  This paper introduces a novel two-stage machine learning-based surrogate
modeling framework to address inverse problems in scientific and engineering
fields. In the first stage of the proposed framework, a machine learning model
termed the "learner" identifies a limited set of candidates within the input
design space whose predicted outputs closely align with desired outcomes.
Subsequently, in the second stage, a separate surrogate model, functioning as
an "evaluator," is employed to assess the reduced candidate space generated in
the first stage. This evaluation process eliminates inaccurate and uncertain
solutions, guided by a user-defined coverage level. The framework's distinctive
contribution is the integration of conformal inference, providing a versatile
and efficient approach that can be widely applicable. To demonstrate the
effectiveness of the proposed framework compared to conventional single-stage
inverse problems, we conduct several benchmark tests and investigate an
engineering application focused on the micromechanical modeling of
fiber-reinforced composites. The results affirm the superiority of our proposed
framework, as it consistently produces more reliable solutions. Therefore, the
introduced framework offers a unique perspective on fostering interactions
between machine learning-based surrogate models in real-world applications.
