AI models can find patterns and make predictions, but their reasoning is often inscrutable. This “black box” issue makes AI less reliable and less scientifically useful. However, a team led by Dion Hafner (a computer scientist at the University of Copenhagen) devised a clever neural network to predict rogue waves. By restricting inputs to meaningful wave measurements and tracing how they flowed through the network, the team extracted a simple five-part equation encapsulating the AI’s logic. Economist adds: To generate a human-comprehensible equation, the researchers used a method inspired by natural selection in biology. They told a separate algorithm to come up with a slew of different equations using those five variables, with the aim of matching the neural network’s output as closely as possible. The best equations were mixed and combined, and the process was repeated. The result, eventually, was an equation that was simple and almost as accurate as the neural network. Both predicted rogue waves better than existing models.
The first part of the equation rediscovered a bit of existing theory: it is an approximation of a well-known equation in wave dynamics. Other parts included some terms that the researchers suspected might be involved in rogue-wave formation but are not in standard models. There were some puzzlers, too: the final bit of the equation includes a term that is inversely proportional to how spread out the energy of the waves is. Current human theories include a second variable that the machine did not replicate. One explanation is that the network was not trained on a wide enough selection of examples. Another is that the machine is right, and the second variable is not actually necessary.
