Unleashing the power of water: Researchers build analog computer to forecast chaotic futures

In their benchmark tests, this analog computer proved proficient at remembering input data and accurately predicting future events. It even outperformed a high-performance digital computer in some cases. But how does it all work?

Imagine two people at the edge of a river. One of them simply throws rocks into the water. Let's call him Bob. Meanwhile, the other party is watching carefully, observing the pattern. Before long, the person gains insight into which stone Bob will throw next.

Reservoir computers mimic the reasoning process that occurs in the thrower's brain. They can learn from past inputs to forecast future events. Although reservoir computers were initially proposed using neural networks, which are computer programs inspired by the structure of neurons in the brain, they can also be constructed using simple physical systems. These analog computers represent data continuously, unlike digital computers that represent data with abrupt binary "zero" and "one" states.

How analog computers will predict chaotic futures

The continuous representation of data enables analog computers to model certain natural events, specifically those occurring in a chaotic time series, more effectively than digital computers. To understand how this works, imagine having a record of daily rainfall for the past year and a bucket of water nearby. In this scenario, the bucket becomes our "computational reservoir."

We simulate the daily rainfall by tossing stones into the bucket. A small stone represents a day of light rain, while a large stone stands for heavy rain. When there's no rain, we simply don't throw any stones. Each stone creates water waves interacting with one another as they slash around the bucket.

At the end of this process, the state of the water in the bucket provides us with a prediction. If the wave interactions generate large new waves, we can anticipate heavy rainfall. On the other hand, if the interactions result in small waves or cancel each other out, we should expect only light rain or no rain at all.

The reservoir computer makes weather forecasts by leveraging the evolution of waves in the bucket, which adheres to the same laws of physics governing rainfall patterns and various other natural and socio-economic processes. Consequently, reservoir computers have the potential to predict financial markets and certain human activities as well.

The researchers employed compact soliton-like waves for their reservoir computer, commonly observed in bathroom sinks or drinking fountains. In their setup, a thin layer of water flows over a slightly inclined metal plate, and a small electric pump modulates the flow speed to generate solitary waves.

In collaboration with Andrey Pototsky, one of the researchers, a mathematical model was developed to understand the physical properties of solitary waves better.

Looking ahead, the researchers plan to miniaturize their computer into a microfluidic processor—a chip that operates similarly to the silicon chips found in smartphones. This microfluidic reservoir computer could provide reliable long-term forecasts for climate change, bushfires, and financial markets. Moreover, it could do so at a significantly lower cost and with broader accessibility compared to current supercomputers.

Study abstract:

Several theoretical works have shown that solitons---waves that self-maintain constant shape and velocity as they propagate---can be used as a physical computational reservoir, a concept where machine learning algorithms designed for digital computers are replaced by analog physical systems that exhibit nonlinear dynamical behaviour. Here we propose and experimentally validate a novel reservoir computing (RC) system that for the first time employs solitary-like (SL) waves propagating on the surface of a liquid film flowing over an inclined surface. We demonstrate the ability of the SL wave RC system (SLRC) to forecast chaotic time series, also producing experimental evidence of the possibility to combine RC with nonlinear vector autoregression techniques not only in a computer program but also in a physical systems.