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Inverse Design for Generating Initial Conditions in Scientific Simulations
DescriptionWe propose a conditional normalizing flow (CNF) surrogate model to solve generative, many-to-one inverse problems in scientific simulations governed by partial differential equations (PDEs) with time-evolving interactions between heterogeneous materials. We present two case studies: electrostatic potential and heat diffusion, which serve as proxy simulations for generating diverse sets of initial conditions that can reproduce an observed output state (transient or steady). Finally, we provide a comprehensive overview of the synthetic datasets, the model specification, each stage of the experimental workflow, evaluation of training performance, and uncertainty quantification for the generated samples.