PhysForge

PhysForge is a prototype application for exploring partial-differential-equation (PDE) discovery from spatiotemporal data. It combines a PyTorch neural surrogate, automatic differentiation, thresholded least-squares regression, and a FastAPI interface.

The project is an engineering and learning prototype, not a validated scientific instrument. Results from noisy, sparse, or experimental data should not be treated as reliable equation identification without an external benchmark and uncertainty analysis.

Method

Given a CSV containing x, t, and u, the application:

1. fits a neural surrogate for u(x,t);
2. evaluates spatial and temporal derivatives with automatic differentiation;
3. constructs a candidate library such as u, u_x, u_xx, and u*u_x;
4. uses iterative thresholded least squares to select active terms; and
5. reports coefficients, residual diagnostics, and term-stability estimates.

The implementation is in app_simplified/app.py.

Run locally

cd app_simplified
python -m pip install -r requirements.txt
python app.py

The service starts at http://localhost:8000; its health endpoint is http://localhost:8000/health.

Sample data

The repository includes generated datasets for the heat, Burgers, and KdV equations. These datasets provide controlled demonstrations with known generating equations. Their presence does not by itself validate recovery of the correct terms or coefficients.

No reproducible end-to-end benchmark table is currently published. A scientific validation should report, over fixed train/test splits and multiple random seeds:

• field prediction error on held-out points;
• derivative error against known derivatives;
• active-term precision and recall;
• relative coefficient error;
• PDE residual on held-out data; and
• sensitivity to noise, sampling density, and sparsity thresholds.

Until those measurements are recorded, the sample equations should be described as intended test cases rather than validated recoveries.

Tests

python -m pytest -q

The test suite covers input validation, selected API and persistence behavior, and controlled sparse-regression fixtures. It is not a substitute for the end-to-end PDE-discovery benchmark described above.

Repository layout

app_simplified/        FastAPI application, discovery pipeline, and sample data
tests/                 Unit and controlled-fixture tests
docs/api.md            API notes
demo_minimal_pinn.py   Standalone heat-equation PINN demonstration

References

• Raissi, Perdikaris, and Karniadakis (2019), Physics-informed neural networks.
• Brunton, Proctor, and Kutz (2016), Sparse identification of nonlinear dynamics.

License

MIT. See LICENSE.