any embedded defects [1]. In traditional ultrasonic NDE, it is common to assume that the object under inspection is constructed from isotropic and homogeneous materials. However, in many components of interest, this is not the case and the presence of heterogeneous and locally anisotropic microstructures can distort the transmitted ultrasonic signals. This can cause a significant degree of uncertainty when it comes to detecting and characterising flaws within the structure [2; 3; 4; 5]. Reliably imaging defects embedded in austenitic steel welds using ultrasound is an outstanding industrial challenge [6; 7; 8]. These welds are commonly found in heavy industry because of their strength and resistance to corrosion. However, due to repeated thermal cycling throughout their build process, the polycrystalline structures of the welds undergo epitaxial growth, where their major crystal axes align with the direction of heat flow. This results in the creation of a locally anisotropic microstructure consisting of large grains which exhibit length scales commensurate with that of the ultrasonic wave. The coupling of these length scales results in significant scattering and refraction of the ultrasonic wave by the weld microstructure, and so when traditional NDE imaging techniques (which typically assume a constant, isotropic velocity across the medium) are applied, the resulting images suffer from significant defocusing and can fail to reliably highlight any embedded defects. However, in the case that a priori knowledge of a weld's spatially varying microstructural descriptors is available, it has been shown that the distortion of the wave paths can be compensated for to create more accurate and reliable defect reconstructions [2; 3; 4]. Although the microstructural maps required for this correction can be acquired experimentally, such procedures for characterising in the bulk are not strictly non-destructive and hence cannot be used in situ [6; 9]. However, these approaches, coupled with models of the welding process and subsequent wave propagation problems [10; 11; 12; 13; 14] provide essential insight into the structure and crystallography of these materials and their effects on the probing waves. An alternative approach to characterising a weld's microstructure is to pose the question as an inverse problem; given the scattered ultrasonic wave data, can we exploit tomographic methods to map the spatially varying material properties of the component? There already exists a rich literature on this type of tomographic inverse problem within the seismology and medical imaging fields [15; 16; 17; 18; 19; 20; 21; 22], and more recently it has come to the forefront of ultrasonic NDE research [3; 4]. However, due to the high dimensional, non-linear nature of the problem, many of these approaches incur significant computational expense and are not suitable for real-time implementation. This is problematic not only for inspection in the field, where online computing resources may be scarce, but also for the increasingly common requirement for in-process inspection, which is particularly important for dynamic monitoring of modern, additive manufacturing processes. One solution to the real-time tomography problem is to examine the potential of deep neural networks (DNNs).