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Register a new userA framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks
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Added by
Teeratorn Kadeethum
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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This work is the first to employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) towards learning a forward and an inverse solution operator of partial differential equations (PDEs). Even though the proposed framework could be applied as a surrogate model for the solution of any PDEs, here we focus on steady-state solutions of coupled hydro-mechanical processes in heterogeneous porous media. Strongly heterogeneous material properties, which translate to the heterogeneity of coefficients of the PDEs and discontinuous features in the solutions, require specialized techniques for the forward and inverse solution of these problems. Additionally, parametrization of the spatially heterogeneous coefficients is excessively difficult by using standard reduced order modeling techniques. In this work, we overcome these challenges by employing the image-to-image translation concept to learn the forward and inverse solution operators and utilize a U-Net generator and a patch-based discriminator. Our results show that the proposed data-driven reduced order model has competitive predictive performance capabilities in accuracy and computational efficiency as well as training time requirements compared to state-of-the-art data-driven methods for both forward and inverse problems.
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Conditional Generative Adversarial Networks (cGANs) are generative models that can produce data samples ($x$) conditioned on both latent variables ($z$) and known auxiliary information ($c$). We propose the Bidirectional cGAN (BiCoGAN), which effectively disentangles $z$ and $c$ in the generation process and provides an encoder that learns inverse mappings from $x$ to both $z$ and $c$, trained jointly with the generator and the discriminator. We present crucial techniques for training BiCoGANs, which involve an extrinsic factor loss along with an associated dynamically-tuned importance weight. As compared to other encoder-based cGANs, BiCoGANs encode $c$ more accurately, and utilize $z$ and $c$ more effectively and in a more disentangled way to generate samples.
Conditional generative adversarial networks (cGAN) have led to large improvements in the task of conditional image generation, which lies at the heart of computer vision. The major focus so far has been on performance improvement, while there has been little effort in making cGAN more robust to noise. The regression (of the generator) might lead to arbitrarily large errors in the output, which makes cGAN unreliable for real-world applications. In this work, we introduce a novel conditional GAN model, called RoCGAN, which leverages structure in the target space of the model to address the issue. Our model augments the generator with an unsupervised pathway, which promotes the outputs of the generator to span the target manifold even in the presence of intense noise. We prove that RoCGAN share similar theoretical properties as GAN and experimentally verify that our model outperforms existing state-of-the-art cGAN architectures by a large margin in a variety of domains including images from natural scenes and faces.
We present cudaclaw, a CUDA-based high performance data-parallel framework for the solution of multidimensional hyperbolic partial differential equation (PDE) systems, equations describing wave motion. cudaclaw allows computational scientists to solve such systems on GPUs without being burdened by the need to write CUDA code, worry about thread and block details, data layout, and data movement between the different levels of the memory hierarchy. The user defines the set of PDEs to be solved via a CUDA- independent serial Riemann solver and the framework takes care of orchestrating the computations and data transfers to maximize arithmetic throughput. cudaclaw treats the different spatial dimensions separately to allow suitable block sizes and dimensions to be used in the different directions, and includes a number of optimizations to minimize access to global memory.
We consider the hypothesis testing problem of detecting conditional dependence, with a focus on high-dimensional feature spaces. Our contribution is a new test statistic based on samples from a generative adversarial network designed to approximate directly a conditional distribution that encodes the null hypothesis, in a manner that maximizes power (the rate of true negatives). We show that such an approach requires only that density approximation be viable in order to ensure that we control type I error (the rate of false positives); in particular, no assumptions need to be made on the form of the distributions or feature dependencies. Using synthetic simulations with high-dimensional data we demonstrate significant gains in power over competing methods. In addition, we illustrate the use of our test to discover causal markers of disease in genetic data.
In this paper, a novel framework is proposed to perform data-driven air-to-ground (A2G) channel estimation for millimeter wave (mmWave) communications in an unmanned aerial vehicle (UAV) wireless network. First, an effective channel estimation approach is developed to collect mmWave channel information, allowing each UAV to train a stand-alone channel model via a conditional generative adversarial network (CGAN) along each beamforming direction. Next, in order to expand the application scenarios of the trained channel model into a broader spatial-temporal domain, a cooperative framework, based on a distributed CGAN architecture, is developed, allowing each UAV to collaboratively learn the mmWave channel distribution in a fully-distributed manner. To guarantee an efficient learning process, necessary and sufficient conditions for the optimal UAV network topology that maximizes the learning rate for cooperative channel modeling are derived, and the optimal CGAN learning solution per UAV is subsequently characterized, based on the distributed network structure. Simulation results show that the proposed distributed CGAN approach is robust to the local training error at each UAV. Meanwhile, a larger airborne network size requires more communication resources per UAV to guarantee an efficient learning rate. The results also show that, compared with a stand-alone CGAN without information sharing and two other distributed schemes, namely: A multi-discriminator CGAN and a federated CGAN method, the proposed distributed CGAN approach yields a higher modeling accuracy while learning the environment, and it achieves a larger average data rate in the online performance of UAV downlink mmWave communications.
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