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A key element of materials discovery and design is to learn from available data and prior knowledge to guide the next experiments or calculations in order to focus in on materials with targeted properties. We suggest that the tight coupling and feedback between experiments, theory and informatics demands a codesign approach, very reminiscent of computational codesign involving software and hardware in computer science. This requires dealing with a constrained optimization problem in which uncertainties are used to adaptively explore and exploit the predictions of a surrogate model to search the vast high dimensional space where the desired material may be found.