chebgreen: Learning and Interpolating Continuous Empirical Green's Functions from Data

They allow us to mathematically express the governing fundamental laws, as rate forms [1]. Researchers have worked on data-driven approaches and deep learning techniques to solve PDEs for various systems [2, 3, 4, 5, 6, 7]. Although they hold significant practical importance, the exact PDEs governing many important phenomena remain unknown across fields, including physics, chemistry, biology, and materials science. Thus, there also has been significant work in discovering [8, 9, 10, 11, 12, 13, 14, 15, 16] the underlying PDEs from observational data. Operator Learning represents another significant research avenue; aiming to approximate the solution operator associated with a hidden partial differential equation [17]. Notable contributions in this field include, but are not limited to, Deep Operator Networks [18], Fourier Neural Operators [19], Graph Neural Operator [20], Multipole Graph Neural Operator [21], and Geometry-informed Neural Operator [22]. A detailed overview of the topic can be found in the guide on operator learning [17].