Physics-Constrained ML for Transport
Embedding conservation laws and known limits into transport models keeps predictions physically valid and improves extrapolation beyond the training data.
The case for constraints
A purely data-driven transport model can fit its training set yet violate basic physics, such as producing transport in a stable region or breaking conservation. Physics-constrained models build known laws into the architecture or loss so predictions stay valid even where data are sparse.
Ways to impose physics
- Hard constraints: architectures that guarantee non-negative diffusivity or exact conservation
- Soft constraints: penalty terms in the loss for violating a known relation
- Structural priors: enforce the correct threshold behavior for turbulent onset
- Symmetry: build in invariances the physics requires
For turbulent transport, the most important constraint is the critical-gradient threshold: flux should be near zero below the instability boundary and rise above it. Encoding this prevents the spurious residual transport that destabilizes coupled simulations.
Benefits
Physics constraints reduce the data needed, improve extrapolation to unseen conditions, and make predictions more trustworthy for engineering use. They also make models easier to debug, because violations of a known law are immediately visible.
Tradeoffs
Hard constraints can complicate training and, if the assumed physics is wrong, bias results. Soft constraints are flexible but only approximately enforced. The right balance depends on how well the physics is known versus how much must be learned from data.
For modeling profiles of concepts like the Hyperion breeder, physics-constrained transport gives more reliable extrapolation toward an untested design point than unconstrained fits. Predictions remain simulations for a machine under design and are cross-checked against gyrokinetics, but the constraints raise confidence that the extrapolation respects known physics.