3D representation of soil structure using Generative Adversarial Networks

Many environmental studies - from agriculture and forestry to flood prediction/control and natural resources conservation - require a deep understanding of soil processes and sub-surface water flow dynamics. Comprehensive knowledge of soil physical properties such as porosity and structure is an essential requirement for site-specific precision agriculture. The most popular method of representing pore space and structure in 3D is with soil tomography data. However, since tomography analysis is expensive and time-consuming, there is no opportunity to obtain direct tomography data for large areas.

We present a study using an artificial intelligence (AI) system that can produce high-resolution 3D representations of pore space across the study area using existing terrain data and soil tomography information from a limited number of locations. The core of the AI system is Generative Adversarial Networks - a relatively new breed of deep learning systems in which networks compete against each other to create a better learning of the underlying dynamics of the system. The problem of obtaining 3D soil representation is intricate since it requires learning complex distributions of properties in 3 dimensions, given only a few sparse samples from the distributions. In other words, we learn a probability p(x) to observe a given 3D structure by looking at the real data. Eventually, the problem is to maximize the conditional probability p(x|y), where y are our sparse measurements. To solve this problem, we propose to reformulate it to fitting three neural networks.

The AI system consists of an encoder that maps y to a latent space (h); a generator that takes the latent representation (h) of the measurements and a random noise vector (z) as inputs and maps them to a 3D structure (xhat); and finally, a neural network called the discriminator. The discriminator compares the generated reconstruction (xhat) and the real domain (x). The goal of the generator is to fool the discriminator by maximizing the combined loss function. Separately, the parameters of the encoder and generator will be updated to ensure that the generated structure indeed coincides with our measurements (y) at the sampling locations. Given the field dataset and the above-developed algorithm, we infer the 3D structure between the sampling points.