From Data-Driven to Physically Constrained Modeling: Artificial Intelligence Based on the Principle of Compromise in Competition

Li Guo; Jinghai Li

doi:10.1016/j.eng.2026.07.029

Engineering ›› :202607029 DOI: 10.1016/j.eng.2026.07.029

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From Data-Driven to Physically Constrained Modeling: Artificial Intelligence Based on the Principle of Compromise in Competition

Li Guo ^a^,^b
, Jinghai Li ^a^,^*

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Abstract

Mainstream data-driven artificial intelligence (AI) is currently encountering significant challenges in handling the spatiotemporal dynamics and critical transitions of complex systems, especially when the governing equations are unknown or difficult to formulate analytically. In 2019, we proposed the concept of and suggested a preliminary framework for the integration of complex systems principles into AI [1]. In this paper, we explore one such implementation pathway: introducing the principle of compromise in competition (CIC) between maximum dissipation and minimum dissipation [2] as a physical constraint to enhance the stability and interpretability of AI models in specific complex-system problems. It should be noted that, in recent years, methods such as physics-informed neural networks (PINNs) and diffusion models have incorporated physical or statistical mechanics principles to varying degrees [3–9]; however, they remain inadequate in addressing the specific class of complexity characterized by multi-mechanism dominance and mesoregime stability. This paper focuses on filling this gap and proposes a framework approach based on the principle of CIC. The key to implementing this framework lies in quantifying energy dissipation rates across different systems and identifying their extremal characteristics. Building on our previous exploratory studies [10,11], this paper further explores more specific pathways for advancement.

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Li Guo, Jinghai Li. From Data-Driven to Physically Constrained Modeling: Artificial Intelligence Based on the Principle of Compromise in Competition. Engineering 202607029 DOI:10.1016/j.eng.2026.07.029

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