Revolutionizing Simulations with AI-Driven Grid Generation

In a groundbreaking advancement from the Skoltech AI Center, researchers have created a novel neural network architecture that automates the generation of structured curved coordinate grids. These grids are vital for accurate simulations across a wide array of fields including physics, biology, and finance. Their work, showcasing both the efficiency and transformative potential of AI in grid generation, has been prominently featured in the prestigious Scientific Reports journal.

Structured coordinate grids play a crucial role in numerical calculations. As Bari Khairullin, a Ph.D. student at Skoltech and the lead author, explains, these grids decompose complex spatial environments into manageable segments, enabling precise calculations of variables such as temperature, speed, and pressure. In physics, these grids are essential for simulating fluid dynamics; in biology, they are used for modeling tissue growth and drug distribution; and in finance, they assist in predicting market behavior.

Traditional methods of generating these grids relied on numerical solutions to partial differential equations, yet they were limited in terms of analytic precision. The innovative AI-driven approach surmounts these limitations by treating the neural network as a diffeomorphism, allowing for exact Jacobian evaluation and rapid mesh refinement in just one forward pass.

The researchers explored two methodologies: one involved incorporating physics-informed loss terms, known as Physics-Informed Neural Networks (PINNs), and the other involved a novel method deriving analytical formulas. These techniques ensure control over grid quality by maintaining the non-degeneracy of mapping, thereby preventing issues like mesh folding and guaranteeing bijectivity.

One significant advancement over prior architectures, such as MGNet, is the introduction of residual connections across all layers. This design models the transformation process as a sequence of incremental deformations, which enhances the accuracy and regularity of the grids produced. Initial experiments reveal that the PINN-based method can generate high-quality grids even in complex geometrical domains, highlighting its potential for solving partial differential equations where precise geometric representation is essential.

Sergey Rykovanov, head of the Artificial Intelligence and Supercomputing Laboratory at Skoltech, points out that this approach marks a significant leap forward in structured grid generation. Plans are already in motion to extend these methods to 3D domains, promising substantial improvements in computational simulations. Preliminary computations are already leveraging the power of the Zhores supercomputer at Skoltech for these tasks.

Key Takeaways:

• The Skoltech AI Center’s new neural network architecture revolutionizes structured grid generation, enhancing computational accuracy in scientific fields.
• This AI-powered approach surpasses traditional methods by enabling exact Jacobian evaluation and swift mesh refinement, which are crucial for accurate simulations.
• The architecture, featuring residual connections, models transformations as small, controlled deformations, ensuring high-quality grid outcomes.
• Future research is set to apply these innovations to 3D simulations, potentially revolutionizing fields that require precise geometric modeling for accurate calculations.