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We adopt a technique, known in the machine learning community as transfer learning, to reduce the bias of computer simulation using very sparse experimental data. Unlike the Bayesian calibration, which is commonly used to estimate the simulation bias, the transfer learning approach discussed in this article involves calculating an artificial neural network surrogate model of the simulations. Assuming that the simulation code correctly predicts the trends in the experimental data but it is subject to unknown biases, we then partially retrain, or transfer learn, the initial surrogate model to match the experimental data. This process eliminates the bias while still taking advantage of the physics relations learned from the simulation. Transfer learning can be easily adapted to a wide range of problems in science and engineering. In this article, we carry out numerical tests to investigate the applicability of this technique to predict the observable outcomes of inertial confinement fusion (ICF) experiments under new conditions. Using our synthetic validation data set, we demonstrate that an accurate predictive model can be built by retraining an initial surrogate model with experimental data volumes so small that they are relevant to the ICF problem. This opens up new opportunities for knowledge transfer and building predictive models in physics. After implementing transfer learning in a standard neural network, we successfully extended the method to a more complex, generative adversarial network architecture, which will be needed for predicting not only scalars but also diagnostic images in our future work.