---
library_name: matrixpfn
tags:
  - preconditioner
  - sparse-linear-systems
  - graph-neural-network
  - pytorch
---

# matrixpfn-base

GNN-based learned preconditioner for sparse linear systems.

**Version**: 20260309-0350

## Usage

```python
import numpy as np
from scipy.io import mmread
from matrixpfn import MatrixPFN

pfn = MatrixPFN.from_pretrained("Csed-dev/matrixpfn-base")

A = mmread("matrix.mtx")  # any scipy sparse matrix
b = A @ np.random.randn(A.shape[0])

result = pfn.solve(A, b)  # accepts scipy sparse directly
print(f"Converged: {result.converged} in {result.iterations} iterations")
```

## Architecture

| Parameter | Value |
|-----------|-------|
| Network | ContextResGCN |
| Layers | 24 |
| Embed | 128 |
| Hidden | 512 |
| Context pairs | 10 |
| Parameters | 2,056,706 |
| dtype | float32 |

## Training

- **epochs**: 5000
- **best_loss**: 0.006055
- **loss_function**: l1_direct
- **batch_size**: 256
- **matrices_per_epoch**: 4
- **domains**: diffusion, diffusion_advection, graph_laplacian, elasticity, stokes, sbm, spectral_stress, variable_diffusion, variable_advection, enhanced_diffusion, enhanced_advection, random_sparse, directed_power_law
- **grid_sizes**: [16, 24, 32, 48]

## Benchmark

| domain | grid | converged | avg_iters | avg_residual |
|--------|------|-----------|-----------|--------------|
| diffusion | 16x16 | 0/20 | 300.0 | 3.96e-02 |
| diffusion | 24x24 | 0/20 | 300.0 | 3.40e-02 |
| diffusion | 32x32 | 0/20 | 300.0 | 2.43e-02 |
| diffusion | 48x48 | 0/20 | 300.0 | 3.41e-02 |
| diffusion | 64x64 | 0/20 | 300.0 | 4.11e-02 |
| diffusion_advection | 16x16 | 0/20 | 300.0 | 3.69e-02 |
| diffusion_advection | 24x24 | 0/20 | 300.0 | 2.91e-02 |
| diffusion_advection | 32x32 | 0/20 | 300.0 | 2.59e-02 |
| diffusion_advection | 48x48 | 0/20 | 300.0 | 2.95e-02 |