Self-organizing topological solitons in machine-learned potential models enable large-scale liquid crystal simulations

Knotted structures have long been recognized for their unusual properties and are difficult to maintain stability, making them a major challenge for practical application. Arunkumar Bhupathy from Hiroshima University, along with Darian Hall and Ivan I. Smaluk from the University of Colorado Boulder, demonstrated a route to overcoming this limitation by studying stable knot structures called helinotons in chiral liquid crystals. The team has developed a machine learning potential to accurately model the complex interactions between these structures, enabling the simulation of their self-assembly into adaptive crystalline alignments. This work, which also includes contributions from Gerardo Campos-Villalobos, Rodolfo Subert and Marjolein Dijkstra from Utrecht University, provides a powerful new framework for understanding and potentially exploiting the behavior of complex topological textures, opening the door to new materials and devices.

Helinoton interactions and coarse-grained modeling

Scientists have developed a multiscale modeling approach to study helinotons, topological defects in chiral liquid crystals. This study combines detailed physics-based simulations and machine learning to create a simplified model that accurately represents helinoton interactions, significantly reducing computational demands and allowing investigation of helinoton behavior at previously unattainable scales. The research team began by simulating helinoton interactions using the Frank-Osen free energy functional, a method that accurately captures the energetic costs associated with deforming liquid crystals. The researchers then used machine learning algorithms to develop a coarse-grained potential to simplify and represent the helinoton interaction.

This process involved defining a symmetry function and training a model based on data from detailed simulations, which successfully captured the chiral nature of the system without explicitly using chiral descriptors. This innovative approach allows scientists to treat helinotons as effective particles, allowing them to self-assemble into complex crystal structures. The resulting coarse-grained potential accurately reproduces the results of detailed simulations while significantly reducing computational costs, enabling large-scale simulations and providing a framework for understanding the behavior of helinotons. The research team demonstrated that this model accurately captures the anisotropic interactions between these particles, reproduces experimentally observed aggregates, and provides a basis for studying collective phenomena.

Machine learning model Heliknoton self-assembly interaction

Scientists have created a new methodology to model the interactions and self-assembly of helinotons, a topological texture found within chiral liquid crystals. This approach starts with fine-grained simulations based on Frank Osen’s free energy functional and combines detailed physics-based simulations with machine learning to enable large-scale simulations to accurately understand the energy costs associated with deforming the liquid crystal director region. These simulations generate comprehensive datasets of interaction energies and form the basis of machine learning approaches. The researchers then used machine learning algorithms to develop an effective coarse-grained potential to simplify and represent the interactions between helinotons.

This involved training the model on interaction energies obtained from fine-grained simulations, allowing the model to learn the complex relationships governing solitonic interactions. This innovative approach allows scientists to treat helinotons as quasiparticles and self-assemble them into complex crystal structures. By accurately capturing the anisotropic interactions between these particles, this model reproduces experimentally observed aggregates and provides a framework for studying collective phenomena. The resulting coarse-grained potential spans a wide range of energies, reflecting long-range perturbations of the surrounding helical field, accelerating the design and discovery of knotted metamatter with tunable symmetry.

Self-assembly of helinoton modeled with machine learning

Scientists have achieved a breakthrough in modeling complex topological textures, particularly knotted solitonic structures called helinotons found in chiral liquid crystals. This study provides a powerful new framework for understanding and designing materials with complex topologies by successfully modeling these structures at scale using a machine learning approach that accurately captures complex interactions. The researchers treated each helinoton as a valid particle and developed a coarse-grained potential to simulate its behavior, accurately reproducing the observed self-assembly of helinotons into complex crystalline aggregates. The method uses fine-grained simulations based on the Frank-Oseen free energy functional to calculate the interaction energies between pairs of helinotons and trains a machine learning model to efficiently predict these energies. Experiments reveal that the trained coarse-grained potential accurately reproduces the anisotropic pair interaction potential of helinotons in a liquid crystal cell, demonstrating accurate decay of interactions over distances exceeding a few micrometers. This achievement enables large-scale simulations of interacting solitons, accelerating the design and discovery of knotted metamaterials with customized properties, and opening new possibilities in areas such as advanced optics and materials science.

Helinoton interactions modeled with machine learning

This study establishes a new framework for modeling topological solitons, specifically knotted structures known as helinotons, as quasiparticles defined by their geometric center and orientation. Scientists have developed a machine-learned coarse-grained potential that accurately captures the complex interactions between these structures in chiral liquid crystals. This enables simulations that go far beyond the scope of traditional fine-grain methods and successfully reproduces the crystal aggregates observed in experiments. The researchers’ approach enables large-scale simulations of these complex systems by significantly reducing computational costs while maintaining accuracy, opening new avenues for studying emergent collective phenomena across a wide variety of soft and hard condensed matter systems, not just chiral liquid crystals. Although the current study focuses on chiral liquid crystals, this methodology is broadly applicable to any particulate topological texture. The researchers recognize that the accuracy of the coarse-grained potential is limited by the range of parameters explored during training, and plan to extend this range to incorporate material constants, allowing efficient exploration of a wider parameter space without the need for retraining the potential, further increasing the predictive power and versatility of the developed modeling framework.