The aim of this article is to explore potential directions for the development of artificial intelligence (AI). It points out that, while current AI can handle the statistical properties of complex systems, it has difficulty effectively processing and fully representing their spatiotemporal complexity patterns. The article also discusses a potential path of AI development in the engineering domain. Based on the existing understanding of the principles of multilevel complexity, this article suggests that consistency among the logical structures of datasets, AI models, model-building software, and hardware will be an important AI development direction and is worthy of careful consideration.
1. Introduction
Discussions on the development and potential applications of AI have sparked a new wave of global interest. Numerous perspectives have emerged, focusing on how to improve AI’s modeling efficiency and enhance its reasoning, predictive, and application capabilities, while minimizing computational resource requirements [
1,
2]. These problem-oriented discussions are undoubtedly important and urgent. However, it may be even more important to consider the sustainable future and long-term development of AI [
3,
4]. We believe that transitioning from “black-box” statistical patterns to a mode grounded in the scientific principles of the engineering domain could be a more profound direction for AI and one that is worthy of attention.
This perspective naturally raises several questions that urgently require exploration:
(1) Is the current logical architecture of AI reasonable, and will it continue to be used?
(2) How should the logical architecture of AI, as applied in the engineering domain, develop in future?
(3) What measures should be taken to explore the direction of future AI development?
This article briefly discusses these three issues; it is our hope that it will prompt more in-depth and extensive discussions.
2. How reasonable and enduring is AI’s current logical architecture?
When studying complex systems, particularly in engineering research, ensuring consistency among the logical structures of the research objects, constructed physical models, software systems, and hardware platforms [
5,
6] is a foundational requirement for ensuring the functionality, reliability, and scalability of application systems. Here, the term logical structure refers to the system’s framework, its fundamental building modules, and the interconnections and collaborative relationships among these modules. Physical models are abstractions and mappings of the research objects based on existing knowledge; they should reflect scientists’ current understanding of the essential logical structures of the research objects. Software systems encode in computers the solution procedures for physical models; their logical structure should naturally be consistent with that of the physical model for clarity and functionality. This consistency ensures that the code is not only easy to maintain but also largely capable of replicating the spatiotemporal evolution of the research object, thereby allowing researchers to gain a deeper understanding of the object’s structural and functional characteristics.
Furthermore, the logical structure of the hardware platform should be consistent with that of the software system to provide clear architectural support for the efficient operation and upgrading of the software system. This is an important foundation for rationally allocating the computing power, optimizing communication and storage loading. A notable example of this requirement is the central processing unit (CPU)–graphics processing unit (GPU) hybrid architecture in high-performance scientific computing [
5,
6].
The AI discussed in this article primarily refers to the current AI based on artificial neural networks (ANNs), particularly deep learning technology. This branch of AI—known as the connectionism paradigm because it uses interconnected networks of artificial neurons—involves basic procedures such as analyzing and processing input data to build datasets, designing AI models, training them for modeling, and deploying the AI models as tools to address complex problems [
7,
8]. In fact, AI itself is a complex system; therefore, in engineering research and applications of AI, it is essential to ensure that the research subject, constructed physical model, software system, and hardware platform all possess the same overarching logical structure.
Putting the hardware platform aside, it is possible to compare the AI research process with that of the aforementioned complex system, as follows: Datasets are the foundation of AI modeling; they originate from the research object and reflect its essential characteristics and structures. They also reflect an in-depth understanding of the object, so they should possess the same connotations as the physical model. An AI model can be viewed as a combination of the physical model and the software used to achieve its objective. Compared with the diverse physical models of various complex systems that have been created based on existing knowledge from different fields, AI models are relatively rough and are insufficient to reflect the principles of complexity. After identifying the modeling objective, the AI model is typically classified into one of several mathematical problem categories (e.g., classification or regression). The design of the AI modeling software used is also closely related to the AI model. Once an AI model is determined, the modeling training methods, which are based on mathematics and statistics, are fundamentally predetermined, and software implementation is correspondingly carried out.
As shown in
Fig. 1, it will become very important in future for the object, physical model, software, and hardware of complex systems to have consistent logical structures that can be mapped onto the whole AI process. This mapping highlights the unique characteristics of AI research compared with complex system studies, while emphasizing their underlying similarities.
Current ANN technology is based on the pioneering work of Hopfield and Hinton, utilizing the principle of energy minimization [
9] and the Boltzmann distribution [
10]. It also relies on the Universal Approximation Theorem [
11,
12], which was proposed and proved in 1989—that is, a feed-forward neural network with a single hidden layer, containing an adequate number of nodes and appropriate nonlinear activation functions, can approximate any continuous function defined on a compact set with arbitrary precision. This theorem theoretically confirms the strong expressive capabilities of neural networks, indicating that they can be regarded as powerful data-fitting tools.
