Research on learning Green's function with implicit neural networks (NN) to solve Poisson equations: - Exploration of different implicit NN architectures (SIREN, MLP) and input coding (Positional Encoding, Multiresolution Hash Encoding). - Incorporation of domain knowledge to approximate the low frequencies of Green's function, reducing learning time by a factor 30. - Design of a multi-level integration scheme, making the complexity in operations and memory of our method linearithmic.