We study the problem of synthetic generation of samples of environmental features for autonomous vehicle navigation. These features are described by a spatiotemporally varying scalar field that we refer to as a threat field. The threat field is known to have some underlying dynamics subject to process noise. Some "real-world" data of observations of various threat fields are also available. The assumption is that the volume of ``real-world'' data is relatively small. The objective is to synthesize samples that are statistically similar to the data. The proposed solution is a generative artificial intelligence model that we refer to as a split variational recurrent neural network (S-VRNN). The S-VRNN merges the capabilities of a variational autoencoder, which is a widely used generative model, and a recurrent neural network, which is used to learn temporal dependencies in data. The main innovation in this work is that we split the latent space of the S-VRNN into two subspaces. The latent variables in one subspace are learned using the ``real-world'' data, whereas those in the other subspace are learned using the data as well as the known underlying system dynamics. Through numerical experiments we demonstrate that the proposed S-VRNN can synthesize data that are statistically similar to the training data even in the case of very small volume of ``real-world'' training data.

First of all, Why VRNN? -- It's the result of the attempt to include the latent random variables into the hidden state of the RNN by combining the elements of the variational autoencoder. Learning generative models for sequences is a very challenging task. Significant work in this direction exists because of Dynamic Bayesian Networks (DBNs) such as Hidden Markov Models (HMMs) and Kalman Filters, but the dominance of DBN-based approaches has now been recently overturned by an interest in the recurrent neural network-based approaches. We know that RNN is very special in the sense that it is able to handle both the variable-length input and output and, by training an RNN to predict the next output in a sequence, given all the previous outputs, it can be used to model joint probability distribution over sequences. RNNs possess both a richly distributed internal state representation and flexible non-linear transition functions (which determine the evolution of the internal hidden state) giving them high expressive power and as a consequence of which RNNs have gained significant popularity as generative models for highly structured sequential data such as natural speech. By highly structured data, the authors meant that the data is characterized by two properties.

Generating graph structures is a challenging problem due to the diverse representations and complex dependencies among nodes. In this paper, we introduce Graph Variational Recurrent Neural Network (GraphVRNN), a probabilistic autoregressive model for graph generation. Through modeling the latent variables of graph data, GraphVRNN can capture the joint distributions of graph structures and the underlying node attributes. We conduct experiments on the proposed GraphVRNN in both graph structure learning and attribute generation tasks. The evaluation results show that the variational component allows our network to model complicated distributions, as well as generate plausible structures and node attributes.