An examination of successful AI applications in fields such as computer vision and natural language processing reveals that the deep networks used in these scenarios contain trillions of parameters at most. However, there is no logical relationship or structural correspondence between these parameters and the object being modeled. This results in both the training process and the model itself becoming “black boxes,” meaning that the training process and model have not been sufficiently linked with the complex system’s spatiotemporal structural evolution patterns. This is one of the main challenges encountered when further developing the engineering applications of AI.
Although this problem seems less pronounced when dealing with tasks such as language processing and image processing, it becomes particularly significant when handling objects characterized by multilevel complexity and by compromise in competition (CIC) among multiple dominant mechanisms that lead to spatiotemporal structure changes [
13]—especially in the engineering domain. This is because existing AI training processes and models overlook the fundamental principles inherent in complex systems. As a result, they fail to reasonably reflect the logical structure of the object being processed, relying instead on repetitive statistical iterative modeling. This approach not only consumes substantial computational resources and time but also makes precise reasoning and prediction difficult; it then becomes difficult to capture the structural features resulting from the multiple dominant mechanisms, and the model becomes prone to overfitting problems.
On the other hand, the complexity of large language models (LLMs) lies in their statistical learning from vast textual data combined with positional encoding and self-attention mechanisms to implicitly model the temporal dependencies in text, such as word order and contextual logic. While this enables an LLM to generate coherent text, it is fundamentally different from feature extraction based on physical principles. Therefore, it is not appropriate to apply LLM modeling methods and trained LLMs directly to engineering practices involving dynamic spatiotemporal systems; at least, doing so is not an optimal choice. This is because the spatiotemporal dynamics of complex structures are physically and closely related and are governed by system stability [
6,
14]; thus, they should not be considered independently. The characteristics of spatiotemporal dynamics and their interaction patterns remain challenging to fully capture solely through the statistical analysis of data.
It can thus be stated that, from the perspectives of both AI model design and AI modeling methodology, the current logical architecture of AI does not adequately reflect the multilevel, multiscale, and spatiotemporal characteristics inherent in the processing objects. As a result, AI models are unable to implicitly extract, process, present, and utilize these physical characteristics in the data in a reasonable, adequate, and effective manner. This is a fundamental issue that must be addressed when applying AI to engineering systems.
In other words, AI models currently tend to mine the statistical properties of complex systems and do so proficiently, while under-emphasizing the spatiotemporal complexity patterns of the systems. In fact, a clear understanding of the formation mechanisms of the system’s statistical properties, its spatiotemporal complexity patterns, and their interactions, along with the effective application of this knowledge, can reasonably reduce the dimensionality of the system, significantly lower the complexity of system modeling, and enhance the interpretability of the modeling process and the model created. This is crucial for efficiently constructing and applying AI models based on complexity principles [
6,
15].
In addition, during the process of AI modeling, if fundamental factors such as the inherent stability constraints of complex systems are not applied during iterations [
14], the resulting model will be unable to reflect the relationships between structural parameters. Furthermore, solely relying on extensive computational resources and trial-and-error costs to approximate a system’s complex structure may result in a model that only satisfies mathematical optimization conditions. Applying such models to actual engineering systems often yields unsatisfactory results.
It can be seen that the introduction of physical principles—even at a preliminary stage—will play a significant role in improving the functionality of AI systems. Although current AI technologies have achieved remarkable accomplishments in many fields, and numerous successful cases have been accumulated, their ability to handle complex systems in engineering remains inadequate, particularly when data is limited. This is because, in a complex system, different regimes follow entirely distinct physical stability conditions. In AI modeling approaches, it is inevitably insufficient to use a unified loss function to express this diversity of stability conditions. These conditions must be reflected in both the AI modeling process and the resulting AI models.
In conclusion, it can be assumed that the current logical architecture of AI lacks a physical connection with the complexity principles of its processing objects. This is a fundamental issue worthy of being given high priority. The need for in-depth research on the logical architecture of AI should not be ignored merely because AI currently demonstrates outstanding performance in certain domains. AI should gradually incorporate a greater understanding of complexity principles in order to support and drive its development. In other words, the logical architecture of AI should evolve as our understanding of complexity principles deepens.
3. How should the logical architecture of AI, as applied in the engineering domain, develop in future?
The initial purpose of developing AI was to enhance human understanding and knowledge of the complex world. AI training models should rely on reliable data that reflect physical laws, obtained through in-depth research on natural systems, social phenomena, earth ecosystems, and production processes. However, most datasets used for AI training exhibit spatiotemporal averaging characteristics, which limit the potential predictive performance of the resulting AI models. Therefore, fully focusing on the physical logical structure of scientific data systems [
16] should be the primary task of AI development.
