In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[EX Q]: Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, the uses have been restricted by the fact the training data are obtained using PDE solvers. Thereby, the uses were limited to domains, where the PDE solver was applicable, but no further. 

 We present methods for training on small domains, while applying the trained models on larger domains, with consistency constraints ensuring the solutions are physically meaningful even at the boundary of the small domains. We demonstrate the results on an air-pollution forecasting model for Dublin, Ireland.
[EX A]: We present RNNs for training surrogate models of PDEs, wherein consistency constraints ensure the solutions are physically meaningful, even when the training uses much smaller domains than the trained model is applied to.

[EX Q]: One of the challenges in the study of generative adversarial networks is the instability of its training. 
 In this paper, we propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator.
 Our new normalization technique is computationally light and easy to incorporate into existing implementations. 
 We tested the efficacy of spectral normalization on CIFAR10, STL-10, and ILSVRC2012 dataset, and we experimentally confirmed that spectrally normalized GANs (SN-GANs) is capable of generating images of better or equal quality relative to the previous training stabilization techniques.
[EX A]: We propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator of GANs.

[EX Q]: Inspired by neurophysiological discoveries of navigation cells in the mammalian
 brain, we introduce the first deep neural network architecture for modeling Egocentric
 Spatial Memory (ESM). It learns to estimate the pose of the agent and
 progressively construct top-down 2D global maps from egocentric views in a spatially
 extended environment. During the exploration, our proposed ESM network
 model updates belief of the global map based on local observations using a recurrent
 neural network. It also augments the local mapping with a novel external
 memory to encode and store latent representations of the visited places based on
 their corresponding locations in the egocentric coordinate. This enables the agents
 to perform loop closure and mapping correction. This work contributes in the
 following aspects: first, our proposed ESM network provides an accurate mapping
 ability which is vitally important for embodied agents to navigate to goal locations.
 In the experiments, we demonstrate the functionalities of the ESM network in
 random walks in complicated 3D mazes by comparing with several competitive
 baselines and state-of-the-art Simultaneous Localization and Mapping (SLAM)
 algorithms. Secondly, we faithfully hypothesize the functionality and the working
 mechanism of navigation cells in the brain. Comprehensive analysis of our model
 suggests the essential role of individual modules in our proposed architecture and
 demonstrates efficiency of communications among these modules. We hope this
 work would advance research in the collaboration and communications over both
 fields of computer science and computational neuroscience.
[EX A]:
first deep neural network for modeling Egocentric Spatial Memory inspired by neurophysiological discoveries of navigation cells in mammalian brain