jdtoscano94/NABLA-SciML

What it solves

NABLA-SciML provides a unified framework for implementing Scientific Machine Learning (SciML) methods to study complex physical systems—such as turbulent flows and cerebrospinal fluid flow—that are difficult to analyze using traditional techniques.

How it works

The project implements several advanced neural architectures and optimization techniques designed for physics-informed learning, including:

• Physics-Informed Neural Networks (PINNs) and DeepONets.
• Kolmogorov-Arnold Networks (KANs) and their variants, such as Kurkova-Kolmogorov-Arnold Networks (KKANs) and cKANs.
• Residual-Based Attention (RBA) and a Variational Framework for Residual-Based Adaptivity (vRBA) to improve model stability and reliability.
• A custom Self-Scaling Broyden (SSBroyden) optimizer for high-accuracy training.

Who it’s for

Researchers and engineers in the field of Scientific Machine Learning who need reproducible implementations of neural PDE solvers and operator learning frameworks.

Highlights

• Supports both PyTorch and JAX.
• Includes a specialized SSBroyden optimizer for increased accuracy.
• Provides a comprehensive comparison between MLP and KAN representations for differential equations.
• Offers tutorials and video guides for beginners to PINNs and DeepONets.