Promote a Constant to a Parameter

One of AnyPINN's key design choices is that fixed constants and learnable parameters share the same interface. This guide shows how to turn a known value into something the network recovers, in a single line.

---

The pattern

In every equation callable, arguments are accessed the same way regardless of whether they're fixed or learnable:

def my_ode(x: Tensor, y: Tensor, args: ArgsRegistry) -> Tensor:
    beta = args["beta"]    # Could be Argument or Parameter
    value = beta(x)        # Both are callable: Argument(v)(x) returns v
    ...

This uniformity means the equation never needs to change when you switch a constant to a learnable parameter.

---

Before: fixed constant

from anypinn.core import Argument

props = ODEProperties(
    ode=my_ode,
    y0=torch.tensor([...]),
    args={
        "beta": Argument(0.3),      # Fixed at 0.3
        "gamma": Argument(0.1),     # Fixed at 0.1
    },
)

# create_problem (no params for beta)
params = ParamsRegistry({})

After: learnable parameter

from anypinn.core import Argument, Parameter

props = ODEProperties(
    ode=my_ode,
    y0=torch.tensor([...]),
    args={
        # "beta" removed from fixed args
        "gamma": Argument(0.1),     # Still fixed
    },
)

# create_problem (beta is now learnable)
params = ParamsRegistry({
    "beta": Parameter(config=hp.params_config),  # (1)!
})

1. hp.params_config can be ScalarConfig(init_value=0.1) for a constant parameter or MLPConfig(...) for a function-valued parameter.

That's it. The ODE callable, the fields, and the training script are unchanged.

---

Choosing scalar vs function-valued

Config	When to use	What it learns
ScalarConfig(init_value=0.1)	The parameter is a single number (e.g. a rate constant)	One scalar value
MLPConfig(in_dim=1, out_dim=1, ...)	The parameter varies over the domain (e.g. a time-varying coefficient)	A function θ(x)

Both produce a callable that takes x and returns a tensor, so the ODE function works identically either way.

---

Adding validation

When you promote a constant, add it to the ValidationRegistry so training logs show how well the recovery is going:

validation: ValidationRegistry = {
    "beta": 0.3,  # The true value you just removed from args
}

For function-valued parameters, provide the ground-truth function:

validation: ValidationRegistry = {
    "beta": lambda t: 0.3 * torch.ones_like(t),
}