Predicting weather is not easy. The weather's governing equations don't change from day to day Complex systems can suddenly change their behavior with little warning and potentially catastrophic consequences.
Most real world systems are like this. The Gulf Stream in the North Atlantic is part of an ocean conveyor belt that helps regulate the climate. The equations that describe these circulating currents are slowly changing due to the influx of fresh water. The circulation has slowed, but it may stop suddenly in the not too distant future.
There is a physicist at Arizona State University. Do you know if it will be ok in the future?
Researchers have shown that machine learning can predict tipping-point transitions in nonstationary systems, as well as features of their behavior after they have tipped. One day the new techniques could be used in many fields.
Four years ago, a group of Edward Ott, a leading chaos researcher at the University of Maryland, released results of their research. A recurrent neural network can be used to predict the evolution of stationary chaotic systems, which don't have tipping points. The network had no information about the underlying equations.
Deep neural networks feed data through a stack of artificial neurons for tasks like speech recognition and natural language processing. Neural networks are able to learn by adjusting the strength of their connections. Ott and his team used a less expensive method of training to adjust only a few connections. The task of predicting chaotic evolution is suited to the simplicity of the software.
It was thought that machine learning wouldn't be able to predict tipping-point transitions in nonstationary systems. Ott said that what is happening in the future is evolving by different rules. Trying to predict the outcome of a baseball game is like trying to predict the outcome of a cricket game.
In the last two years, Ott's group and several others have shown that reservoir computing works well for these systems too.
In a paper published in 2021, Lai and his team gave their computer program access to the slowly drifting value of a parameter that would eventually send a model system over a tipping point, but they didn't give any information about the system's governing equations. We know that the carbon dioxide concentration in the atmosphere is rising, but we don't know how this will affect the climate. The team was able to predict the value at which the system would eventually become unstable by using past data. Last year, Ott's group published results.
The paper was posted online in July and is currently undergoing peer review. They fed their neural network data recorded in a simulation to the network without knowing it. In many cases the algorithm could predict the tipping point and give a probability distribution of possible post- tipping behaviors.
The network performed better when trained on noisy data. Predicting is usually hampered by noise in real world systems. It helped by exposing the system to a wider range of possible behaviors. The neural network will be able to recognize noise and the system's average behavior thanks to the tweaking of the Reservoir computing procedure. Michael Graham is a fluid dynamicist at the University of Wisconsin Madison.
A class of tipping points is marked by an especially stark change in behavior.
If the state of a system is plotted as a point moving around in an abstract space of all its possible states, what would happen? Chaos in evolution would look like a mess, while systems that go through regular cycles would trace out a repeating path. A tipping point could cause an initial chaotic motion to spill out into a larger region, or it could cause an initial spiral out of control. Neural networks can find hints of the system's fate in its past exploration of relevant regions.
transitions in which a system is suddenly expelled from one region and its evolution takes place in a distant region are more difficult. You are wandering into territory you have never seen as the dynamics change. Such transitions are typicallyhysteretic, meaning they are not easy to reverse. Killing too many top predator can cause the prey population to explode, if you add a predator back again.
When trained on data from a system showing a hysteretic transition, it was possible to predict an imminent tipping point, but it got the timing wrong and failed to predict the system's behavior. The hybrid approach was tried by the researchers. The hybrid algorithm was able to predict statistical properties of future behavior even when the knowledge based model failed.
A machine learning researcher at the Nordic Institute for Theoretical Physics in Sweden hopes the recent work will serve as a catalyst for further studies, including comparisons between the performance of reservoir computing and that of deep learning. It would bode well for the possibility of studying tipping points in large, complex systems if reservoir computing can hold its own against more resource intensive methods.
There is a lot to be done in this field. It is open.
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