Forschungsprojekt ::

Latente score-basierte Partikelfilterung in hohen Dimensionen

Projektbeschreibung

Despite recent advances, data assimilation remains fundamentally challenging. The advanced methods as particle filters still struggle to perform well in high-dimensional systems. To overcome this limitation, the Latent Score-based Particle Filter (LSPF) is proposed as a novel, AI-enhanced assimilation algorithm. This framework integrates two cutting-edge AI strategies: the Latent Data Assimilation (LDA) to compress the state into a low-dimensional latent space, thereby mitigating the "curse of dimensionality", and diffusion models to generate scores that intelligently guide particles toward high-likelihood regions and prevent weight degeneration. Additionally, representation of model error within the LDA framework will be thoroughly examined. This project will systematically develop, theoretically underpin, and numerically validate the LSPF, progressing from a proof-of-concept to a robust high-dimensional framework using AI surrogate models.