Saturday 29 November 2025
A team of researchers has made a significant breakthrough in developing a new class of generative models that can efficiently generate complex data on curved surfaces, such as geospatial data or protein backbones.
Generative models are artificial intelligence algorithms that learn to create new data samples from existing data. They have become increasingly popular in recent years due to their ability to generate realistic images, videos, and music. However, most of these models are designed for use on flat surfaces, such as pictures or sound waves.
The problem is that many real-world datasets do not live on flat surfaces. For example, geospatial data, which includes information about the Earth’s surface, such as terrain elevation and land cover type, lives on a curved surface called a Riemannian manifold. Similarly, protein backbones, which are essential for understanding the structure of proteins, exist in three-dimensional space.
The researchers developed a new class of generative models called Generalised Flow Maps (GFMs) that can efficiently generate complex data on curved surfaces. GFMs use a combination of mathematical techniques and machine learning algorithms to learn the underlying patterns in the data and generate new samples that are similar in structure and distribution to the original data.
One of the key innovations of GFMs is their ability to handle the curvature of the surface. This is achieved through the use of a special type of mathematical object called a Riemannian manifold, which allows the model to learn the underlying patterns in the data while taking into account the curved nature of the surface.
The researchers tested GFMs on several datasets, including geospatial data and protein backbones. The results were impressive, with GFMs able to generate high-quality samples that closely matched the original data.
GFMs also have several practical applications. For example, they could be used to generate synthetic geospatial data for use in training artificial intelligence models or for generating realistic terrain maps. They could also be used to predict the structure of proteins, which is essential for understanding their function and developing new treatments for diseases.
Overall, the development of GFMs represents a significant advance in the field of generative models and has the potential to revolutionize the way we work with complex data on curved surfaces.
In recent years, generative models have become increasingly popular due to their ability to generate realistic images, videos, and music. However, most of these models are designed for use on flat surfaces, such as pictures or sound waves.
Cite this article: “Curved Generations: A New Class of Generative Models for Complex Data”, The Science Archive, 2025.
Generative Models, Artificial Intelligence, Complex Data, Curved Surfaces, Geospatial Data, Protein Backbones, Riemannian Manifold, Machine Learning, Mathematical Techniques, Flow Maps.
