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Suite Overview

Welcome to the technical documentation for Shardian, the high-performance physics-informed artificial intelligence suite for computational fluid dynamics (CFD) and mesoscale atmospheric modeling.

Shardian integrates neural-symbolic representations directly into standard numerical solver loops. By representing deep learning models as closed-form algebraic expressions, Shardian achieves state-of-the-art simulation accuracy with zero neural network runtime overhead.

The Hybrid AI-Physics Paradigm

Traditional machine learning approaches for physical simulations fail because: 1. High Computational Overhead: Evaluating deep neural networks (DNNs) at every grid cell and time step in a CFD or WRF simulation is extremely slow. 2. Lack of Conservational Constraints: Pure black-box models violate mass, momentum, and energy conservation. 3. Out-Of-Distribution (OOD) Divergence: Neural networks diverge when tested on flow regimes or boundary conditions outside their training set.

Shardian bypasses these limitations using Symbolic Regression (EML-SR). We train deep networks on high-fidelity DNS (Direct Numerical Simulation) data, extract the underlying physical relations as closed-form equations, and inject them directly into traditional conservation equations (RANS for CFD, MOST/PBL for WRF).

graph TD
    A["DNS / High-Fidelity Data"] --> B["EML-SR Training"]
    B --> C["Symbolic Expression Extraction"]
    C --> D["Native Code C++ / Fortran"]
    D --> E["Standard Numerical Solver (OpenFOAM / WRF)"]
    E --> F["Physically Constrained, Ultra-Fast Simulation"]

Solvers in the Suite

The Shardian suite is split into two independent simulation engines:

1. Shardian Aero (Computational Fluid Dynamics)

  • Target: Engineering flows, aerodynamics, and turbine modeling.
  • Solver: AdvancedZonalModel integrated into OpenFOAM.
  • Mechanism: Implements a zonal turbulence formulation that adjusts viscosity corrections dynamically based on local Reynolds numbers and velocity shear tensors.
  • Key Benefit: Predicts flow separation and reattachment lengths within experimental ranges on coarse meshes, with execution times nearly identical to standard \(k-\omega\) SST models.

2. Shardian Atmos (Mesoscale Meteorology)

  • Target: Wind energy resource assessment, weather forecasting, and microclimate modeling.
  • Solver: Coupled EML-SR surface and boundary layer schemes in WRF.
  • Mechanism: Models thermodynamic land-atmosphere coupling and vegetation canopy resistance dynamically.
  • Key Benefit: Eliminates the daytime "warm bias" and nocturnal decoupling in continental simulations. Distributed as a portable Singularity container (shardian_atmos.sif).

Architecture Diagram

The workspace coordinates the training, weight export, and runtime execution of both solvers:

graph LR
    subgraph "Training (Python/JAX)"
        EML["eml-sr-core"]
    end
    subgraph "Shardian Aero (C++)"
        OF["applications/openfoam_cfd"]
    end
    subgraph "Shardian Atmos (Fortran)"
        WRF["applications/wrf"]
    end
    subgraph "Licensing (Go/SQLite)"
        LS["applications/license-server"]
    end

    EML -->|export_aero_weights.py| OF
    EML -->|export_fortran_models.py| WRF
    OF -->|HTTPS Auth Ping| LS
    WRF -->|HTTPS Auth Ping| LS