More Like this

1. Solving Shared Problems at the Food, Energy, and Water Nexus

   https://doi.org/10.1029/2021EO153130  

   Zhuang, Jie; L�ffler, Frank; Sayler, Gary; Yu, Guirui; Jiang, Guibin (January 2021, Eos)

   null (Ed.)

   A 15-year-old partnership among Chinese and U.S. scientists studying challenges in our food, energy, and water systems has revealed that solutions are best achieved through international collaboration. 

   more » « less
2. Solving Optimization Problems with Blackwell Approachability

   https://doi.org/10.1287/moor.2023.1376  

   Grand-Clément, Julien; Kroer, Christian (January 2023, Mathematics of Operations Research)

   In this paper, we propose a new algorithm for solving convex-concave saddle-point problems using regret minimization in the repeated game framework. To do so, we introduce the Conic Blackwell Algorithm + ([Formula: see text]), a new parameter- and scale-free regret minimizer for general convex compact sets. [Formula: see text] is based on Blackwell approachability and attains [Formula: see text] regret. We show how to efficiently instantiate [Formula: see text] for many decision sets of interest, including the simplex, [Formula: see text] norm balls, and ellipsoidal confidence regions in the simplex. Based on [Formula: see text], we introduce [Formula: see text], a new parameter-free algorithm for solving convex-concave saddle-point problems achieving a [Formula: see text] ergodic convergence rate. In our simulations, we demonstrate the wide applicability of [Formula: see text] on several standard saddle-point problems from the optimization and operations research literature, including matrix games, extensive-form games, distributionally robust logistic regression, and Markov decision processes. In each setting, [Formula: see text] achieves state-of-the-art numerical performance and outperforms classical methods, without the need for any choice of step sizes or other algorithmic parameters. Funding: J. Grand-Clément is supported by the Agence Nationale de la Recherche [Grant 11-LABX-0047] and by Hi! Paris. C. Kroer is supported by the Office of Naval Research [Grant N00014-22-1-2530] and by the National Science Foundation [Grant IIS-2147361]. 

   more » « less
3. Computing Spectra without Solving Eigenvalue Problems

   https://doi.org/10.1137/17M1156721  

   Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana (January 2019, SIAM Journal on Scientific Computing)
4. DeepOPF-V: Solving AC-OPF Problems Efficiently

   https://doi.org/10.1109/TPWRS.2021.3114092  

   Huang, Wanjun; Pan, Xiang; Chen, Minghua; Low, Steven H. (January 2022, IEEE Transactions on Power Systems)
5. 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. 

   more » « less