Skip to content

anypinn.cli.scaffold.van_der_pol.ode_csv

Van der Pol oscillator — mathematical definition.

DU0 = 0.0 module-attribute

MU_KEY = 'mu' module-attribute

NOISE_STD = 0.05 module-attribute

TRUE_MU = 1.0 module-attribute

T_TOTAL = 20 module-attribute

U0 = 2.0 module-attribute

U_KEY = 'u' module-attribute

validation: ValidationRegistry = {} module-attribute

create_data_module(hp: ODEHyperparameters)

Source code in src/anypinn/cli/scaffold/van_der_pol/ode_csv.py 
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
def create_data_module(hp: ODEHyperparameters):
    from anypinn.catalog.van_der_pol import VanDerPolDataModule

    def vdp_unscaled(x: Tensor, y: Tensor, args: ArgsRegistry) -> Tensor:
        u, v = y
        mu = args[MU_KEY]
        du = v
        dv = mu(x) * (1 - u**2) * v - u
        return torch.stack([du, dv])

    gen_props = ODEProperties(
        ode=vdp_unscaled,
        y0=torch.tensor([U0, DU0]),
        args={
            MU_KEY: Argument(TRUE_MU),
        },
    )

    return VanDerPolDataModule(
        hp=hp,
        gen_props=gen_props,
        noise_std=NOISE_STD,
        validation=validation,
        callbacks=[DataScaling(y_scale=1.0)],
    )

create_problem(hp: ODEHyperparameters) -> ODEInverseProblem

Source code in src/anypinn/cli/scaffold/van_der_pol/ode_csv.py 
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
def create_problem(hp: ODEHyperparameters) -> ODEInverseProblem:
    props = ODEProperties(
        ode=vdp_scaled,
        y0=torch.tensor([U0]),
        order=2,
        dy0=[torch.tensor([DU0])],
        args={},
    )

    fields = FieldsRegistry(
        {
            U_KEY: Field(config=hp.fields_config),
        }
    )
    params = ParamsRegistry(
        {
            MU_KEY: Parameter(config=hp.params_config),
        }
    )

    def predict_data(x_data: Tensor, fields: FieldsRegistry, _params: ParamsRegistry) -> Tensor:
        u_pred = fields[U_KEY](x_data)
        return u_pred.unsqueeze(1)

    return ODEInverseProblem(
        props=props,
        hp=hp,
        fields=fields,
        params=params,
        predict_data=predict_data,
    )

vdp_scaled(x: Tensor, y: Tensor, args: ArgsRegistry, derivs: list[Tensor] | None = None) -> Tensor

Native second-order Van der Pol ODE (scaled time).

Source code in src/anypinn/cli/scaffold/van_der_pol/ode_csv.py 
49
50
51
52
53
54
55
56
57
58
59
60
61
62
def vdp_scaled(
    x: Tensor,
    y: Tensor,
    args: ArgsRegistry,
    derivs: list[Tensor] | None = None,
) -> Tensor:
    """Native second-order Van der Pol ODE (scaled time)."""
    assert derivs is not None
    u = y[0]  # (m, 1)
    du_dtau = derivs[0][0]  # (m, 1) — derivative w.r.t. scaled time tau in [0,1]
    mu = args[MU_KEY]
    # Physical ODE: d2u/dt2 = mu*(1-u^2)*du/dt - u
    # With tau = t/T: d2u/dtau2 = T*mu*(1-u^2)*du/dtau - T^2*u
    return (T_TOTAL * mu(x) * (1 - u**2) * du_dtau - T_TOTAL**2 * u).unsqueeze(0)