PINNs is a deep learning framework that trains neural networks to solve supervised learning tasks while respecting physical laws described by nonlinear partial differential equations.
The framework addresses the problem of solving and discovering partial differential equations by encoding physical constraints directly into neural network training. Rather than treating PDEs as separate from machine learning, PINNs embed the governing equations as prior information within the network's loss function. This approach works by training networks on data while simultaneously enforcing that predictions satisfy the underlying physics, creating data-efficient surrogate models that are fully differentiable with respect to all input coordinates and parameters. The framework handles two main problem classes: data-driven solution of PDEs, where the equations are known and solutions must be inferred, and data-driven discovery of PDEs, where the governing equations themselves must be learned from observational data. The implementation provides both continuous time and discrete time model variants depending on the nature and arrangement of available data.
Developers working on inverse problems, surrogate modeling, or scientific computing where physical laws constrain the solution space should consider this approach. It suits projects where traditional numerical methods are computationally expensive or where limited experimental data must be leveraged effectively. The framework is particularly valuable when you need fully differentiable models that can serve as building blocks in larger computational pipelines.
The repository is no longer under active maintenance. The README explicitly recommends using implementations available in PyTorch, JAX, and TensorFlow v2 instead of this original codebase.