Furthermore, the physical logical structure behind the data must necessarily originate from its corresponding research objects. Therefore, exploring this logical structure from a physical perspective will enhance the application effects of AI much more directly. As determined through the recent development of mesoscience [
6], complex systems often exhibit multilevel characteristics, with each level featuring multiscale structures (i.e., the element scale, mesoscale, and system scale). Complex spatiotemporal structures typically emerge in the mesoregime of the mesoscale on each level (determined by operational conditions, as described below). Despite the diversity, different levels follow this common rule and are interrelated, showing that this rule has a certain degree of universality [
13].
More specifically, each level is jointly dominated by at least two dominant mechanisms (e.g.,
and
). As the relative dominance capabilities of
A and
B change, the mesoscale structure of the system exhibits two relatively simple structures: one dominated by
A and another by
B, named Regime-
A and Regime-
B, respectively. When
A and
B cannot fully suppress the other’s dominance, a CIC between them must be established for their coexistence, leading to the emergence of complex structural patterns (the
A/
B mesoregime, named Regime-
A/
B) and critical phenomena as regime transitions. The most notable feature of this phenomenon is the coexistence and mutual dependence of ordered and disordered behaviors. This means that there are three regimes and two critical points should be formulated. The CIC principle can be mathematically expressed as a multi-objective optimization problem [
6]. Although this logical framework requires further validation and application in more systems [
6], it can be considered as a preliminary scheme for expressing physical logic. Guo et al. [
14] have demonstrated that guiding AI modeling with the CIC principle is a promising new approach.
Although the future direction of AI is unpredictable, the logical architecture of AI should better align with that of multilevel complexity. At present, two critical hyperparameters of deep neural network models—namely, the number of hidden layers and the number of nodes per layer—are determined by factors such as problem complexity, requiring multiple modeling validations for optimization. As a result, the design of a model’s network structure is currently independent of the physical principles governing the problem it is intended to solve. Additionally, model training is now essentially an optimization process that is similarly independent of the system’s physical context. The internal complexity, commonality, and diversity of different physical levels are often overlooked during training, and interactions between levels are not adequately addressed. To put it differently, relevant complexity principles are not utilized in AI model training.
Undoubtedly, it is a major challenge to use AI technology to discover the evolutionary patterns of internal structures in complex systems. The evolution of a system’s structures is governed by physical principles, particularly the principle of stability. Numerous research tools have shown that incorporating physical principles and structural information is feasible and effective when dealing with complex systems. For instance, in computational fluid dynamics, shifting the computational grids of the Navier–Stokes (NS) equation from volume-averaged to structure-based by considering the principle of grid stability significantly increases computational accuracy, with the establishment of system stability conditions as the key. Similarly, when employing AI technology to model complex systems, introducing key physical constraints of the system can improve the model’s predictive capability regarding dynamic behaviors. This approach of integrating physical principles with AI technology not only increases the interpretability of models but also ensures accurate predictions, even when encountering new scenarios. In this way, overfitting during the training of AI models can be effectively prevented, and the models’ generalization capability can be improved.
Therefore, the CIC principle for multilevel complexity should be gradually integrated into the design, training, optimization, and application processes of AI systems. Detailed discussions can be found in Refs. [
14,
15]. Along this development path, three key issues must be further addressed: What is the relationship between the fundamental principles underlying AI, human intelligence, and complex systems? Are these principles identical? How can existing complexity principles be effectively integrated into current AI systems? These issues call for extensive interdisciplinary cooperation, since incorporating the physical principles of objects into the logical architecture of AI is a challenge that no single discipline can address on its own. AI experts, domain experts, mathematicians, and engineers must be involved.
4. What actions should be taken to further explore the direction of AI development?
First, the principles of multilevel complexity mentioned above should be given full consideration, and their logical architecture should be deeply investigated to confirm their necessity and reasonableness while further concretizing them. In this process, a consensus among science communities could be gradually reached and improved upon. Based on this foundation, an analysis of the current logical architecture of AI should be conducted to identify which aspects can be improved and which can be further developed. Critically, it is essential to explore how these improvements can be integrated with the aforementioned consistent logical structure to promptly form a complete, science-based AI development framework.
Preliminary attempts have already been made in this regard. Guo et al. [
14] has proposed a mesoscience-guided deep learning (MGDL) modeling method, which integrates multilevel complexity principles into the processes of dataset construction and model training. Applying the CIC principle of mesoscience, the meso-scientific constraints of
are integrated into the loss function. MGDL was validated using a typical complex system in chemical engineering: the bubbling fluidized bed. The results indicated that—when the size of the training dataset is relatively small—MGDL exhibits significant advantages in convergence stability and prediction performance compared with traditional modeling methods.
