Operator Regression

Operator regression is a machine learning technique focused on approximating mathematical operators, often those describing complex physical systems modeled by partial differential equations, using neural networks. Current research emphasizes developing efficient and accurate neural operator architectures, such as DeepONets and their variants, often incorporating techniques like latent space representations to handle high-dimensional data and improve computational efficiency. This approach is proving valuable for tasks like material modeling, solving PDEs at scale, and analyzing multi-agent systems, offering a data-driven alternative to traditional numerical methods with potential for improved accuracy and scalability.