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nn-opinf

NN-OpInf is a PyTorch-based approach to operator inference that uses composable, structure-preserving neural networks to represent nonlinear operators. It extends classical operator inference by replacing polynomial operators with learned neural operators, enabling data-driven reduced-order modeling for systems that do not admit simple polynomial structure.

Features

  • Operator and model abstractions for building learned reduced-order models
  • Structure-preserving operator classes (e.g., SPD, skew-symmetric, composite)
  • Training utilities with normalization, batching, and optimization settings
  • Beta stepper utilities for time integration workflows
  • End-to-end examples for advection and Burgers-style problems

Installation

From the repo root:

python -m pip install -e .

Optional extras:

python -m pip install -e ".[WithMPI]"
python -m pip install -e ".[WithH5py]"

Quickstart

import numpy as np
import nnopinf
import nnopinf.operators as operators
import nnopinf.models as models
import nnopinf.training

n_samples = 200
state_dim = 3
A = np.array([[0.0, 1.0, 0.0],
              [-1.0, 0.0, 0.5],
              [0.0, -0.5, 0.0]])
x = np.random.randn(n_samples, state_dim)
y = x @ A.T

x_var = nnopinf.Variable(size=state_dim, name="x", normalization_strategy="MaxAbs")
y_var = nnopinf.Variable(size=state_dim, name="y", normalization_strategy="MaxAbs")
x_var.set_data(x)
y_var.set_data(y)

op = operators.StandardOperator(
    n_outputs=state_dim,
    depends_on=(x_var,),
    n_hidden_layers=2,
    n_neurons_per_layer=16,
)
model = models.Model([op])

settings = nnopinf.training.get_default_settings()
settings["num-epochs"] = 100
settings["batch-size"] = 50

nnopinf.training.train(model, variables=[x_var], y=y_var, training_settings=settings)

Quadratic operator example

import numpy as np
import nnopinf
import nnopinf.operators as operators
import nnopinf.models as models

state_dim = 3
x = np.random.randn(10, state_dim)

x_var = nnopinf.Variable(size=state_dim, name="x")
x_var.set_data(x)

quad_op = operators.QuadraticOperator(n_outputs=state_dim, acts_on=x_var)
model = models.Model([quad_op])

inputs = {"x": x_var.data_}
y = model.forward(inputs)

Repository layout

  • nnopinf/: core library Stable components: operators, models, variables, training Beta component: steppers
  • examples/: end-to-end workflows and saved model artifacts
  • docs/: Sphinx sources and generated HTML documentation
  • test/: unit tests for operators, models, variables, and training utilities

Beta Capabilities

The nnopinf.steppers module should be treated as beta functionality. Its interfaces are still evolving and are less stable than the core operator, model, variable, and training APIs.

Documentation

Sphinx sources live in docs/source/. Generated HTML documentation is in docs/generated_docs/.