Evidence Board
Measured model vs Verlet baseline
PINN
VERLET
ERROR
Trace source:
measured_exported_model
Position Error
-- km
Energy Drift
-- %
Momentum Drift
-- %
PINN Latency
-- ms
Status
--
Position Error Mag
Energy Invariant
Momentum Invariant
Parametric Solver
Hybrid Kepler Model
MODEL PENDING
Real-time inference
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Speedup: --
Architecture Document
KeplerLab PINN V1
1. Formulation
A multi-layer perceptron constrained by normalized Keplerian ODE residuals computed with PyTorch autograd.grad.
2. Inputs & Scaling
Time t is normalized so 2*pi equals one orbital period. Length is scaled to semi-major axis a = 1; velocity is scaled to sqrt(mu/a), so mu = 1.
3. Network
| Time Embedding | Fourier features, 10 integer harmonics |
|---|---|
| Hidden Layers | 4 layers |
| Width | 64 neurons |
| Activation | Tanh |
| Total Params | 14,084 |
| Output | [x, y, vx, vy] |
4. Physics Residuals
The network minimizes:
L_phys = || x_ddot + x/r^3 ||^2 + || y_ddot + y/r^3 ||^2
Evaluation
Validation Metrics
The headline PINNs are trained per scenario and measured from exported weights. GTO High-E remains the stress test because periapsis dynamics are stiff.
Parametric Surrogate
The generalized path uses a Kepler-anomaly baseline plus a bounded neural residual. It is reported separately from the single-scenario PINNs.