A screen assembly has a material that conforms to the borehole shape after insertion. The assembly comprises a compliant layer that takes the borehole shape on expansion. The outer layer is formed having holes to permit production flow. The material that is selected preferably swells with heat and preferably comprises a shape memory foam that is thermoset. The base pipe can have a screen over it to act as an underlayment for support of the conforming layer or alternatively for screening. The conforming layer can expand by itself or expansion can also occur from within the base pipe.