A complex system, such as the infrastructure of a power grid or the Earth’s global climate, can appear stable even as it approaches a sudden, potentially irreversible tipping point. Modeling the behavior of a complex system is inherently challenging because of the many dependencies, competing forces, relationships and other interactions among its components and with its environment.
A new book by Arizona State University Regents Professor Ying-Cheng Lai explores how reservoir computing can help researchers detect those hidden risks using historical data, even when the equations governing a system are unknown.
Lai, an electrical engineering faculty member in the School of Electrical, Computer and Energy Engineering, part of the Ira A. Fulton Schools of Engineering at ASU, is a renowned expert in nonlinear dynamics and complex systems and presents reservoir computing as a bridge between machine learning and physics. By learning how a system’s behavior changes over time, the approach can support adaptable digital twins that simulate unseen conditions and help researchers and engineers anticipate problems ranging from ecological collapse to failures in engineered systems.
In this Q&A, Lai covers the difference between chaos and randomness, ideas that inspired the book and the promise and limitations of reservoir computing. He also discusses his group’s work on ecological digital twins, transformer models and quantum reservoir computing, as well as his interest in forecasting major climate tipping points.
Question: Much of your career has focused on nonlinear and complex dynamical systems. For someone outside your field, what makes a system chaotic, and how is chaos different from randomness? Can you provide a familiar example?
Answer: In simple terms, a chaotic system is one that follows exact, deterministic rules, meaning it is not purely random, but is incredibly sensitive to its starting conditions. Randomness implies a lack of underlying rules or predictability from step to step. Chaos, by contrast, is fully deterministic, but because even tiny variations in the initial state grow exponentially over time, long-term prediction becomes practically impossible.
A classic and familiar example is the weather. In 1963, meteorologist Edward Lorenz demonstrated this using a simplified model of atmospheric convection, giving birth to the famous butterfly effect metaphor: the idea that a tiny perturbation, like a butterfly flapping its wings, can trigger large and unpredictable consequences in a complex system such as the Earth’s weather.
I have a very personal example of this “sensitive dependence on initial conditions.” Back in the spring of 1989, I was a second-year PhD student at the University of Maryland looking to change my research focus. My top choice was theoretical condensed matter physics, so I scheduled an appointment with a prominent professor in that field. I waited for an hour, but he never showed up. Disappointed but undeterred, I turned to the nonlinear dynamics group, where I was warmly welcomed by a professor who became my lifelong mentor and collaborator.
If that first professor had shown up for our meeting, I would most likely have become a condensed matter theorist. That one small deviation 37 years ago completely altered my professional trajectory. It is a good example of how small deviations lead to drastically different outcomes, showing that life itself is full of chaos.
Question: How is reservoir computing related? What does it allow researchers to do, and how is it different from the forms of artificial intelligence or machine learning we hear about today?
Answer: Reservoir computing enters the picture when we want to predict the invisible, specifically, sudden, catastrophic changes or tipping points in complex systems. It lets researchers look at data from a system that currently appears perfectly stable and predict a total collapse or crisis before it happens, without knowing the exact mathematical equations driving the system.
It differs from the standard artificial intelligence most people hear about because of its adaptability. Standard AI is typically trained to recognize patterns in data it has already seen. Reservoir computing, however, acts as a bridge between machine learning and the physics of dynamical systems. It doesn’t just memorize a system’s current conditions; it learns how that climate changes. This allows us to build digital twins, or computational surrogates that can accurately mirror and anticipate how a system will behave under entirely new, unseen conditions in the future.
Question: Your new book brings reservoir computing and nonlinear dynamics together. What prompted you to write it, and how does it reflect the evolution of your research?
Answer: The motivation for this book arose from a persistent question that has driven my research for many years: how can we predict the invisible? We wanted to know if we could anticipate catastrophic tipping points, like a sudden ecological collapse, purely from historical data that shows no visible signs of distress, and without knowing the underlying equations. Traditional tools were insufficient because they either required mathematical conditions that nature rarely grants or provided warnings that arrived too late.
As our research evolved, we realized reservoir computing was more than just a specific predictive tool. It proved to be a fundamental bridge between the theory of dynamical systems and the adaptable power of modern machine learning. We began applying these methods to everything from predicting chaos to building digital twins that can anticipate unseen future conditions. I wrote this book because we needed a unified text to aggregate these expanding, disparate frontiers into a single, coherent narrative.
Question: Digital twins are gaining attention across engineering, including for manufacturing processes. How can reservoir computing help create a digital twin of a complex, changing system, and how could that help scientists or engineers anticipate problems or make better decisions?
Answer: A digital twin is a virtual model of a real-world system, such as an ecosystem or a manufacturing process. Traditional models often only capture a system’s behavior under current, stable conditions. Reservoir computing takes this a step further by creating an adaptable digital twin.
