Physics Constraints

Inject domain knowledge into MLP training — prevent the model from learning physically impossible patterns.

MLP only

Physics constraints only work with method="mlp". GP models inherently respect smoothness but don't support explicit physical constraints.

Available Constraints

Monotonicity

Enforce output monotonicity with respect to a parameter.

from prandtl import Monotonicity

Monotonicity(param_idx=0, sign=1, weight=0.1)
# CL must increase with alpha (param_idx=0). sign=+1 = monotonically increasing.

Parameter	Description
param_idx	Which input parameter to constrain
sign	+1 for increasing, -1 for decreasing
weight	How strongly to enforce (0.01–1.0)

Convexity

Enforce output convexity/concavity.

from prandtl import Convexity

Convexity(param_idx=0, sign=-1, weight=0.05)
# Output is concave w.r.t param_idx=0 (e.g., drag polar curvature)

Boundary Value

Pin output to a known value at specific parameter values.

from prandtl import BoundaryValue

BoundaryValue({"alpha": 0.0}, {"CL": 0.0}, weight=10.0)
# At alpha=0°, CL must equal 0. High weight = strict constraint.

Parameter	Description
condition	Dict of parameter values defining the boundary
target	Dict of output values at that boundary
weight	Constraint weight (higher = stricter, 1–100)

Putting It Together

from prandtl import Monotonicity, BoundaryValue, Convexity

constraints = [
    Monotonicity(param_idx=0, sign=1, weight=0.1),
    BoundaryValue({"alpha": 0.0}, {"CL": 0.0}, weight=10.0),
    Convexity(param_idx=0, sign=-1, weight=0.05),
]

surrogate = pr.Surrogate(
    params=["alpha", "mach"], outputs=["CL", "CD"], method="mlp"
)
surrogate.fit(X, Y, physics=constraints, n_iter=500, lr=0.01)

Constraints are applied as soft regularization terms in the loss function — they guide the model toward physically plausible solutions without making convergence impossible.