## 1 Frame of Reference  
Materials design is aimed at tailoring materials structure at various hierarchical levels (microstructural, atomic, etc.) in the chain of process-structure-property-performance (PSPP) to achieve desired properties and performance goals for a given application [1,2] According to the definition of materials design \"an activity that is top-driven, simulation supported, decision-based design of materials hierarchy to satisfy a ranged set of product-level performance requirements [2]\", to achieve the above-mentioned purpose requires systematic and adaptive designing of decision workflows in the chain of PSPP that are less sensitive to various types of variations and uncertainties involved [3]. Conceptually, the process involves the design of materials (process route, composition, etc.) to achieve trade-offs among conflicting criteria. To explore design set points that satisfy desired properties and performance goals, either experimental trial-and-error approaches or methods for model-based realization of engineered systems in simulation-based designs are employed to explore different phases/operations involved in a sequential manufacturing process. Experimental trial-and-error approaches are often very expensive in terms of both cost and time. The significant development of computational methods and tools based on first-principles and experimentalations, and the enormous increase in the computing power of computers have enabled designers and engineers to simulate material properties and behavior in complex engineering applications with real-time conditions to avoid lengthy and expensive cycles of experimental trial-and-error methods. The deficiency in the existing linear and nonlinear correlation methods attributed to simplifying assumptions and idealizations, nondeterministic simulations, and limited experimental data due to heavy computational time and cost, necessitates a design method that can give sufficient confidence to designers in decision making. This further necessitates extending designers' abilities in the understanding and prediction of process behaviors in design by managing the uncertainties in decision workflows in the chain of PSPP [3]. Complex relationships exist between the processing inputs and the resulting microstructure, and between microstructural parameters and material properties. These relationships are difficult to manage by existing linear and nonlinear correlation methods attributed to simplifying assumptions and idealizations, non-deterministic simulations, and limited experimental data due to heavy computational time and cost. Because of these issues, uncertainty management is a significant challenge in the design of complex engineering systems with hierarchical, multiscale, and heterogeneous characteristics [4, 5, 6, 7]. There have been many propositions from numerous researchers suggesting computational platforms from the perspective of decision-based design to support designers in design space exploration with an appreciative capture of uncertainty [8]. [PERSON] et al. [9] categorized the uncertainties involved in the materials design process as _Natural Uncertainty_ (NU), _Model Parameter Uncertainty_ (MPU), _Model Structure Uncertainty_ (MSU), and _Propagated Uncertainty_ (PU). In response, several researchers put forward useful contributions addressing a single or combination of the uncertainties involved. For example, the _Robust Concept Exploration Method_ (RCEM) [10] and its variances: RCEM with _Design Capability Indices_ (RCEM-DCI) [11] and RCEM with _Error Margin Indices_ (RCEM-EMI) [12], _Inductive Design Space Exploration_ (IDEM) [9], and _Concept Exploration Framework_ (CEF) [13,14], provide platforms to support design space exploration based on the compromise Design Support Problem (cDSP) construct. Some robust design methods and tools have also been developed to manage the uncertainties involved in the design process [15,16].