It doesn’t just learn how the system operates right now. It learns how the system’s underlying dynamics shift as parameters gradually change over time. For scientists and engineers, this means they can use the digital twin to simulate future, unseen conditions. Instead of waiting for a complex system to fail, whether that is an ecosystem facing climate change or a manufacturing process breaking down, they can use the twin to foresee tipping points and catastrophic collapses that are hidden in the data. This allows them to make proactive decisions and adjust the system to prevent a crisis before it ever occurs.
Question: What are you and your research group working on now? Walk us through one or two active projects, including the problem you are trying to solve and what meaningful progress would look like.
Answer: Right now, my research group is focusing on three main areas.
First, we are working on developing digital twins for ecological systems. As I mentioned earlier, ecosystems are subject to slowly changing parameters, such as shifting carrying capacities due to climate change. These gradual shifts can lead to sudden, irreversible tipping points, like species extinction, even when the environment currently appears perfectly healthy. Meaningful progress would be successfully using our digital twins to monitor real-world ecological data and reliably forecast these collapses early enough to allow for intervention.
Second, we are exploring how to exploit transformers, the same underlying machine learning architecture that powers advanced AI language models, to predict complex dynamical systems. While reservoir computing is incredibly powerful, we are investigating how these other AI tools offer distinct advantages, giving scientists an even broader toolkit to anticipate the unexpected.
Finally, we are working on quantum reservoir computing for magnetic navigation in GPS-denied environments. When standard GPS is unavailable, we must rely on detecting weak physical signals, such as Earth’s magnetic anomalies, often in environments with extreme noise. Meaningful progress in this project would be demonstrating that our quantum reservoir framework can successfully process these weak signals and provide accurate, reliable navigation where traditional systems fail.
Question: How could this research help scientists or engineers monitor or respond to changes in a complex system? Can you give us an example?
Answer: Let’s look at an ecosystem facing the gradual effects of climate change. Right now, scientists might monitor a specific habitat and see that a local species’ population is perfectly stable. The environment looks completely healthy to the naked eye, and standard statistical models show no signs of distress. However, underlying factors, such as the environment’s carrying capacity or temperature, are slowly shifting.
Using our reservoir computing framework, researchers could create a digital twin of this ecosystem. By feeding it the available historical data, the digital twin learns the hidden dynamics of how the system changes over time. It could detect that, despite the current stability, the ecosystem is hurtling toward a hidden tipping point. The digital twin could warn scientists that, under the current trajectory, the species will undergo a sudden, irreversible collapse in the near future.
By making this invisible threat visible, our framework gives conservationists the crucial lead time they need to respond, allowing them to intervene, protect the habitat or adjust policies long before the catastrophe actually strikes.
Question: What prevents reservoir computing from being used more widely outside of a research setting? And how do limited, incomplete or noisy data affect what these systems can reliably predict?
Answer: One of the biggest hurdles to moving reservoir computing out of the lab and into the real world is the quality of the data. In controlled research settings, we often work with pristine, continuous data. In the real world, data is messy; it is often limited, incomplete or corrupted by noise. Traditionally, this is a major problem. If data is too sparse, a machine learning model might not capture the true underlying dynamics. If the data is too noisy, the system might learn the noise instead of the actual physical rules, which ruins its ability to make reliable predictions.
However, overcoming these exact challenges is a major focus of my new book and our ongoing research.
Instead of viewing noise purely as an obstacle, we are finding ways to exploit the benefits of noise during the training process to make the machine learning models more robust. To handle situations where data is scarce, we are exploring meta-learning, essentially teaching the system how to learn efficiently from very few examples. We are also developing methods to deal with situations of incomplete data and/or partial state observation, and for processing signals in extreme noise to detect very weak physical phenomena. So, while messy and incomplete data is the primary barrier to widespread real-world adoption, we are actively building the tools to overcome it.
Question: What questions are you most interested in pursuing next, and what developments in this field do you believe could have the greatest impact?
Answer: Looking ahead, the question I am most interested in pursuing is how we can apply these tools to one of the most pressing issues of our time: anticipating the potential collapse of the Atlantic Meridional Overturning Circulation, or AMOC. AMOC is a massive system of ocean currents, and its collapse would be a catastrophic tipping point for the global climate. I want to develop reliable methods, using reservoir computing and modern AI, to foresee this kind of global-scale transition from data before it is too late.
Alongside that, we are exploring how transformer architectures can be used to solve highly challenging prediction and signal-processing problems in large-scale complex dynamical systems.
As for what could have the greatest impact, I believe the vast potential of quantum reservoir computing is a true frontier. We are working hard to develop these quantum systems, and as they mature, they could revolutionize our ability to process extreme noise and detect incredibly weak signals. This will open new capabilities for sensing, navigation and predicting the hidden dynamics of the natural world.
