Title: Neural Network Solver for Small Quantum Clusters
Machine learning approaches have recently been applied to the study of various problems in physics. Most of these studies are focused on interpreting the data generated by conventional numerical methods or the data on an existing experimental database. An interesting question is whether it is possible to use a machine learning approach, in particular a neural network, for solving the many-body problem. In this paper, we present a neural network solver for the single impurity Anderson model, the paradigm of an interacting quantum problem in small clusters. We demonstrate that the neural-network-based solver provides quantitative accurate results for the spectral function as compared to the exact diagonalization method. This opens the possibility of utilizing the neural network approach as an impurity solver for other many-body numerical approaches, such as the dynamical mean field theory. more »« less
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.
Abstract. Advances in ambient environmental monitoring technologies are enabling concerned communities and citizens to collect data to better understand their local environment and potential exposures. These mobile, low-cost tools make it possible to collect data with increased temporal and spatial resolution, providing data on a large scale with unprecedented levels of detail. This type of data has the potential to empower people to make personal decisions about their exposure and support the development of local strategies for reducing pollution and improving health outcomes. However, calibration of these low-cost instruments has been a challenge. Often, a sensor package is calibrated via field calibration. This involves colocating the sensor package with a high-quality reference instrument for an extended period and then applying machine learning or other model fitting technique such as multiple linear regression to develop a calibration model for converting raw sensor signals to pollutant concentrations. Although this method helps to correct for the effects of ambient conditions (e.g., temperature) and cross sensitivities with nontarget pollutants, there is a growing body of evidence that calibration models can overfit to a given location or set of environmental conditions on account of the incidental correlation between pollutant levels and environmental conditions, including diurnal cycles. As a result, a sensor package trained at a field site may provide less reliable data when moved, or transferred, to a different location. This is a potential concern for applications seeking to perform monitoring away from regulatory monitoring sites, such as personal mobile monitoring or high-resolution monitoring of a neighborhood. We performed experiments confirming that transferability is indeed a problem and show that it can be improved by collecting data from multiple regulatory sites and building a calibration model that leverages data from a more diverse data set. We deployed three sensor packages to each of three sites with reference monitors (nine packages total) and then rotated the sensor packages through the sites over time. Two sites were in San Diego, CA, with a third outside of Bakersfield, CA, offering varying environmental conditions, general air quality composition, and pollutant concentrations. When compared to prior single-site calibration, the multisite approach exhibits better model transferability for a range of modeling approaches. Our experiments also reveal that random forest is especially prone to overfitting and confirm prior results that transfer is a significant source of both bias and standard error. Linear regression, on the other hand, although it exhibits relatively high error, does not degrade much in transfer. Bias dominated in our experiments, suggesting that transferability might be easily increased by detecting and correcting for bias. Also, given that many monitoring applications involve the deployment of many sensor packages based on the same sensing technology, there is an opportunity to leverage the availability of multiple sensors at multiple sites during calibration to lower the cost of training and better tolerate transfer. We contribute a new neural network architecture model termed split-NN that splits the model into two stages, in which the first stage corrects for sensor-to-sensor variation and the second stage uses the combined data of all the sensors to build a model for a single sensor package. The split-NN modeling approach outperforms multiple linear regression, traditional two- and four-layer neural networks, and random forest models. Depending on the training configuration, compared to random forest the split-NN method reduced error 0 %–11 % for NO2 and 6 %–13 % for O3.
