Research: Adapt the Physics, Not the Weights - Forecasting a Turbulent Flow Through Parameter Drift

What we did:
Niva ran a pre-registered study asking where a learned world model should carry a physical parameter that drifts in deployment. On two-dimensional Kolmogorov flow, a chaotic turbulent flow, the Reynolds number (Re) was changed by -10% to +40% after training, with the new value withheld. We compared neural operators that carry Re in their weights, infer it from context, or take it as an input against a hybrid: a physics solver that carries the Reynolds-number law, plus a small learned residual trained once at the nominal Re and then frozen, which identifies Re at run time from 11 noisy frames. Every model was scored by forecast horizon as a share of an oracle's, on 300 fresh trajectories per condition, with three training seeds and criteria frozen in advance.

Headline numbers:

• After a 25% rise in Re, a Fourier neural operator (FNO) handed the true new value keeps 67% of the oracle's forecast horizon, and 83% when its training range also covers the new Re. The hybrid, which must identify Re itself, keeps 97%.
• Across the full -10% to +40% range, the hybrid keeps 92 to 98% of the oracle, 1.5 to 2.2 times an FNO trained on 1,024 conditions, and matches the best FNO without drift. Its learned part is seven times smaller and trained at one condition; a network six times larger does not help.
• The solver alone, missing a drag term, absorbs the missing physics into the fitted parameter: it reads Re 38.8 for a true 50 and keeps 16%. The frozen residual removes that bias. With a second omitted effect chosen blind by an independent selector, the hybrid keeps 83 to 87%, and drift costs it at most 4 points.
• When the omitted drag itself drifts with viscosity, the hybrid falls to 38%, and the identified Re slides as the observation window grows, a warning that needs no ground truth. The price is compute: 141 seconds per state against 0.22 for the FNO on a datacenter GPU; fine-tuning the FNO for as long leaves it at 7% or less.

Why it matters:

1. Knowing a parameter is not the same as using it: Handing a network the parameter as an input is the standard way to make a world model aware of its conditions. Here the network was handed the right value and still lost a third of its horizon outside its training range; wider training narrowed the gap without closing it. Where a parameter's effect follows a known law, supplying the law outperforms learning it from examples.
2. Physics and learning each fix the other's failure: A physical model that omits something fits its parameters wrong, because the fitted value absorbs whatever is missing. A network that learns the dynamics cannot extrapolate how they change. Learning only the omission, once, at one condition, and leaving the parameter's law to the physics, recovers both the right parameter and the forecast.
3. The failure mode is visible at run time: The design holds only while what was learned does not itself drift. When it did, the identified parameter moved with how much data it saw. That check needs no ground truth, so a deployed system can tell when its split between physics and learning has broken.

Bottom line:
Where a world model carries a physical parameter decides whether it survives a change in that parameter. In the weights the forecast collapses; inferred from context it survives at about half strength; as an input the network finds the right value and still cannot use it. Carried as physical law in the dynamics, with learning confined to what does not drift, it keeps 92 to 98% of the oracle across every drift tested. The result covers one flow, full-field observations and simple omitted physics; the next experiment tests whether the principle needs a full solver or only the drifting law in explicit form. Within that scope it supports the principle Niva builds Manifold on: physical law carried in the dynamics, with what changes identified at run time.