Inference

sindae.algorithms.inference

Embed a trained MLP back into a new (or the same) DAE problem and solve for the trajectory consistent with the learned dynamics. The network is enforced as a hard GBM output constraint by default (slack_coef=0, a square system solved by POUNCE), or relaxed via an $\ell_1$ slack (slack_coef > 0) when the trained network does not fit the inference problem’s dynamics exactly.

make_inference_model builds the inference NLP.
solve_inference builds and solves it.

Because the mechanistic equations remain hard constraints, predictions stay physically consistent even at initial conditions never seen during training.

Usage¶

import numpy as np
from sindae import extract_instance_data
from sindae.algorithms.inference import solve_inference

# New initial conditions — the discretization may also differ from training.
val_problem = MyProblem(
    ics=np.array([[5.0, 0.3]]),
    input_dim=2, z_dim=1, t_span=(0, 80), nfe=20, ncp=2,
)

inference_m = solve_inference(
    val_problem, mlp,
    data=trained_data,        # normalization stats from training
    slack_coef=1e-5,          # small l1 relaxation; use 0.0 for a hard constraint
)
prediction = extract_instance_data(val_problem, inference_m)

API reference¶

`make_inference_model`¶

make_inference_model(
    problem: ProblemDefinition,
    mlp: SimpleMLP,
    traj_indices: List[int],
    data: InstanceData,
    slack_coef: float = 0.0,
) -> pyo.ConcreteModel

Build an inference NLP: DAE + trained NN embedded as a GBM constraint.

Parameters

problem (ProblemDefinition) — Inference problem — may have different ICs / dynamics from training. Must implement build_trajectory / discretize / get_input_vars / get_output_vars.
mlp (SimpleMLP)
traj_indices (List[int])
data (InstanceData) — Provides input_mean/std and output_mean/std from training.
slack_coef (float, default 0.0) — When 0 (default) the NN equality is a hard GBM output constraint (square system, no objective). When > 0 the constraint is relaxed with ℓ₁ slack variables and the objective is slack_coef * mean(sp + sn). The model is then over-determined with a least-infeasibility flavour.

Returns

m (pyo.ConcreteModel) — Extra attribute: m._traj_t_sorted : List[List[float]]

`solve_inference`¶

solve_inference(
    problem: ProblemDefinition,
    mlp: SimpleMLP,
    data: InstanceData,
    traj_indices: Optional[List[int]] = None,
    slack_coef: float = 0.0,
    solver_options: Optional[dict] = None,
    nlp_solver: str = 'pounce',
    tee: bool = False,
    timer: Optional[HierarchicalTimer] = None,
) -> pyo.ConcreteModel

Build and solve the inference NLP, returning the solved model.