Efficient rendering of photo‐realistic virtual worlds is a long standing effort of computer graphics. Modern graphics techniques have succeeded in synthesizing photo‐realistic images from hand‐crafted scene representations. However, the automatic generation of shape, materials, lighting, and other aspects of scenes remains a challenging problem that, if solved, would make photo‐realistic computer graphics more widely accessible. Concurrently, progress in computer vision and machine learning have given rise to a new approach to image synthesis and editing, namely deep generative models. Neural rendering is a new and rapidly emerging field that combines generative machine learning techniques with physical knowledge from computer graphics, e.g., by the integration of differentiable rendering into network training. With a plethora of applications in computer graphics and vision, neural rendering is poised to become a new area in the graphics community, yet no survey of this emerging field exists. This state‐of‐the‐art report summarizes the recent trends and applications of neural rendering. We focus on approaches that combine classic computer graphics techniques with deep generative models to obtain controllable and photorealistic outputs. Starting with an overview of the underlying computer graphics and machine learning concepts, we discuss critical aspects of neural rendering approaches. Specifically, our emphasis is on the type of control, i.e., how the control is provided, which parts of the pipeline are learned, explicit vs. implicit control, generalization, and stochastic vs. deterministic synthesis. The second half of this state‐of‐the‐art report is focused on the many important use cases for the described algorithms such as novel view synthesis, semantic photo manipulation, facial and body reenactment, relighting, free‐viewpoint video, and the creation of photo‐realistic avatars for virtual and augmented reality telepresence. Finally, we conclude with a discussion of the social implications of such technology and investigate open research problems.
Heider, Yousef; Suh, Hyoung Suk; Sun, WaiChing(
, International Journal for Numerical and Analytical Methods in Geomechanics)
Abstract
Supervised machine learning via artificial neural network (ANN) has gained significant popularity for many geomechanics applications that involves multi‐phase flow and poromechanics. For unsaturated poromechanics problems, the multi‐physics nature and the complexity of the hydraulic laws make it difficult to design the optimal setup, architecture, and hyper‐parameters of the deep neural networks. This paper presents a meta‐modeling approach that utilizes deep reinforcement learning (DRL) to automatically discover optimal neural network settings that maximize a pre‐defined performance metric for the machine learning constitutive laws. This meta‐modeling framework is cast as a Markov Decision Process (MDP) with well‐defined states (subsets of states representing the proposed neural network (NN) settings), actions, and rewards. Following the selection rules, the artificial intelligence (AI) agent, represented in DRL via NN, self‐learns from taking a sequence of actions and receiving feedback signals (rewards) within the selection environment. By utilizing the Monte Carlo Tree Search (MCTS) to update the policy/value networks, the AI agent replaces the human modeler to handle the otherwise time‐consuming trial‐and‐error process that leads to the optimized choices of setup from a high‐dimensional parametric space. This approach is applied to generate two key constitutive laws for the unsaturated poromechanics problems: (1) the path‐dependent retention curve with distinctive wetting and drying paths. (2) The flow in the micropores, governed by an anisotropic permeability tensor. Numerical experiments have shown that the resultant ML‐generated material models can be integrated into a finite element (FE) solver to solve initial‐boundary‐value problems as replacements of the hand‐craft constitutive laws.
Rivas, Ryan; Paul, Sudipta; Hristidis, Vagelis; Papalexakis, Evangelos E.; Roy-Chowdhury, Amit K.(
, 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.
Walker, Nicholas, Kellar, Samuel, Zhang, Yi, Tam, Ka-Ming, and Moreno, Juana. Neural Network Solver for Small Quantum Clusters. Retrieved from https://par.nsf.gov/biblio/10388249. Crystals 12.9 Web. doi:10.3390/cryst12091269.
@article{osti_10388249,
place = {Country unknown/Code not available},
title = {Neural Network Solver for Small Quantum Clusters},
url = {https://par.nsf.gov/biblio/10388249},
DOI = {10.3390/cryst12091269},
abstractNote = {Machine learning approaches have recently been applied to the study of various problems in physics. Most of these studies are focused on interpreting the data generated by conventional numerical methods or the data on an existing experimental database. An interesting question is whether it is possible to use a machine learning approach, in particular a neural network, for solving the many-body problem. In this paper, we present a neural network solver for the single impurity Anderson model, the paradigm of an interacting quantum problem in small clusters. We demonstrate that the neural-network-based solver provides quantitative accurate results for the spectral function as compared to the exact diagonalization method. This opens the possibility of utilizing the neural network approach as an impurity solver for other many-body numerical approaches, such as the dynamical mean field theory.},
journal = {Crystals},
volume = {12},
number = {9},
author = {Walker, Nicholas and Kellar, Samuel and Zhang, Yi and Tam, Ka-Ming and Moreno, Juana},
}
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