Then, guided by the principles and logical architecture of complexity, several typical cases from the engineering domain could be systematically chosen, utilizing their high-quality data resources that meet the conditions outlined in Ref. [
16]. A problem-driven approach could be adopted to construct datasets and AI models based on the new logical structure. At the same time, the possibility of differences among domains should be considered. Based on this, long-term development trends could be identified and research plans could be proposed, while coordinating short-term, medium-term, and long-term research and development (R&D) plans.
Subsequently, with a unified logical architecture as the foundation, objects, AI models, model-building software, and hardware with consistent logical structures could be clearly defined to explore a path of fundamental development for low-cost, high-efficiency, interpretable, and practical AI, as well as high-performance computing technologies.
Through these explorations, there is potential for the development of a brand new AI system, R&D model, and corresponding computational paradigms; based on these, an engineering intelligentization paradigm framework that integrates the principles of multilevel complexity science could be established, as outlined in
Fig. 2. This framework is expected to exhibit the following characteristics:
• A multilevel structure. Initially, it is necessary to determine the data source’s level in order to decide whether the complex system is single-level or multilevel; this is followed by task assignment to the corresponding level for processing. For instance, chemical engineering typically involves three levels: the chemical reaction, the process occurring in the reactors, and the process system engineering.
• A multiscale structure at each level. Complex structures emerge at the mesoscale between the element and system scales. Through physical analysis and/or possible AI-based reasoning, two dominant mechanisms, A and B, are identified for each level. With three regimes—Regime-A, Regime-A/B, and Regime-B—being distinguished for each level, their regime-specific stability condition constraints are defined as follows: , , and . This means that the structures in Regime-A and Regime-B are simple, governed by a single extremum condition, whereas Regime-A/B (the mesoregime) is significantly more complex, featuring the coexistence of ordered and disordered behavior. Thus, it must be jointly governed by two extremum conditions, that is, and must CIC within the mesoregime.
•
Three-regime AI model building. Within Regime-
A or Regime-
B, general mathematical and statistical methods can be used, under their corresponding stability condition constraints. In the complex Regime-
A/
B mesoregime, the construction of AI models must be conducted under the dominance of the stability condition constraint
, as shown in Ref. [
14]. Of course, formulating two critical points between three regimes is a challenge to be resolved [
6].
•
AI in Regime-A/B mesoregime modeling. Solving the mesoregime is a major challenge, even for the entire complexity science community. One solution option would be possible under the assumption that mechanisms
A and
B are equally important. In this way, the stability condition constraint for the Regime-
A/
B mesoregime can be transformed into a single object problem
[
17], which will serve as the primary constraint during AI model training. The most critical step is to obtain the analytical expressions of the dominant mechanisms,
A and
B. Here, physical analysis and AI-assisted analysis can mutually assist each other.
•
A dataset. Theoretically, all data must meet the requirements of the above operations to be included in the dataset [
16]. In practical application scenarios, due to current limitations in data-acquisition technology, some data may not fully meet the requirements. In such cases, the data should be clearly annotated for subsequent continuous improvement and refinement.
•A software/hardware system. Based on the aforementioned logical architecture, the software system and hardware platform required for AI are constructed. This involves even more complicated problems in computational science that are beyond our capability to discuss.
In conclusion, the path to engineering intelligentization based on complexity principles lies in ensuring consistent logical structures among the dataset, AI model, model-building software, and hardware platform of an AI system. As this is a scientific choice for developing AI based on the common principles of complexity, the development of AI and the study of complexity principles should promote and complement each other. In this process, it is essential to break free from habitual thinking in order to promote transdisciplinary science and extensive multi-domain cooperation. This is both a challenge presented by AI and a difficult problem that requires collaboration among all disciplines and engineering fields.
As AI continues to evolve, incorporating new advancements from complexity principle research will become an important direction for its further development. In particular, there is great potential and feasibility for AI in understanding and handling the logical architecture of systems that coexist within ordered and disordered behaviors in spatiotemporally dynamic structures. The understanding of multilevel complexity based on mesoscience described herein can serve as a starting point for conducting critical transdisciplinary research that integrates mesoscience with AI.
Finally, it should be noted that this article is based on the authors’ personal and—due to the underdeveloped state of this particular area—limited knowledge accumulated through engineering practice. If readers find flaws or gaps in our arguments, we would be very happy to receive any comments and suggestions.
Acknowledgments
We would like to express our sincere gratitude to Chao Dong, Jianhua Chen, Wei Wang, and Wei Ge for their valuable comments on this article and to Jian Wang for her assistance in preparing the manuscript. We are also very grateful for the supports of Chinese Academy of Sciences and Gates Foundation.
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