The field of dynamical systems and neural networks is witnessing a significant shift towards the development of innovative methods for discovering governing equations, modeling complex systems, and understanding the underlying geometry of neural networks. Researchers are exploring new approaches to learn emergent dynamics from sparse and noisy observations, and to identify the underlying physics of reaction-diffusion systems. The use of variational neural networks and thermodynamic Lagrangians is becoming increasingly popular for modeling dissipative dynamical systems. Additionally, the development of novel control schemes, such as model predictive control, is being investigated for applications like aquifer thermal energy storage systems. Noteworthy papers in this area include:

• The Data Driven Discovery of Emergent Dynamics in Reaction Diffusion Systems from Sparse and Noisy Observations, which presents a conceptual framework for learning Soft Artificial Life models from observed data.
• The Automatic Regression for Governing Equations with Control (ARGOSc) paper, which introduces an extension of the ARGOS framework to incorporate external control inputs into the system identification process.
• The Variational Neural Networks for Observable Thermodynamics (V-NOTS) paper, which develops an efficient data-based computing framework for modeling dissipative dynamical systems using observable variables.