Ghost Battery

Formula 1 cars deploy and recover electrical energy over a lap, but how much energy a car has available at any moment is not part of public telemetry. Public sources such as FastF1 and OpenF1 report quantities like speed, throttle, brake and position — not the state of the car's energy store.

The idea is to explore whether that hidden energy state could be estimated from public data by combining physics-based models with machine learning, and whether such an estimate — with its uncertainty stated clearly — could help reason about the energy cost and value of an overtaking attempt.

• It is a concrete example of what interests me about physics-informed machine learning: combining physical knowledge with machine learning to estimate something that cannot be observed directly.
• Neither approach looks sufficient on its own. A purely physical model would need car parameters that are not public, and a purely data-driven model would have no ground truth to learn from.
• Any honest answer has to come with uncertainty, and has to be clear about what is measured and what is only estimated.
• The data is public, so the problem can be explored without access to team data.

Proposed approach only. Nothing in this section has been implemented or tested. It is a conceptual sketch of how the problem might be approached, and it is likely to change as I learn more.

Measured, derived and inferred

One principle I would want to keep is a strict distinction between what is observed and what is estimated. Every quantity would be treated as one of three kinds:

Conceptual pipeline

A possible sequence of stages, from public data to decision support:

1. Public TelemetryMeasured

   Car and timing data from public Formula 1 sources such as FastF1 and OpenF1.

2. ↓
   Physics ReconstructionDerived

   Would reconstruct physical quantities that are not reported directly.

3. ↓
   Power BalanceDerived

   Would relate the reconstructed motion to power demand using a physics-based model.

4. ↓
   Constrained State EstimationInferred

   Could track the hidden energy state with an Extended Kalman Filter and RTS smoothing, subject to physical constraints.

5. ↓
   ML Residual CorrectionInferred

   A model such as LightGBM could correct systematic error left by the physics-based estimate.

6. ↓
   Estimated Energy StateInferred

   Would be a normalized energy-budget index with uncertainty — not a battery percentage.

7. ↓
   Attack IntelligenceInferred

   Would use the estimate to reason about the energy cost and value of overtaking.

Possible tools

Python with NumPy and SciPy for physics-based modeling and state estimation, LightGBM for a possible residual model, and FastF1 and OpenF1 for data. These are candidates, not choices that have been tried.

What the output would be

Not a battery percentage. The true value is not publicly available, so the most that could honestly be claimed is a normalized energy-budget index with uncertainty.

• Physics-informed machine learning fundamentals: the different ways physical knowledge and machine learning models can be combined.
• State estimation: Kalman filters, the Extended Kalman Filter, and smoothing methods such as Rauch–Tung–Striebel (RTS) smoothing.
• Vehicle dynamics basics: how speed, acceleration, forces and power relate.
• How Formula 1 power units deploy and recover electrical energy, and the rules that limit it.
• What public telemetry from FastF1 and OpenF1 actually contains, including its sampling, noise and gaps.
• Uncertainty quantification, and how an estimate can be checked when there is no ground truth to compare against.

For now, the focus is on learning the fundamentals above. As my understanding grows, possible next steps would be:

1. Start small: reconstruct basic physical quantities from public telemetry and check whether they are physically plausible.
2. Work out whether a constrained state estimator can track a hidden energy state in a meaningful way, and what its uncertainty would look like.
3. Decide how any estimate could be evaluated without ground truth, and what a machine learning residual model could even be trained against.
4. Only then, consider whether the estimate says anything useful about overtaking.

The idea will probably change along the way.