The paper introduces PINN Adaptive ColLocation and Experimental Points Selection (PINNACLE), an algorithm that jointly optimizes the selection of all training point types in Physics-Informed Neural Networks (PINNs). PINNACLE automatically adjusts the proportion of collocation points as training progresses, leveraging cross-information among different point types. The algorithm is based on an analysis of PINN training dynamics using the Neural Tangent Kernel (NTK) and defines a new notion of convergence degree, which characterizes how much a candidate set of training points helps in the training convergence. The authors theoretically show that selecting training points that maximize the convergence degree leads to lower generalization error bounds for PINNs. Empirical results demonstrate that PINNACLE outperforms existing point selection methods in various problem settings, including forward, inverse, and transfer learning problems.The paper introduces PINN Adaptive ColLocation and Experimental Points Selection (PINNACLE), an algorithm that jointly optimizes the selection of all training point types in Physics-Informed Neural Networks (PINNs). PINNACLE automatically adjusts the proportion of collocation points as training progresses, leveraging cross-information among different point types. The algorithm is based on an analysis of PINN training dynamics using the Neural Tangent Kernel (NTK) and defines a new notion of convergence degree, which characterizes how much a candidate set of training points helps in the training convergence. The authors theoretically show that selecting training points that maximize the convergence degree leads to lower generalization error bounds for PINNs. Empirical results demonstrate that PINNACLE outperforms existing point selection methods in various problem settings, including forward, inverse, and transfer learning problems.