Design Memristor Model & Inference Task

Your initial task is to design a simplified, yet representative, memristor device model that captures essential non-linear I-V characteristics and state dynamics. Implement this model within a `MemristorArraySimulator` class capable of simulating an NxN array. Concurrently, define a specific Bayesian inference task, such as estimating parameters of a material's degradation curve (e.g., `y = A * exp(-B*t) + noise`), where `A` and `B` are the parameters to be inferred using a memristor-based approximate Bayesian inference approach. Articulate how the memristor array would map the input data and perform the necessary computations for this task.