Across the physical world, many intricate structures form via symmetry breaking. When a system with inherent symmetry transitions into an ordered state, it can form stable imperfections known as topological defects. Such defects are found everywhere, from the large-scale structure of the universe to everyday materials, making them a powerful way to study how order emerges in complex systems.
We have a tool to study these defects: nematic liquid crystals. In these materials, molecules can rotate freely while remaining roughly aligned, providing a clear and controllable platform for observing how defects form, move, and reorganize. These defect structures are usually described using the Landau–de Gennes theory, which mathematically captures how molecular order breaks down in defect cores where orientation becomes undefined.
Now, researchers led by Professor Jun-Hee Na from Chungnam National University, Republic of Korea, have developed a faster way to predict stable defect configurations using deep learning.
Their method, published in the journal Small on November 25, 2025 , replaces time-consuming conventional numerical simulations, generating results in milliseconds rather than hours.
"Our approach complements slow simulations with rapid, reliable predictions, facilitating the systematic exploration of defect-rich regimes," says Prof. Na.
The model employs a 3D U-Net architecture, a convolutional neural network widely used in scientific and medical image analysis, to capture both global orientational order and local defect structures. The framework works by directly linking prescribed boundary conditions to the final equilibrium structure. Boundary information is fed into the neural network, which then predicts the complete molecular alignment field, including defect locations and shapes. The model was trained on data generated using conventional simulations covering a wide range of alignment patterns. Once trained, it can accurately predict new configurations it has never seen, with results that agree closely with both simulations and experiments.
The model learns the underlying physical behavior directly from data rather than relying on explicit equations. This allows it to handle highly complex situations, such as higher-order topological defects, where defects can merge, split, or rearrange. Experimental tests confirmed that the network correctly reproduced these behaviors, demonstrating its robustness across a wide variety of conditions.
By allowing researchers to rapidly explore large design spaces, this approach also opens new possibilities for rapidly designing materials with specific defect architectures for sophisticated 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.
