Over the last few decades, anomalous diffusion processes, in which the mean squares particle displacement does not grow linearly with time, have been observed in a wide variety of practical applications. Mathematically, these physical processes are described by generalized time-fractional partial differential equations (PDEs), involving generalized (nonlocal) time fractional derivatives. In these models, there are several crucial physical parameters, e.g., diffusion coefficient, source and order, that are not directly measurable and instead have to be estimated from indirect observations of the solutions to the PDEs. This leads to a wide variety of parameter identification problems of estimating physical parameters in the mathematical models. Due to their enormous practical significance, it represents one of the most actively researched areas in mathematics. This class of problems is mathematically and numerically very challenging due to a lack of well-posedness in terms of existence, uniqueness and continuous dependence on the problem data, and the inevitable presence of noise in the observational data. Due to the high complexity of relevant mathematical models, there are many open questions in the mathematical theory and numerical simulation that have held them back from wider adoption. Thus, there is an imperative need to address these outstanding mathematical and numerical challenges, especially unique and stable determination and robust reconstruction algorithms. This issue is particularly challenging for the generalized diffusion models, since their solution theory is only poorly developed. Indeed, the nonlocality of the generalized derivative and the presence of nonlinear term make inapplicable many crucial tools, such as e.g., product rule, Laplace transform, and integration by part, and limited smoothing properties of solution operators preclude a straightforward development of the numerical approximations. This project consists of five work packages, covering singular sources, recovery of nonlinear terms, variable order model, stability estimates via transformation, and tools for practical inversion. All these packages aim at addressing different challenges associated with parameter identifications for anomalous diffusion from both mathematical and numerical perspectives, via a synergy of the expertise of French and Hong Kong teams. The project outputs will provide the much needed analytic and numerical insights into anomalous diffusion processes.