Combining simulation and learning: Digital twins

While the idea of a digital twin (DT) originated in manufacturing, in recent years, the concept has become of great interest for many domains in science [8,9]. Simply put, a digital twin is an ideal concept—a digital representation of a real-world object that closely mirrors its physical counterpart. This digital representation takes the form of a computer-based simulation model, while the real-world object can encompass systems or processes, such as an engine, or an economic process. Notably, a crucial attribute of a DT is its ability to continuously adapt and learn over time [10].

This characteristic closely resembles the adaptive behavior observed in certain complex systems, referred to as complex adaptive systems (CAS), which dynamically respond to environmental changes [11]. These systems have been explored in fields like biology, epidemiology, and economics, where they serve as models for understanding dynamic interactions. However, the concept of a DT distinguishes itself from conventional CAS in several ways. First, a DT should be recognized as a purposefully engineered construct, as opposed to a naturally occurring entity. It provides a certain level of interpretability and replicates key aspects of the underlying system. This makes a digital twin a pragmatic prediction instrument which will be judged based on the quality of its predictions forming the output of the model.

Another significant differentiation lies in the fact that a DT not only generates “simple” predictions but also facilitates the exploration of “What-If” scenarios. This means it enables the examination of virtual interventions. Examples for such interventions are the following:

• Economics: Policy alterations and their effect on the economy
• Epidemiology: Alternative vaccination strategies and their effect on an epidemic spread.

Fig 1 shows a visualization of both concepts behind a digital twin: simulation (Fig 1A) and learning (Fig 1B). The DT possesses a defined structure, e.g., given by a complex network, and exhibits activity patterns providing a dynamic simulation that mirrors a corresponding “physical twin” (PT). By introducing interventions, e.g., to the structural network, it becomes possible to explore consequences of “What-If” scenarios, leading to modified predictions. Employing analytical techniques from machine learning or statistics enables then a comparative analysis of these predictions, ultimately facilitating informed decision-making. The learning aspect of a DT is emphasized in Fig 1B. In contrast to traditional simulations, a DT undergoes a series of updates allowing to adjust its parameters by taking into consideration new data.

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Fig 1. An overview of a DT and the interplay between simulation and learning.

(A) The DT can make predictions and enables interventions. (B) The DT learns over time by calibrating its parameters on new data.

https://doi.org/10.1371/journal.pcsy.0000002.g001

Beyond digital twins: Complexity data science

In our opinion, the fusion of simulation and learning, as intrinsic to DT, holds immense promise that extends beyond the realm of digital twins. At its most fundamental level, the amalgamation of complexity science and data science can aptly be termed as “complexity data science,” signifying the emergence of a distinct and innovative field in its own right.

An example of the advantage derived from this integration is the problem of explainable AI [12,13]. As complexity science deals with the study of complex systems, allowing for the simulation of crucial real-world phenomena, such systems not only excel at capturing essential functional elements, but also provide interpretable models. However, achieving accurate predictions with such models requires calibration, akin to the iterative update process observed in digital twins. That means by leveraging interpretable models derived from complexity science, we can move away from opaque black-box models commonly found in data science, such as deep learning networks, towards more explainable solutions.

Another example for the benefit of complexity data science is that it allows for data-driven complex systems. Traditionally, a complex system is either a good or a bad model for a certain phenomenon from the start without the possibility of adjustments. Now we have the possibility to not only adjust parameters of the model but also its structure itself. This enables an increased flexibility to allow for the eventual convergence of the model toward the desired solution.