Researchers at the Eastern Institute of Technology (EIT) in Ningbo have created a novel method to derive precise mathematical equations that describe the mechanical behavior of solid materials, directly from experimental data. Published in Science Advances, the study introduces a framework that identifies constitutive models—equations that define how materials respond to forces—for a variety of substances, including alloy steels, lithium metal, and filled rubbers. This approach outperforms traditional empirical models in accuracy while maintaining clear, interpretable mathematical expressions. This marks a significant step forward in solid mechanics, where such models are essential for predicting material behavior under various conditions. Constitutive models are the backbone of solid mechanics, used to describe how materials deform and respond to stress. Traditionally, these models are built using physical intuition and then fine-tuned with experimental data. However, this method has limitations, as the initial assumptions about the equation structure can restrict the model's ability to accurately describe complex material behaviors. The new framework flips this process: it begins with raw experimental data and uses artificial intelligence to automatically discover the best equations to describe the material’s properties. A major technical challenge in this process is encoding both the structure of the equations and the material-specific parameters in a way that computers can search through efficiently. The researchers solved this by representing mathematical equations as graphs—structures where nodes represent mathematical operators or variables, and edges show how they are connected. This graph-based approach allows the system to explore different equation structures and adjust parameters simultaneously, making the search for optimal models more efficient and flexible. The GraphED framework iteratively generates and evaluates candidate equations, refining them until they produce accurate, compact, and interpretable constitutive laws. The team tested this method on several materials, including alloy steels, lithium metal, and filled rubbers. For alloy steels, the framework uncovered equations that accurately describe how the material behaves under different strain rates and stress levels. When compared to widely used models like the Johnson–Cook model, the new equations provided more precise predictions. For lithium metal, a material crucial for batteries, the model captured the complex behavior influenced by temperature and strain rates, outperforming traditional approaches. In the case of filled rubbers, GraphED identified a simple yet highly accurate equation that works across various compositions and temperatures. This new approach has the potential to revolutionize not only material science but also other fields that rely on deriving physical laws from data. By using graph-based artificial intelligence, researchers can uncover mathematical relationships that were previously difficult to identify, opening the door to more accurate models and a deeper understanding of complex systems.