Euler

experimental.network_dynamics.solvers.Euler()

Euler method

For ODEs: Standard Euler when noise_sample=0 For SDEs: Euler-Maruyama when noise_sample provided

Methods

Name	Description
step	Euler integration step: y_{n+1} = y_n + dt * f(t, y_n) + noise.

step

experimental.network_dynamics.solvers.Euler.step(
    dynamics_fn,
    t,
    state,
    dt,
    params,
    noise_sample=0.0,
)

Euler integration step: y_{n+1} = y_n + dt * f(t, y_n) + noise.

Args: dynamics_fn: Dynamics function (t, state, params) -> (derivatives, auxiliaries) t: Current time state: Current state [n_states, n_nodes] dt: Time step params: Parameters noise_sample: Pre-scaled noise increment

Returns: Tuple of (next_state, auxiliaries): - next_state: Next state [n_states, n_nodes] - auxiliaries: Auxiliary variables at current time [n_auxiliaries, n_nodes]

# Euler { #tvboptim.experimental.network_dynamics.solvers.Euler }

```python
experimental.network_dynamics.solvers.Euler()
```

Euler method

For ODEs: Standard Euler when noise_sample=0
For SDEs: Euler-Maruyama when noise_sample provided

## Methods

| Name | Description |
| --- | --- |
| [step](#tvboptim.experimental.network_dynamics.solvers.Euler.step) | Euler integration step: y_{n+1} = y_n + dt * f(t, y_n) + noise. |

### step { #tvboptim.experimental.network_dynamics.solvers.Euler.step }

```python
experimental.network_dynamics.solvers.Euler.step(
    dynamics_fn,
    t,
    state,
    dt,
    params,
    noise_sample=0.0,
)
```

Euler integration step: y_{n+1} = y_n + dt * f(t, y_n) + noise.

Args:
    dynamics_fn: Dynamics function (t, state, params) -> (derivatives, auxiliaries)
    t: Current time
    state: Current state [n_states, n_nodes]
    dt: Time step
    params: Parameters
    noise_sample: Pre-scaled noise increment

Returns:
    Tuple of (next_state, auxiliaries):
        - next_state: Next state [n_states, n_nodes]
        - auxiliaries: Auxiliary variables at current time [n_auxiliaries, n_nodes]