The field of physics-informed neural networks (PINNs) is rapidly advancing, with a focus on improving the accuracy and efficiency of solving partial differential equations (PDEs). Recent developments have led to the creation of new frameworks and techniques that can handle complex nonlinear systems, stiff biophysical dynamics, and multiscale problems. One of the key trends is the incorporation of physical laws and conservation principles into the learning process, which has been shown to improve the accuracy and robustness of PINN solutions. Another important direction is the development of methods that can adapt to new problem instances and parameters without requiring retraining, enabling faster and more efficient simulations. Notable papers in this area include: One-Shot Transfer Learning for Nonlinear PDEs with Perturbative PINNs, which proposes a framework for solving nonlinear PDEs using one-shot transfer learning and perturbative PINNs. Enhancing PINN Accuracy for the RLW Equation: Adaptive and Conservative Approaches, which develops improved PINN approaches for solving the regularized long wave equation. INC: An Indirect Neural Corrector for Auto-Regressive Hybrid PDE Solvers, which introduces a novel indirect neural corrector for stabilizing hybrid PDE solvers. A Bi-fidelity based asymptotic-preserving neural network for the semiconductor Boltzmann equation and its inverse problem, which presents a bi-fidelity framework for solving the semiconductor Boltzmann equation. Physics-Informed Neural Networks for Nonlinear Output Regulation, which addresses the output regulation problem for nonlinear systems using PINNs. Extended Physics Informed Neural Network for Hyperbolic Two-Phase Flow in Porous Media, which employs an extended PINN framework to solve the Buckley-Leverett equation. Enforcing hidden physics in physics-informed neural networks, which introduces an irreversibility-regularized strategy to enforce hidden physical laws in PINNs. An Exterior-Embedding Neural Operator Framework for Preserving Conservation Laws, which proposes a universal conserving framework for enforcing conservation laws in neural operators.