Crafted by undergraduate researchers at Boise State, this video is designed to be a seminal resource for our fellow students, those who will follow in our footsteps, and professionals in the fields of deep learning, scientific computing, and numerical analysis.
Join us as we delve into an innovative intersection between physics and machine learning, showcasing the power and potential of PINNs in modeling and solving nonlinear partial differential equations. Here's what awaits:
1. Introduction to Neural Networks and PINNs:
Fundamentals of Neural Networks: A foundational exploration
Physics-Informed Neural Networks (PINNs): A scholarly overview
2. Case Study: 2D Heat Equation with Hard Boundary and Initial Conditions:
Objective, Data Inputs, Expected Output, Constraints
Loss Function: Analyzing formulation and defining end goals
3. PINN Implementation:
Deep Learning Stack: Featuring Python, DeepXDE, TensorFlow, NumPy, Matplotlib
Step-by-step guide and insights for hands-on implementation
4. Challenges Faced:
Learning the Boundary Condition: A mathematical perspective
Implementing Residual Minimization Biases: Techniques and lessons learned
Additional Resources
Our Code:
github.com/aid...
Research Papers:
Raissi, M., Perdikaris, P., & Karnidadkis, G.E. (2018). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations." Brown University
Wight, C. (2020). "Numerical Approximations of Phase Field Equations with Physics Informed Neural Networks." Utah State University.
Mattey, R. & Ghosh, S. (2021). "A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations." Michigan Technical University.
Videos:
NVIDIA Physics Informed Neural Networks [ • Video ]
Neural Networks from Scratch in Python [ • Neural Networks from S... ]
The basics of neural networks, and the math behind how they learn [ • But what is a neural n... ]
Connect with Us:
Justin Young: www.linkedin.c...
Aidan Scudder: www.linkedin.c...
Thanks for Watching!
#AI #MachineLearning #PINNs #NonlinearPDEs #PhysicsModeling #DeepLearning #ScientificComputing
Негізгі бет Modeling Nonlinear Complex PDEs with AI: A Physics-Informed Neural Network (PINN) Tutorial
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