Solving Partial Differential Equations with Deep Learning

Traditional numerical methods for solving partial differential equations can be computationally expensive and difficult to scale. Modern deep learning techniques offer a powerful alternative, allowing researchers and engineers to solve complex physical systems efficiently. This text-based course guides you from the fundamental mathematical definitions of partial differential equations to implementing AI-driven solvers. You will understand how neural networks approximate complex physical behaviors and apply these modern methods to real-world scientific problems. What you'll learn: Understand the foundational mathematics of partial differential equations and traditional solver limitations; Explore how deep learning architectures represent physical fields; Implement Physics-Informed Neural Networks to solve boundary value problems; Apply generative AI models and neural operators to accelerate scientific simulations; Write clean PyTorch code to train models on physical data; Evaluate model accuracy and convergence using standard scientific computing metrics. You will begin with core concepts and mathematical formulations before moving on to hands-on code examples, progressing from basic neural network approximations to advanced physics-informed architectures. Designed for beginners to scientific machine learning, this course requires only basic Python knowledge and introductory calculus. Start reading today to unlock the potential of deep learning in scientific computing.