Deep learning the holographic black hole with charge

Abstract

We use the deep learning algorithm to learn the Reissner-Nordström(RN) black hole metric by building a deep neural network. Plenty of data is made in boundary of AdS and we propagate it to the black hole horizon through AdS metric and equation of motion(e.o.m)We label this data according to the values near the horizon, and together with initial data constitute a data set. Then we construct corresponding deep neural network and train it with the data set to obtain the Reissner-Nordstrom(RN) black hole metric. Finally, we discuss the effects of learning rate, batch-size and initialization on the training process. * recent years, deep leaning architectures such as deep neural network, deep belief network, is rapidly riding. Now they are widely used in signal and information processing, such as speech recognition, computer vision, natural language processing and machine translation.A natural question raised immediately is wether there are some deep relations between holography and machine leaning. In other words, can one construct the gravity holographically from boundary systems through training the deep neural network? Before people realized this relation, someone have studied the connection between deep learning and the renormalization group of a tensor network [12,13]. This is a support that AdS space can be emerged from deep learning because the so-called multiscale entanglement renormalization ansatz(MERA) network was regard as a discrete time slice from holographic point of view [14], and following study motivated by this was discussed in [15]. Recently Hashimoto et.al. have achieved the metric of an AdS black hole via deep neural network with boundary input data[16]. Our work is base on [16] and test it into the Reissner-Nordstrom(RN)

Deep learning and AdS/QCD

“…In the growing subject (see Ref. [26] for a recent summary of data science application to string theory), the idea of equating a holographic spacetime with neural network [11,12,16,17,[27][28][29] may be intertwined with machine learning string landscapes initiated by Refs. [30][31][32][33].…”

Recognition of industrial machine parts based on transfer learning with convolutional neural network

“…For the augmented data, under the condition of using a stochastic gradient descent optimizer, different learning rates are set and the loss function value is observed during the training of the model. Compare the loss function values of the first 200 iterations of training with learning rates [30][31][32] of 0.0001, 0.001, 0.01 and 0.1 respectively, as shown in Fig 8.…”

Bulk reconstruction of metrics inside black holes by complexity

“…Nevertheless, various methods have been developed to reconstruct bulk spacetime metrics by the data of dual quantum field theories (QFTs). 1 Successful methods include the holographic renormalization [5], the reconstruction using bulk geodesics and light cones [6][7][8][9][10][11][12], the reconstruction [13][14][15][16][17][18][19][20][21][22][23][24][25] using holographic entanglement entropy [26,27], 2 the inversion formula [37] of the holographic Wilson loops [38][39][40][41], and the machine learning holography [42][43][44][45][46][47]. 3 However, all of these methods do not reconstruct the static black hole 1 Here we focus on only the bulk reconstruction of spacetime metrics.…”

“…2 Related methods include the one [28][29][30][31] using tensor networks [32,33] through the entanglement properties and the one [34] using bit threads [35,36]. 3 The holographic bulk spacetime is identified with neural networks [42][43][44][45][46][47][48][49][50][51], and the spacetimes are emergent. See [52] for a review of data science approach to string theory, and also see [53] for applications of machine learning to material sciences.…”