Skip to content

anypinn.cli.scaffold.fitzhugh_nagumo.ode_synthetic

FitzHugh-Nagumo neuron model — mathematical definition.

A_KEY = 'a' module-attribute

B = 0.8 module-attribute

EPSILON_KEY = 'epsilon' module-attribute

I_EXT = 0.5 module-attribute

NOISE_STD = 0.05 module-attribute

TRUE_A = 0.7 module-attribute

TRUE_EPSILON = 0.08 module-attribute

T_TOTAL = 50 module-attribute

V0 = -1.0 module-attribute

V_KEY = 'v' module-attribute

W0 = 1.0 module-attribute

W_KEY = 'w' module-attribute

validation: ValidationRegistry = {EPSILON_KEY: lambda x: torch.full_like(x, TRUE_EPSILON), A_KEY: lambda x: torch.full_like(x, TRUE_A)} module-attribute

create_data_module(hp: ODEHyperparameters)

Source code in src/anypinn/cli/scaffold/fitzhugh_nagumo/ode_synthetic.py 
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
def create_data_module(hp: ODEHyperparameters):
    from anypinn.catalog.fitzhugh_nagumo import FitzHughNagumoDataModule

    def fhn_unscaled(x: Tensor, y: Tensor, args: ArgsRegistry) -> Tensor:
        v, w = y
        eps = args[EPSILON_KEY]
        a = args[A_KEY]
        dv = v - v**3 / 3 - w + I_EXT
        dw = eps(x) * (v + a(x) - B * w)
        return torch.stack([dv, dw])

    gen_props = ODEProperties(
        ode=fhn_unscaled,
        y0=torch.tensor([V0, W0]),
        args={
            EPSILON_KEY: Argument(TRUE_EPSILON),
            A_KEY: Argument(TRUE_A),
        },
    )

    return FitzHughNagumoDataModule(
        hp=hp,
        gen_props=gen_props,
        noise_std=NOISE_STD,
        validation=validation,
    )

create_problem(hp: ODEHyperparameters) -> ODEInverseProblem

Source code in src/anypinn/cli/scaffold/fitzhugh_nagumo/ode_synthetic.py 
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
142
143
def create_problem(hp: ODEHyperparameters) -> ODEInverseProblem:
    props = ODEProperties(
        ode=fhn_scaled,
        y0=torch.tensor([V0, W0]),
        args={},
    )

    fields = FieldsRegistry(
        {
            V_KEY: Field(config=hp.fields_config),
            W_KEY: Field(config=hp.fields_config),
        }
    )
    params = ParamsRegistry(
        {
            EPSILON_KEY: Parameter(config=hp.params_config),
            A_KEY: Parameter(config=hp.params_config),
        }
    )

    def predict_data(x_data: Tensor, fields: FieldsRegistry, _params: ParamsRegistry) -> Tensor:
        v_pred = fields[V_KEY](x_data)
        return v_pred.unsqueeze(1)  # (N, 1, 1) — only v is observed

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

fhn_scaled(x: Tensor, y: Tensor, args: ArgsRegistry) -> Tensor

Scaled FHN ODE for training. Time scaled by T_TOTAL.

Source code in src/anypinn/cli/scaffold/fitzhugh_nagumo/ode_synthetic.py 
55
56
57
58
59
60
61
62
63
def fhn_scaled(x: Tensor, y: Tensor, args: ArgsRegistry) -> Tensor:
    """Scaled FHN ODE for training. Time scaled by T_TOTAL."""
    v, w = y
    eps = args[EPSILON_KEY]
    a = args[A_KEY]

    dv = (v - v**3 / 3 - w + I_EXT) * T_TOTAL
    dw = eps(x) * (v + a(x) - B * w) * T_TOTAL
    return torch.stack([dv, dw])