DD-ANN: A High-Performance Computing Framework Integrating Physics-Informed Neural Networks and Domain Decomposition Techniques

The SRIP 2026 project at the Indian Institute of Technology Gandhinagar proposes the DD-ANN (Domain Decomposition Accelerated Neural Networks) framework, whose core is integrating Physics-Informed Neural Networks (PINNs) with classical domain decomposition techniques. The goal is to build a scalable high-performance computing framework for solving electrostatic models in computational chemistry (e.g., linearized Poisson-Boltzmann equation, COSMO model). The project is currently in the critical phase of domain decomposition integration, with a tech stack based on modern Python scientific computing tools like PyTorch, and the codebase has been open-sourced (GitHub link: https://github.com/Krishna-24-24/DD-ANN).

In the field of scientific computing, traditional partial differential equation (PDE) solving methods (such as Finite Element Method (FEM) and Finite Difference Method (FDM)) face challenges of high computational cost in scenarios involving complex geometries, high-dimensional problems, or fast inference. As mesh-free solvers, Physics-Informed Neural Networks (PINNs) can directly learn PDE solutions, but they are limited in large-scale problems because a single network struggles to capture both global and local features. To address these bottlenecks, the project explores combining domain decomposition techniques with PINNs.

Physics-Informed Neural Networks (PINNs)

Proposed by Raissi et al. in 2019, during training, it considers both observational data (boundary/initial conditions, experimental measurements) and physical laws (PDE residuals encoded into the loss function). It computes high-order derivatives via automatic differentiation, ensuring the solution fits the data while satisfying physical conservation laws.

Domain Decomposition Techniques

A classic divide-and-conquer strategy: split the large computational domain into subdomains, solve each independently, then coordinate the boundary solutions. It is naturally suitable for parallel computing and is a mainstream technique for large-scale PDE solving. Combining it with PINNs can reduce the learning difficulty of a single network and support distributed training.

The project advances in three phases:

1. 1D PDE Solving: Verify core concepts (network architecture design, PDE residual loss calculation, boundary constraint implementation);
2. 2D and 3D Expansion: Introduce hard boundary condition enforcement (modify architecture to automatically satisfy boundaries), Fourier feature embedding (alleviate spectral bias), adaptive loss weighting (dynamically adjust weights of loss terms);
3. Domain Decomposition Integration (In Progress): Explore subdomain division strategies (overlapping/non-overlapping), subdomain boundary coordination mechanisms, parallel training and inference pipeline design.

The DD-ANN framework targets applications in computational chemistry electrostatic models:

• Linearized Poisson-Boltzmann (LPB) Equation: Describes the electrostatic potential distribution of charged biomolecules in electrolyte solutions; the potential changes rapidly near the molecular surface, making it difficult to solve;
• COSMO Model: A continuum solvation energy calculation model widely used in quantum chemistry; applying PINNs is expected to accelerate high-throughput screening.

These scenarios are all computationally intensive and require handling complex 3D geometries, which are the core directions for DD-ANN to tackle.

Tech Stack

• PyTorch: Deep learning framework (automatic differentiation, GPU acceleration);
• NumPy: Numerical computing foundation;
• Matplotlib: Visualization (solution distribution, training curves);
• Jupyter Notebook: Interactive development and documentation.

Academic Foundation

Core references:

1. Raissi et al. (2019): Groundbreaking paper on PINNs, explaining the mathematical framework;
2. Wang et al. (2023): PINNs training guide covering techniques like loss weighting and architecture selection.

DD-ANN represents the integration of traditional numerical analysis and modern deep learning methodologies, with potential including:

1. Improved Computational Efficiency: Parallelism from domain decomposition + fast inference from neural networks;
2. Geometric Adaptability: Mesh-free nature simplifies handling complex geometries;
3. Differentiable Simulation: Provides new approaches for inverse problems and optimization design.

The project provides a reference case from theory to practice for the scientific machine learning (SciML) community, demonstrating the process of transforming cutting-edge research into runnable code.

DD-ANN is currently in the critical phase of domain decomposition integration, and will next tackle real computational chemistry applications. Regardless of the final outcome, the project has contributed valuable experience and code resources. It is recommended that readers who want to get started with PINNs or understand the combination of domain decomposition and deep learning deeply study the project's codebase (https://github.com/Krishna-24-24/DD-ANN) and documentation.