Welcome to the PINA Tutorials

This site collects step-by-step tutorials to help you understand the principles and potential of PINA. Whether you are just getting started or looking to deepen your understanding, these resources will guide you.

For installation instructions and API documentation, visit the PINA documentation.

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 domains with PINA’s BaseDomain 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 Helmholtz 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

• Advection Equation with data driven DeepONet

Supervised Learning

• Introductory Tutorial: Supervised Learning with PINA

• Chemical Properties Prediction with Graph Neural Networks

• Reduced Order Model with Graph Neural Networks for Unstructured Domains

• Data-driven System Identification with SINDy

• Unstructured Convolutional Autoencoders with Continuous Convolution

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

See Also

• Quickstart guide

• API Reference