🚀 Welcome to the PINA Tutorials!

In this folder we collect useful tutorials in order to understand the principles and the potential of PINA. Whether you’re just getting started or looking to deepen your understanding, these resources are here to guide you.

Getting started with PINA

• Introductory Tutorial: A Beginner’s Guide to PINA

• How to build a Problem in PINA

• Introduction to Solver classes

• Introduction to Trainer class

• Data structure for SciML: Tensor, LabelTensor, Data and Graph

• Building geometries with DomainInterface class

• Introduction to PINA Equation class

Physics Informed Neural Networks

• Introductory Tutorial: Physics Informed Neural Networks with PINA

• Enhancing PINNs with Extra Features to solve the Poisson Problem

• Applying Hard Constraints in PINNs to solve the Wave Problem

• Applying Periodic Boundary Conditions in PINNs to solve the Helmotz Problem

• Inverse Problem Solving with Physics-Informed Neural Network

• Learning Multiscale PDEs Using Fourier Feature Networks

• Learning Bifurcating PDE Solutions with Physics-Informed Deep Ensembles

Neural Operator Learning

• Introductory Tutorial: Neural Operator Learning with PINA

• Modeling 2D Darcy Flow with the Fourier Neural Operator

• Solving the Kuramoto-Sivashinsky Equation with Averaging Neural Operator

Supervised Learning

• Introductory Tutorial: Supervised Learning with PINA

• Chemical Properties Prediction with Graph Neural Networks

• Unstructured Convolutional Autoencoders with Continuous Convolution

• Reduced Order Modeling with POD-RBF and POD-NN Approaches for Fluid Dynamics