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1. Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data

   https://doi.org/10.1038/s41467-021-23952-w  

   Miles, Cole; Bohrdt, Annabelle; Wu, Ruihan; Chiu, Christie; Xu, Muqing; Ji, Geoffrey; Greiner, Markus; Weinberger, Kilian Q.; Demler, Eugene; Kim, Eun-Ah (December 2021, Nature Communications)

   null (Ed.)

   Abstract Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data. 

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2. A PNP ion channel deep learning solver with local neural network and finite element input data

   https://doi.org/10.1088/2632-2153/ad7e7a  

   Lee, Hwi; Chao, Zhen; Cobb, Harris; Liu, Yingjie; Xie, Dexuan (October 2024, Machine Learning: Science and Technology)

   Abstract This paper presents a deep learning method for solving an improved one-dimensional Poisson–Nernst–Planck ion channel (PNPic) model, called the PNPic deep learning solver. The solver combines a novel local neural network, adapted from the neural network with local converging inputs, with an efficient PNPic finite element solver, developed in this work. In particular, the local neural network is extended to handle the complexities of the PNPic model—a system of nonlinear convection–diffusion and elliptic equations with multiple subdomains connected by interface conditions. The PNPic finite element solver efficiently generates input and reference datasets for fast training the local neural network, as well as input datasets for quickly predicting PNPic solutions with high accuracy for a family of PNPic models. Initial numerical tests, involving perturbations of model parameters and interface locations, demonstrate that the PNPic deep learning solver can generate highly accurate numerical solutions. 

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3. Learning Trajectories for Real- Time Optimal Control of Quadrotors

   https://doi.org/10.1109/IROS.2018.8593536  

   Tang, Gao; Sun, Weidong; Hauser, Kris (October 2018, IEEE/RSJ Intl Conf on Intelligent Robots and Systems)

   Nonlinear optimal control problems are challenging to solve efficiently due to non-convexity. This paper introduces a trajectory optimization approach that achieves real-time performance by combining machine learning to predict optimal trajectories with refinement by quadratic optimization. First, a library of optimal trajectories is calculated offline and used to train a neural network. Online, the neural network predicts a trajectory for a novel initial state and cost function, and this prediction is further optimized by a sparse quadratic programming solver. We apply this approach to a fly-to-target movement problem for an indoor quadrotor. Experiments demonstrate that the technique calculates near-optimal trajectories in a few milliseconds, and generates agile movement that can be tracked more accurately than existing methods. 

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4. Task-agnostic representation learning of multimodal twitter data for downstream applications

   https://doi.org/10.1186/s40537-022-00570-x  

   Rivas, Ryan; Paul, Sudipta; Hristidis, Vagelis; Papalexakis, Evangelos E.; Roy-Chowdhury, Amit K. (December 2022, Journal of Big Data)

   Abstract Twitter is a frequent target for machine learning research and applications. Many problems, such as sentiment analysis, image tagging, and location prediction have been studied on Twitter data. Much of the prior work that addresses these problems within the context of Twitter focuses on a subset of the types of data available, e.g. only text, or text and image. However, a tweet can have several additional components, such as the location and the author, that can also provide useful information for machine learning tasks. In this work, we explore the problem of jointly modeling several tweet components in a common embedding space via task-agnostic representation learning, which can then be used to tackle various machine learning applications. To address this problem, we propose a deep neural network framework that combines text, image, and graph representations to learn joint embeddings for 5 tweet components: body, hashtags, images, user, and location. In our experiments, we use a large dataset of tweets to learn a joint embedding model and use it in multiple tasks to evaluate its performance vs. state-of-the-art baselines specific to each task. Our results show that our proposed generic method has similar or superior performance to specialized application-specific approaches, including accuracy of 52.43% vs. 48.88% for location prediction and recall of up to 15.93% vs. 12.12% for hashtag recommendation. 

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5. Output Range Analysis for Deep Feedforward Neural Networks

   Dutta, Souradeep; Jha, Susmit; Sankaranarayanan, Sriram; Tiwari, Ashish (April 2018, Proceedings of NASA Formal Methods Symposium (NFM))

   Given a neural network (NN) and a set of possible inputs to the network described by polyhedral constraints, we aim to compute a safe over-approximation of the set of possible output values. This operation is a fundamental primitive enabling the formal analysis of neural networks that are extensively used in a variety of machine learning tasks such as perception and control of autonomous systems. Increasingly, they are deployed in high-assurance applications, leading to a compelling use case for formal verification approaches. In this paper, we present an efficient range estimation algorithm that iterates between an expensive global combinatorial search using mixed-integer linear programming problems, and a relatively inexpensive local optimization that repeatedly seeks a local optimum of the function represented by the NN. We implement our approach and compare it with Reluplex, a recently proposed solver for deep neural networks. We demonstrate applications of our approach to computing flowpipes for neural network-based feedback controllers. We show that the use of local search in conjunction with mixed-integer linear programming solvers effectively reduces the combinatorial search over possible combinations of active neurons in the network by pruning away suboptimal nodes. 

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