## 1 Frame of Reference
As mentioned above, all these platforms and contributions have employed the incomplete, incorrect, and infield models that limit the confidence and freedom of designers in decision making. There is need for a robust, uniform model and method that can give sufficient confidence to designers to manage uncertainties involved in the chain of PSPP and make decisions with satisficing solutions. In this study, we identify, based on the discussion above, three aims that a materials design process should address: (1) guide designers from end property and performance goals to the processing parameters in an inverse, goal-oriented way, (2) provide sufficient freedom and space to designers to adjust errors at every decision node during the design process, i.e., manage propagated uncertainty, and (3) allow designers to timely adjust model parameters for accurate predictions, i.e., Manage Model Parameter Uncertainty (MPU) and Model Structure Uncertainty (MSU). Keeping in mind the above challenges and targets, the following are the questions to be answered in order to achieve the desired outcome. Primary Research Question: How can the design spaces be explored and the mappings in the PSPP chain be coupled using machine learning? * _Research Question 1:_ How can the dataset of inputs and outputs for each mapping of the PSPP be obtained? * _Research Question 2:_ How can the small datasets to predict the outputs be accurately addressed? * _Research Question 3:_ Based on the phenomena, how can the flow of information (forward and backward) across the PSPP chain in the hot stamping process be established? * _Research Question 4:_ How can the uncertainty at each stage as well as the overall process be managed? In this work we have attempted to address the three aims except MPU, which is the subject of our future work. Due to the development of machine learning (ML) based methods, the complex, non-linear relationships can now be modeled efficiently and effectively [17]. ML-based methodshave the ability to capture functional relationships from data and knowledge without knowing the fundamental science-based mechanisms and relationships. Well-established ML-based models, in general, and ANN-based models, in particular, have been developed and employed for tailoring materials properties and design. Several examples can be found in the literature featuring success stories of the application of ML-based models and techniques in the materials design process in general [18; 19; 20; 21; 22; 23; 24; 25; 26] and particularly in the field of processing and manufacturing steel and other alloys [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46]. Existing analytical and computational models and tools enable designers to efficiently solve standard forward problems, i.e., to predict properties and behaviors of particular materials under specific processing conditions. However, the methods to handle inverse problems are less well developed, i.e., to design or engineer new materials with desired properties and performance goals. Materials design problems using ML methods can be described by considering, given dataset (e.g., microstructure-property) obtained from physical experiments and/or computations based on first-principles [17; 47; 48], the best combinations of input parameters that possess the desirable output (e.g., microstructure or properties). Datasets can provide great opportunities for the application of ML-based methods or data-driven techniques to accelerate the tailoring of materials with desired properties. This work focuses on seeking satisficing solutions that can perform well under uncertainty rather than optimal solutions, which perform poor when subjected to uncertainties. Optimal solutions perform well for a very narrow range, but when there is a shift in conditions, their performance suffers [13]. Therefore, designers are required to make decisions with satisficing solution set points that perform well enough under uncertainty.