Learn about distributed multilevel sequential Monte Carlo methods for solving Bayesian inverse problems in partial differential equation models through this 46-minute conference talk. Explore how to identify input parameters of PDE-based models using a computational framework that distributes workload across multiple processing devices while controlling both sampling and discretization errors. Discover the innovative approach of formulating Monte Carlo estimation and finite element approximation errors as a knapsack optimization problem, where computational resources serve as constraints to minimize error within a given budget. Examine the theoretical properties of this distributed multilevel data structure and review preliminary experimental results demonstrating the method's effectiveness in managing the trade-offs between computational efficiency and accuracy in Bayesian parameter identification for complex mathematical models.