The field of stochastic systems is witnessing a significant shift towards the adoption of deep learning techniques. Researchers are exploring the potential of neural networks to automate tasks such as stability analysis, solution approximation, and system identification. A key direction is the development of innovative methods for solving partial differential equations (PDEs) and stochastic differential equations (SDEs), including the use of neural networks to approximate solutions and identify underlying equations from data. Noteworthy papers include:

• Stoch-IDENT, a novel method for identifying Stochastic Partial Differential Equations (SPDEs) from observational data, which establishes a rigorous connection between the spectral properties of the solution's mean and covariance and the identifiability of the underlying SPDEs.
• Data-Augmented Few-Shot Neural Stencil Emulation for System Identification of Computer Models, which proposes a more sample-efficient data-augmentation strategy for generating neural PDE training data from a computer model.
• Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions, which builds on previous work to propose a data-driven artificial neural network solver for Koopman and Fokker-Planck eigenfunctions.