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      Machine learning and polymer self-consistent field theory in two spatial dimensions.

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          Abstract

          A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in the work of Xuan et al. [J. Comput. Phys. 443, 110519 (2021)]. Several innovations and improvements are proposed. (1) A Sobolev space-trained, convolutional neural network is employed to handle the exponential dimension increase of the discretized, local average monomer density fields and to strongly enforce both spatial translation and rotation invariance of the predicted, field-theoretic intensive Hamiltonian. (2) A generative adversarial network (GAN) is introduced to efficiently and accurately predict saddle point, local average monomer density fields without resorting to gradient descent methods that employ the training set. This GAN approach yields important savings of both memory and computational cost. (3) The proposed machine learning framework is successfully applied to 2D cell size optimization as a clear illustration of its broad potential to accelerate the exploration of parameter space for discovering polymer nanostructures. Extensions to three-dimensional phase discovery appear to be feasible.

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          Author and article information

          Journal
          J Chem Phys
          The Journal of chemical physics
          AIP Publishing
          1089-7690
          0021-9606
          Apr 14 2023
          : 158
          : 14
          Affiliations
          [1 ] Department of Mathematics, University of California, Santa Barbara, California 93106, USA.
          [2 ] Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA.
          Article
          10.1063/5.0142608
          37061486
          13c9b5da-6724-461d-b540-c2f53da4a4a7
          History

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