{"product_id":"pinn-with-python-an-introduction-paperback","title":"PINN with Python: An Introduction - Paperback","description":"\u003cp\u003eby \u003cb\u003eG. R. Liu\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ePhysics-Informed Neural Networks (PINNs) are transforming the way we solve complex scientific and engineering problems. This book serves as your essential guide to understanding this powerful technique, which elegantly combines the flexibility of neural networks with the fundamental rigor of physical laws.\u003c\/p\u003e\u003cp\u003ePINNs embed partial differential equations (PDEs), along with their boundary and initial conditions, directly into a neural network's training process via a custom loss function. This means the neural network learns to obey the laws of physics!\u003c\/p\u003e\u003cp\u003eThe solution function is represented by a neural network-a smooth, differentiable model constructed from affine transformations and activation functions. This formulation allows the network to intrinsically satisfy PDEs. Crucially, the derivatives required to enforce these physical constraints are computed using autograd, a lightning-fast, machine-precision technique built into modern machine learning libraries.\u003c\/p\u003e\u003cp\u003eThis comprehensive and practical book delivers: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eCore Theory \u0026amp; Formulations: Understand the foundational principles that make PINNs work.\u003c\/li\u003e\n\u003cli\u003eEssential Techniques: Learn methods for building, training, and applying PINN models.\u003c\/li\u003e\n\u003cli\u003eStep-by-Step Coding: Get hands-on with Python code to implement PINNs from scratch.\u003c\/li\u003e\n\u003cli\u003eCollocation vs. Energy-Based PINNs: Discover the nuances between these two primary approaches, their strengths, and when to use each.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe book dives deep into applications across key PDE types critical in science and engineering: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eStatic Problems: Tackle Poisson equations.\u003c\/li\u003e\n\u003cli\u003eTime-Dependent Systems: Solve heat equations (parabolic) and wave equations (hyperbolic).\u003c\/li\u003e\n\u003cli\u003eEigenvalue Challenges: Solve Helmholtz equations.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eBeyond theoretical concepts, you'll explore in-depth case studies demonstrating how to construct effective PINN models for various PDE types and geometries. We also address real-world challenges, including designing appropriate loss functions, normalizing equation systems, resolving convergence issues, and developing robust training strategies. Benefit directly from the author's research experience, insights, and practical utility codes-all integrated into this invaluable resource.\u003c\/p\u003e\u003cp\u003eWhether you're a researcher pushing boundaries, a student eager to grasp cutting-edge computational methods, or a practitioner seeking advanced solutions, this book will equip you with the essential tools and understanding to deploy PINNs effectively across a wide range of PDE-driven challenges.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 294\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.62 x 10 x 7 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e August 04, 2025\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":67972605346099,"sku":"9781946018052","price":199.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/azB6sBjli79781946018052.webp?v=1794430461","url":"https:\/\/www.vysn.com\/products\/pinn-with-python-an-introduction-paperback","provider":"VYSN","version":"1.0","type":"link"}