The nonlinear filtering problem is a cornerstone of stochastic processes and control theory, where the goal is to infer the conditional distribution of a latent signal from noisy observations. Classical approaches such as particle filters and sequential Monte Carlo methods can become prohibitively expensive in nonlinear and high-dimensional regimes. During the previous NAISS allocation period, this project developed and evaluated deep learning approaches that approximate the full filtering density using neural networks, with complementary methodologies based on (i) deep splitting for the associated Fokker--Planck equation and (ii) deep backward stochastic differential equation formulations, supported by convergence analysis and extensive numerical experiments. These methods were validated through large-scale numerical studies in nonlinear and high-dimensional settings, demonstrating their effectiveness in regimes where classical filters struggle due to dimensionality or computational constraints. The experiments required repeated Monte Carlo simulation and long training horizons, making access to GPU-accelerated cluster resources essential. In particular, the neural network architectures and training pipelines employed in this project have exhibited memory requirements that scale approximately quadratically with the underlying state dimension. The next stage of the project is to extend these deep filtering frameworks from pure state estimation to joint state and parameter estimation. This extension is substantially more challenging, as unknown parameters increase the effective dimension of the inference problem and further create scalability issues for classical methods. Continued access to NAISS GPU resources is therefore crucial to develop, train, and benchmark these methods in high-dimensional and data-intensive regimes.