Physics-informed Neural Networks (PINN)
Table of Contents
1. Why Deep Learning Needs Physics?¶
Why do data-driven ‘black-box’ methods fail?
- May output result that is physically inconsistent
- Easy to learn spurious relationships that look good only on training and test data
- Can lead to poor generalization outside the available data (out-of-sample prediction tasks)
- Interpretability is absent
- Discovering the mechanism of an underlying process is crucial for scientific advancements
Physics-Informed Neural Networks (PINNs)
- Take full advantage of data science methods with the accumulated prior knowledge of scientific theories $\rightarrow$ Improve predictive performance
- Integration of domain knowledge to overcome the issue of imbalanced data & data shortage
1.1. Taxonomy of Informed Deep Learning¶
1.2. Multilayer Feedforward Networks are Universal Approximators¶
- The Universal Approximation Theorem
- Neural Networks are capable of approximating any Borel measurable function
- Neural Networks (1989)
1.3. Neural Networks for Solving Differential Equations¶
- Neural Algorithm for Solving Differential Equations
- Journal of Computational Physics (1990)
- Neural minimization for finite difference equation
- ANN for ODE and PDE
- IEEE on Neural Networks (1998)
