**1. Introduction**

Modern metal additive manufacturing (AM) processes provide greatly expanded opportunities for producing engineered components possessing intricate geometries, novel material chemistries and internal structures. Furthermore, it is possible to tailor the material internal structures (hereafter simply referred to as microstructures) at different locations in the component both during the actual AM process and in subsequent (post-build) heat treatments in the effort to optimize its overall in-service functional performance [1–7]. Over the years, AM processes have been applied successfully in metal products with demonstrated benefits in net shaping, component repair, intricate geometry prototyping and component customization [8–15]. Although both experiments and physics-based multiscale material simulations have the potential to offer the data needed to gain insights into the correlations between the processing conditions and microstructure as well as the associated properties, our focus in this work was confined to experiments. This is mainly because the multiscale material models for

AM metal alloys are still largely under development [16–19]. The AM process usually consists of multiple steps, including substrate treatment, powder delivery, energy delivery, nozzle movement and post-build heat treatments [20–24]. Each of these process steps involves the selection of multiple parameters that could significantly influence the local thermal history and, thereby, the microstructure and associated properties. The central challenges encountered in the experimental exploration of the influence of AM processing conditions and material microstructure come from two main gaps in current capabilities in the field. First, there is a lack of validated high-throughput experimental assays that are cost-effective and require only small amounts of material in different conditions (e.g., a range of chemical compositions and process histories). Second, there is also a lack of established approaches capable of building reliable data-driven process–structure–property (PSP) linkages from limited data (i.e., a relatively small number of data points). This is particularly important for AM metal alloy development using experimental assays, because it is unlikely that one can accumulate the very large datasets needed by conventional machine learning approaches such as neural networks [25–28].

A number of different experimental protocols have been explored in recent literature for the rapid formulation of PSP linkages from experiments in metal AM [29–32]. The central challenges come from the need to prototype a large library of samples spanning the large ranges of chemistries and process histories relevant to metal AM, and subsequently characterizing their microstructures and mechanical properties. In this respect, it should be noted that AM inherently offers many advantages in prototyping libraries of samples with small volumes. Previous studies [32–35] have demonstrated the feasibility of manufacturing compositionally and functionally graded materials with microstructural gradients using a selective laser-melting technique. Similarly, Joseph et al. [36] demonstrated the feasibility of exploring the vast compositional space of high-entropy alloys (HEAs) using the direct laser-fabrication technique. Beyond the prototyping of the sample libraries, one also needs to address the challenges in the high-throughput characterization of the samples. It is important to note that the characterization should include both details of the material microstructures and their mechanical properties in order to meet our target of extracting PSP linkages that can accelerate material innovation for AM. In recent work, Saltzbrenner et al. [31] have demonstrated the viability of prototyping miniaturized tensile test specimens and conducting high-throughput tests in automated protocols. Although this approach has tremendous potential, in practice, it is often challenging to extract reliable and consistently reproducible mechanical properties because of the large heterogeneity exhibited by the AM samples. Since tensile testing requires a statistically homogeneous material condition in the entire gauge section for the successful evaluation of mechanical properties, any significant variation in the local thermal histories at different locations of the gauge section of the tensile test specimen can lead to a large variance in the values of the measured mechanical properties from such measurements. For AM samples, there is a critical need to explore other characterization methods that can evaluate mechanical properties in small material volumes without the need to make standardized tensile test samples.

In recent work [37], it was demonstrated that it is possible to prototype compositionally graded AM samples and characterize their mechanical properties using the stress–strain analysis protocols based on spherical indentation. This strategy appears to exhibit tremendous potential for the high-throughput extraction of the relationships between the processing conditions, microstructural features and properties [38,39]. Although this strategy has produced reliable data points, the size of the dataset (i.e., the number of data points obtained) is still rather small for the extraction of PSP linkages using emergent machine learning techniques. In this paper, we demonstrate novel workflows that extend significantly the previously demonstrated assays in multiple research directions: (i) the prototyping of a much larger library of AM Ti–Mn alloys employing intentionally induced compositional gradients coupled with different post-build heat treatments, and (ii) the use of data-driven model-building strategies such as Gaussian process regression (GPR) [40–46] for extracting practically useful correlations from experimental datasets. GPR offers many potential advantages compared to other machine learning approaches, including the ability to utilize smaller data sets (i.e., smaller numbers of data points) [42,44], rigorous treatment of uncertainty [47,48] and dynamic selection

of new experiments that maximize the expected information gain [49–51]. This work explores and demonstrates a framework for high-throughput experimental assays to facilitate the efficient exploration of the AM process space as well as statistical analyses of the accumulated data using GPR approaches.

#### **2. Methods**
