T02 — Fit the Hybrid GP Model

Goal: Train a HybridStateSpaceModel (mechanistic skeleton + SW-GP residual) on the Box-Behnken dataset from T01 and evaluate held-out prediction accuracy.

Script: examples/02_fit_hybrid_gp_model.py

Prerequisite: Run T01 to generate runs/*.json.

What the script does

1. Loads 26 training runs from runs/ (one run withheld as run_023.json).

2. Calls train_hybrid(trajectories, design_space, n_epochs=100) which:

   • Constructs HybridStateSpaceModel (mechanistic prior + MultiTaskRateGP).

   • Fits the GP via L-BFGS with Adam fallback.

3. Saves the model checkpoint to model.pt.

4. Reports rRMSE on the held-out run.

Running

python examples/02_fit_hybrid_gp_model.py
# → model.pt

Alternatively, via the CLI (trains on all runs):

perfusio train --runs runs/ --model-out model.pt

Key code

from perfusio.hybrid.train import train_hybrid
from perfusio.config import DEFAULT_AMBR250_DESIGN_SPACE
import torch, json
from pathlib import Path

trajectories = [
    torch.tensor(json.loads(p.read_text())["trajectory"], dtype=torch.float64)
    for p in sorted(Path("runs").glob("run_*.json"))
]

model = train_hybrid(trajectories, design_space=DEFAULT_AMBR250_DESIGN_SPACE, n_epochs=100)
torch.save({"model_state": model.state_dict()}, "model.pt")

GP architecture

Component	Detail
Kernel	PerfusionKernel = Matérn-5/2 (state) × Linear (day) × Index (task)
Input dim	17 (9 species + 6 controls + day + task_id)
Tasks	9 (one per output species)
Likelihood	GaussianLikelihood (scalar, shared noise)
Training	L-BFGS → Adam fallback; 100 epochs
Rollout	Monte Carlo (100 paths) or moment-matching

Expected metrics (held-out run 023)

Species	rRMSE target
VCD	< 0.10
Glucose	< 0.15
Titer	< 0.20

Next step

Proceed to T03 — Single-Objective BED.