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  1. Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable when each likelihood evaluation is computationally expensive. New approaches combining variational inference with normalizing flow are characterized by a computational cost that grows only linearly with the dimensionality of the latent variable space, and rely on gradient-based optimization instead of sampling, providing a more efficient approach for Bayesian inference about the model parameters. Moreover, the cost of frequently evaluating an expensive likelihood can be mitigated by replacing the true model with an offline trained surrogate model, such as neural networks. However, this approach might generate significant bias when the surrogate is insufficiently accurate around the posterior modes. To reduce the computational cost without sacrificing inferential accuracy, we propose Normalizing Flow with Adaptive Surrogate (NoFAS), an optimization strategy that alternatively updates the normalizing flow parameters and surrogate model parameters. We also propose an efficient sample weighting scheme for surrogate model training that preserves global accuracy while effectively capturing high posterior density regions. We demonstrate the inferential and computational superiority of NoFAS against various benchmarks, including casesmore »where the underlying model lacks identifiability. The source code and numerical experiments used for this study are available at https://github.com/cedricwangyu/NoFAS.« less
    Free, publicly-accessible full text available October 15, 2023
  2. We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. These networks benefit from a significant reduction in the number of trainable parameters with respect to an equivalent fully connected network. These architectures are also versatile with respect to the input and output dimensionality. For example, encoder-decoder, decoder-encoder or decoder-encoder-decoder architectures are well suited to learn mappings between input and outputs of any dimensionality. We demonstrate the accuracy produced by such architectures when trained on a few high-fidelity and many low-fidelity data generated from models ranging from one-dimensional functions to Poisson equation solvers in two-dimensions. We finally discuss a number of implementation choices that improve the reliability of the uncertainty estimates generated by a dropblock regularizer, and compare uncertainty estimates among low-, high- and multi-fidelity approaches.