Deep learning has achieved significant success in various applications, but its use in solving partial differential equations (PDEs) is a recent development. This paper introduces physics-informed neural networks (PINNs), which embed PDEs into the loss function of neural networks using automatic differentiation. PINNs are simple and can solve different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. They can also solve inverse problems as easily as forward problems. The authors propose a new residual-based adaptive refinement (RAR) method to improve training efficiency. They compare the PINN algorithm with a standard finite element method and present a Python library called DeepXDE, which is designed for both educational and research purposes. DeepXDE supports complex-geometry domains and allows users to monitor and modify the solution process via callback functions. The paper includes a detailed introduction to deep neural networks, automatic differentiation, and the PINN algorithm, followed by a discussion on solving integro-differential equations and inverse problems. The authors demonstrate the capabilities of PINNs and the user-friendliness of DeepXDE through five examples, including the Poisson equation, Burgers equation, Lorenz system, diffusion-reaction system, and Volterra IDE. The results show that PINNs can solve these problems efficiently and accurately, with DeepXDE contributing to the rapid development of Scientific Machine Learning.Deep learning has achieved significant success in various applications, but its use in solving partial differential equations (PDEs) is a recent development. This paper introduces physics-informed neural networks (PINNs), which embed PDEs into the loss function of neural networks using automatic differentiation. PINNs are simple and can solve different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. They can also solve inverse problems as easily as forward problems. The authors propose a new residual-based adaptive refinement (RAR) method to improve training efficiency. They compare the PINN algorithm with a standard finite element method and present a Python library called DeepXDE, which is designed for both educational and research purposes. DeepXDE supports complex-geometry domains and allows users to monitor and modify the solution process via callback functions. The paper includes a detailed introduction to deep neural networks, automatic differentiation, and the PINN algorithm, followed by a discussion on solving integro-differential equations and inverse problems. The authors demonstrate the capabilities of PINNs and the user-friendliness of DeepXDE through five examples, including the Poisson equation, Burgers equation, Lorenz system, diffusion-reaction system, and Volterra IDE. The results show that PINNs can solve these problems efficiently and accurately, with DeepXDE contributing to the rapid development of Scientific Machine Learning.