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1. Solving Bayesian Inverse Problems via Variational Autoencoders

   Goh, H. (January 2021, Proceeding of Machine Learning Research, 2nd Annual Conference on Mathematical and Scientific Machine Learning)

   Joan Bruna, Jan S (Ed.)

   In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-constrained framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty. Numerical results for an elliptic PDE-constrained Bayesian inverse problem are provided to verify the proposed framework. 

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2. Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging

   https://doi.org/10.1609/aaai.v35i3.16366  

   Sun, He; Bouman, Katherine L. (May 2021, Proceedings of the AAAI Conference on Artificial Intelligence)

   Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically focus on recovering a point estimate. This is a serious limitation when working with under-determined imaging systems, where it is conceivable that multiple image modes would be consistent with the measured data. Characterizing the space of probable images that explain the observational data is therefore crucial. In this paper, we propose a variational deep probabilistic imaging approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging (DPI) employs an untrained deep generative model to estimate a posterior distribution of an unobserved image. This approach does not require any training data; instead, it optimizes the weights of a neural network to generate image samples that fit a particular measurement dataset. Once the network weights have been learned, the posterior distribution can be efficiently sampled. We demonstrate this approach in the context of interferometric radio imaging, which is used for black hole imaging with the Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging (MRI). 

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3. α-deep Probabilistic Inference (α-DPI): Efficient Uncertainty Quantification from Exoplanet Astrometry to Black Hole Feature Extraction

   https://doi.org/10.3847/1538-4357/ac6be9  

   Sun, He; Bouman, Katherine L.; Tiede, Paul; Wang, Jason J.; Blunt, Sarah; Mawet, Dimitri (June 2022, The Astrophysical Journal)

   Abstract Inference is crucial in modern astronomical research, where hidden astrophysical features and patterns are often estimated from indirect and noisy measurements. Inferring the posterior of hidden features, conditioned on the observed measurements, is essential for understanding the uncertainty of results and downstream scientific interpretations. Traditional approaches for posterior estimation include sampling-based methods and variational inference (VI). However, sampling-based methods are typically slow for high-dimensional inverse problems, while VI often lacks estimation accuracy. In this paper, we proposeα-deep probabilistic inference, a deep learning framework that first learns an approximate posterior usingα-divergence VI paired with a generative neural network, and then produces more accurate posterior samples through importance reweighting of the network samples. It inherits strengths from both sampling and VI methods: it is fast, accurate, and more scalable to high-dimensional problems than conventional sampling-based approaches. We apply our approach to two high-impact astronomical inference problems using real data: exoplanet astrometry and black hole feature extraction. 

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4. InfoVAE: Balancing Learning and Inference in Variational Autoencoders

   https://doi.org/10.1609/aaai.v33i01.33015885  

   Zhao, Shengjia; Song, Jiaming; Ermon, Stefano (July 2019, Proceedings of the AAAI Conference on Artificial Intelligence)

   A key advance in learning generative models is the use of amortized inference distributions that are jointly trained with the models. We find that existing training objectives for variational autoencoders can lead to inaccurate amortized inference distributions and, in some cases, improving the objective provably degrades the inference quality. In addition, it has been observed that variational autoencoders tend to ignore the latent variables when combined with a decoding distribution that is too flexible. We again identify the cause in existing training criteria and propose a new class of objectives (Info-VAE) that mitigate these problems. We show that our model can significantly improve the quality of the variational posterior and can make effective use of the latent features regardless of the flexibility of the decoding distribution. Through extensive qualitative and quantitative analyses, we demonstrate that our models outperform competing approaches on multiple performance metrics 

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5. Normalizing Flows for Intelligent Manufacturing

   https://doi.org/10.1115/MSEC2023-101281  

   Russell, Matthew; Wang, Peng (June 2023, American Society of Mechanical Engineers)

   Abstract Monitoring machine health and product quality enables predictive maintenance that optimizes repairs to minimize factory downtime. Data-driven intelligent manufacturing often relies on probabilistic techniques with intractable distributions. For example, generative models of data distributions can balance fault classes with synthetic data, and sampling the posterior distribution of hidden model parameters enables prognosis of degradation trends. Normalizing flows can address these problems while avoiding the training instability or long inference times of other generative Deep Learning (DL) models like Generative Adversarial Networks (GAN), Variational Autoencoders (VAE), and diffusion networks. To evaluate normalizing flows for manufacturing, experiments are conducted to synthesize surface defect images from an imbalanced data set and estimate parameters of a tool wear degradation model from limited observations. Results show that normalizing flows are an effective, multi-purpose DL architecture for solving these problems in manufacturing. Future work should explore normalizing flows for more complex degradation models and develop a framework for likelihood-based anomaly detection. Code is available at https://github.com/uky-aism/flows-for-manufacturing. 

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