At the Eastern Institute of Technology in Ningbo, China, a new kind of AI is doing something remarkable: it writes down the very equations that describe how materials bend, stretch, and break — all by itself, straight from experiment data. The system, called GraphED, could change the way scientists understand everything from the steel in skyscrapers to the metal inside your phone's battery.
For centuries, the field of solid mechanics has worked the same way. Scientists study how a material behaves and then, guided by intuition, guess a mathematical formula to describe it. Then they tweak the numbers until the guess matches what they actually measure. It works, but it has a built-in limit. "Predetermined equation structures inherently restrict the model's descriptive and predictive capability," said Hao Xu, the study's lead author and a postdoctoral researcher at EIT. In plain words: if you start with a fixed equation shape, you can never capture behaviors that don't fit that shape.
The Ningbo team flipped the whole process. Their AI starts with no formula at all. It looks only at raw experiment data and searches on its own for the best mathematical description. "Our framework shifts the research paradigm: it starts purely from experimental data and employs artificial intelligence to autonomously search for and identify optimal constitutive equations," Xu explained.
The clever trick is how the AI represents math. Most computer models write equations as tree structures, like a family tree of symbols. GraphED instead encodes equations as directed graphs — think of a network diagram where nodes are operators and variables, and the arrows between them show how they connect. This lets the AI optimize both the shape of the equation and the material-specific numbers inside it at the same time, a bottleneck that previous methods couldn't crack. "By representing mathematical equations as graph structures, we enable simultaneous optimization of equation topology and material parameterization," said co-corresponding author Yuntian Chen.
The results, published in Science Advances, span three very different materials. For alloy steels, GraphED discovered explicit equations that beat the widely used Johnson–Cook model in prediction accuracy. For lithium metal — the material powering our batteries, whose behavior is notoriously sensitive to temperature and strain rate — the AI produced concise flow equations that match experiments better than traditional models. And for filled rubbers, it captured a compact equation that stays accurate across different compositions and temperatures.
"Weaknesses in existing empirical models," said corresponding author Dongxiao Zhang, "can be addressed by equation discovery via graph-based AI, providing a powerful new paradigm to assist researchers when traditional model forms fall short."
The beauty is that these equations aren't black boxes. They're human-readable, physically meaningful math that scientists can inspect, trust, and build on. Beyond mechanics, the approach could help any field seeking to discover the hidden laws of nature directly from data — one graph at a time.