## 1 Introduction  
In recent decades, wire-arc directed energy deposition (arc-DED) technology has gained significant traction within the scientific community, emerging as a focal point to produce additive components. A notable advantage of arc-DED lies in its robust deposition ratios, positioning it favorably among other additive methodologies [1, 2]. This heightened attention has catalyzed a surge in research, propelling the exploration of 3D-printed part fabrication [3]. Notably, aerospace applications have taken a prominent role, showcasing promising outcomes [4, 5]. Of the arc-DED techniques, gas metal arc welding (GMAW) stands out for its elevated deposition rates, surpassing other wire-based technologies, such as plasma-based arc-DED and gas tungsten arc welding (GTAW) [6, 7]. The utilization of Invar, an alloy, within this realm adds an intriguing dimension, leveraging its distinctive mechanical properties [8, 9]. Comprising predominantly iron (64%) and nickel (36%) alloys, Invar finds purpose across diverse fields [10, 11]. Renowned for its superior dimensional stability and mechanical process in cryogenic environments, Invar plays a pivotal role in applications demanding precision and reliability, as seen in metrology and aerospace components. The formidable challenge posed by its malleability and low heat conductivity in machining scenarios drives the interest in additive manufacturing for Invar, offering preforms aligning closely with final part geometries [12; 13; 14]. Invar's application through PBF-LB/M has revealed optimal energy density ranges for mechanical properties [15], along with characteristic microstructures [16]. To advance the implementation of arc-DED technology in complex geometries, the fine-tuning of processes from initial passes has emerged as a key focus [17]. Understanding the geometry of zero beads has been central, often centering on models that correlate wire feed speed and travel speed (TS) with bead geometry characteristics [18; 19; 20]. While conventional approaches maintain transverse bead geometry as a constant during deposition, limited studies acknowledge longitudinal variations [21]. [PERSON] et al. [22] reported the real-time determination of weld bead dimensions using passive vision systems and digital image processing. The proper construction of initial beads fundamentally underpins the accurate manufacturing of final walls. [PERSON] et al. [23] delve into layer-by-layer forming characteristics analysis in GMAW-based arc-DED, while [PERSON] et al. [24] address corner piece generation for intricate geometries. Amid the importance of final bead geometry analysis, the challenge of online process control remains pronounced [25]. Infrared pyrometry techniques for melt-pool measurement have found favor within integrated process monitoring systems [26; 27; 28], some even hinting at symmetries in the generated geometries [9], thus offering a realm of exploration for the research community. Regarding arc-DED, as the technology continues to advance, it becomes imperative to explore the testing methodologies to contribute to its optimization. Among the forefront of the testing methods is the integration of artificial intelligence (AI) for defect detection in arc-DED [29]. Researchers have developed sophisticated AI applications, tailored to identifying flaws during the manufacturing process, thus enhancing quality control and efficiency. Additionally, in situ ultrasonic testing (UT) emerges as a pivotal non-destructive technique, utilized during arc-DED component construction. Operating at temperatures up to 100 \({}^{\circ}\)C, UT plays a crucial role in defect detection, ensuring the integrity and reliability of fabricated parts [30]. Furthermore, novel control strategies, such as reinforcement learning, have demonstrated promising outcomes in addressing inherent challenges within arc-DED, such as model non-linearity and process uncertainties.