The fields of partial differential equations (PDEs), heat recovery steam generator (HRSG) control, power system optimization and analysis, and power systems are witnessing significant advancements with the integration of machine learning techniques and physical constraints. A common theme among these areas is the use of neural networks and physics-informed neural networks (PINNs) to improve efficiency, accuracy, and interpretability.

In the field of PDEs, researchers are exploring the use of spectral methods, such as Fourier neural operators, and adaptive spectral layers to capture complex dynamics and global correlations. Generative models, such as transformer-operator frameworks, are also being developed to generate high-resolution PDE solutions from sparse input grids.

In HRSG control, innovative fault-tolerant control strategies are being developed using PINNs and traditional control methodologies. These advanced control frameworks have shown strong potential for industrial deployment, ensuring autonomous fault recovery and enhanced performance.

In power system optimization and analysis, researchers are combining physical constraints with machine learning techniques to develop innovative methods for solving complex optimization problems. Hybrid methods that combine traditional optimization techniques with machine learning approaches are also being explored.

The integration of inverter-based resources in power systems requires innovative control strategies to ensure stability and efficiency. Advanced grid-forming control methods are being developed to handle current limits, modulation limits, and frequency dynamics.

Noteworthy papers in these areas include Beyond Loss Guidance: Using PDE Residuals as Spectral Attention in Diffusion Neural Operators, ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics, and Efficient Generative Transformer Operators For Million-Point PDEs. In HRSG control, notable papers include Fault-Tolerant Temperature Control of HRSG Superheaters and Fault-Tolerant Control of Steam Temperature in HRSG Superheater under Actuator Fault.

The application of neural networks and adaptive control strategies has shown promise in improving the stability and performance of power systems. Overall, the integration of machine learning and physical constraints is revolutionizing these fields and enabling more efficient and accurate simulations, control, and optimization.