Can Neural Networks Think like Geomorphologists?

Jo Martin, University of Colorado, Boulder Boulder Colorado, United States. jo.martin@moosecow.net

Neural networks are a machine learning technique that has found massive success across all disciplines, including earth science. So far, their use has primarily been operational: with scientists improving their river forecasts, automating their mapping tasks, and constructing more accurate geophysical inversions. They have shown a great ability to succeed in solving problems in earth science, but they have not yielded an equivalent leap forward in our theoretical understanding of earth systems. While neural networks are often discussed as “black boxes” this is not inherently the case; they can be interrogated and the patterns they have learned can be understood through the lens of our existing physical theory.

Water leaves a fingerprint on landscapes, but we still struggle to quantify topography in a way that can be quantitatively related to the surface water hydrology that has shaped it. Convolutional neural networks have an ability to approximate arbitrary spatial functions, and so are an exciting tool to help us quantify topography in geomorphically and hydrologically meaningful ways. In this work we focus on the robustness and scrutability (that is, the ability to understand the internal model of the neural network) of a convolutional neural network trained to infer key geomorphological parameters from modeled topography. Much theoretical geomorphological research has revolved around the idea of landscapes as advective/diffusive systems, and the ways in which the Peclet number of such a system is a key control on its morphology. While topographic data is ample, topographic data that can be labeled with quantitative geomorphic parameters is not, so investigating theoretical models with a neural network both helps us learn how we can interpret neural networks within the context of earth science, and helps us learn more about a widely used theoretical tool. A simple convolutional neural network was trained to extract the Peclet number from the final topography of an advective/diffusive model with a normalized root mean squared error of 0.021.

While this performance shows the ability of neural networks to understand and invert simple theoretical models, “unpacking the black box” and making the model scrutable reveals that it appears to have “learned” some fundamental concepts that match the understanding of geomorphologists. The network demonstrates some understanding of the role of valley spacing as a control of the Peclet number. It demonstrates some understanding of drainage density as being closely tied to the Peclet number. It also demonstrates a preference for topographic derivatives tied to the landscape evolution model chosen, like slope and curvature. While a network trained only on numerical models is not in and of itself useful, this work demonstrates the ways in which neural networks can be successfully probed within the context of geomorphic theory.

2026 CSDMS meeting-030

Can Neural Networks Think like Geomorphologists?