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Many of the complex patterns seen in nature arise when symmetry breaks. As a system shifts from a highly symmetrical state into a more ordered one, small but stable irregularities can appear. These features, known as topological defects, show up across vastly different scales, from the structure of the universe to common materials. Because they emerge wherever order forms, they offer scientists a powerful way to understand how complex systems organize themselves.
Nematic liquid crystals provide an especially useful environment for studying these defects. In this type of material, molecules can spin freely while still pointing in roughly the same direction. This combination makes liquid crystals easy to control and observe, allowing researchers to track how defects appear, shift, and reorganize over time. Traditionally, scientists describe these structures using the Landau-de Gennes theory, a mathematical framework that explains how molecular order collapses inside defect cores, where orientation no longer has a clear definition.
AI Steps In to Speed Up Defect Prediction
Researchers led by Professor Jun-Hee Na from Chungnam National University, Republic of Korea, have now introduced a faster way to predict stable defect patterns using deep learning. Their work replaces slow and computationally expensive numerical simulations with an AI-based approach that delivers results far more quickly.
The method, published in the journal Small, can generate predictions in milliseconds rather than the hours typically required by conventional simulations.
"Our approach complements slow simulations with rapid, reliable predictions, facilitating the systematic exploration of defect-rich regimes," says Prof. Na.
Inside the Deep Learning Model
The team built their system using a 3D U-Net architecture, a type of convolutional neural network commonly used in scientific and medical image analysis. This design allows the model to recognize both large-scale alignment and fine local details associated with defects. Instead of running step-by-step simulations, the framework directly connects boundary conditions to the final equilibrium state. Boundary information is supplied to the network, which then predicts the full molecular alignment field, including the shapes and positions of defects.
To train the model, the researchers used data from traditional simulations that covered many different alignment scenarios. After training, the network was able to accurately predict entirely new configurations it had never encountered before. These predictions closely matched results from both simulations and laboratory experiments.
Handling Complex and Merging Defects
Rather than relying on explicit physical equations, the model learns material behavior directly from data. This gives it the flexibility to handle especially complicated cases, including higher-order topological defects where defects can merge, split apart, or rearrange themselves. Experiments confirmed that the AI correctly captured these behaviors, showing that it performs reliably under a wide range of conditions.
Faster Paths to Advanced Materials
Because the approach allows scientists to explore many design possibilities quickly, it also creates new opportunities for designing materials with carefully controlled defect structures. These capabilities are especially valuable for advanced optical devices and metamaterials.
"By drastically shortening the material development process, AI-driven design could accelerate the creation of smart materials for applications ranging from holographic and VR or AR displays to adaptive optical systems and smart windows that respond to their environment," says Prof. Na.
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