SmartMDAO 🚀

Extensible MDAO framework with zero boilerplate integration and plug-and-play optimization.

SmartMDAO is a lightweight, purely Pythonic framework for Multidisciplinary Design Analysis and Optimization (MDAO). Define your disciplines as plain Python functions, and SmartMDAO maps the dependency graph, converges cyclic feedback loops, caches expensive calls, and bridges straight into your optimizer of choice.

🔍 See It In Action

Without SmartMDAO — you hand-write the convergence loop and track state yourself:

y2 = 1.0  # initial guess
for _ in range(100):
    y1 = z1 ** 2 + z2 + x1 - 0.2 * y2
    y2_next = math.sqrt(abs(y1)) + z1 + z2
    if abs(y2_next - y2) < 1e-6:
        break
    y2 = y2_next

With SmartMDAO — declare each discipline once; the y1 ↔ y2 cycle is found and converged for you:

@pipeline.step(outputs=["y1"])
def discipline_1(z1, z2, x1, y2): return z1 ** 2 + z2 + x1 - 0.2 * y2

@pipeline.step(outputs=["y2"])
def discipline_2(z1, z2, y1): return math.sqrt(abs(y1)) + z1 + z2

pipeline.run(z1=1.0, z2=1.0, x1=1.0, y2=1.0)

🌟 Why SmartMDAO?

• Effortless MDA — no DSL, just @pipeline.step and standard type hints. Works with plain types, dataclasses, or your own objects.
• Convergence Beyond Numbers — coupling variables don't have to be floats. Dicts, sets, dataclasses, or any equatable type converge too: SmartMDAO falls back to structural equality when there's no numeric residual to drive to zero, so a feedback loop over a negotiated plan or a resolved dependency set converges exactly like a numeric MDA loop does. See it in action below.
• Built-in Caching — layer @cached (RAM, HDF5, Pickle) onto expensive functions for instant speedups.
• Agnostic MDO — define your OptimizationProblem once, then run it through any backend with a single string: optimize(problem, backend="scipy") or backend="openturns". Bring your own via @register_backend, or drop straight to PipelineEvaluator for full control.
• Type-Safe — static validation catches mismatched disciplines before a single step runs; opt-in runtime checks catch the rest.
• Built Also for Researchers — solvers are plain Protocol classes, so custom MDA convergence algorithms drop in without touching the core framework.

🔄 Convergence Beyond Numbers

OpenMDAO and GEMSEO converge coupled disciplines by driving a numeric residual (|Δ| between successive floats) to zero. That assumption breaks the moment a discipline exchanges something that isn't a number — a resolved set of dependencies, a negotiated plan, a piece of state an AI agent is refining across a feedback loop. SmartMDAO's StandardConvergenceChecker falls back to structural equality for non-numeric values: "did this value change since the last iteration?" is a perfectly good convergence criterion when there's no derivative to speak of.

from smartmdao import Pipeline, IterativeSolver

pipeline = Pipeline(solver=IterativeSolver(max_iterations=10))

depends_on = {
    "billing": frozenset({"database", "auth"}),
    "auth": frozenset({"database"}),
}

@pipeline.step(outputs=["enabled"])
def resolve_dependencies(requested: frozenset, enabled: frozenset) -> frozenset:
    expanded = set(enabled) | set(requested)
    for feature in list(expanded):
        expanded |= depends_on.get(feature, frozenset())
    return frozenset(expanded)

result = pipeline.run(requested=frozenset({"billing"}), enabled=frozenset())
# result["enabled"] -> frozenset({"billing", "auth", "database"}) - converged in
# 2 iterations, with not a single float anywhere in the coupling variable.

Bring your own equatable type — a dict, a set, a frozen @dataclass — and the same IterativeSolver/HybridSolver machinery converges it, no numeric tolerance required.

import math
import logging
from smartmdao import (
    Pipeline,
    HybridSolver,
    PipelineEvaluator,
    OptimizationProblem,
    ConstraintSpec,
    optimize,
    cached,
    MemoryBackend,
    configure_logging
)

# --- Setup Logging and Cache ---
configure_logging(level=logging.WARNING)
mem_cache = MemoryBackend() # HDF5 and Pickle also available

# ==============================================================================
# PART 1: Initialize the Pipeline with the HybridSolver
# ==============================================================================
# The HybridSolver automatically detects and converges cyclic dependencies
pipeline = Pipeline(
    solver=HybridSolver(max_iterations=100, tolerance=1e-6)
)

# ==============================================================================
# PART 2: Define the Sellar Disciplines (MDA)
# ==============================================================================
@pipeline.step(outputs=["y1"])
@cached(mem_cache) # Instantly cache this discipline to speed up evaluations
def discipline_1(z1: float, z2: float, x1: float, y2: float) -> float:
    return (z1 ** 2) + z2 + x1 - (0.2 * y2)

@pipeline.step(outputs=["y2"])
@cached(mem_cache) 
def discipline_2(z1: float, z2: float, y1: float) -> float:
    return math.sqrt(abs(y1)) + z1 + z2

@pipeline.step(outputs=["objective"])
@cached(mem_cache) 
def compute_objective(x1: float, z2: float, y1: float, y2: float) -> float:
    return (x1 ** 2) + z2 + (y1 ** 2) + math.exp(-y2)

@pipeline.step(outputs=["constraint_1"])
@cached(mem_cache) 
def compute_constraint_1(y1: float) -> float:
    """Constraint formulation: 3.16 - y1 <= 0"""
    return 3.16 - y1

@pipeline.step(outputs=["constraint_2"])
@cached(mem_cache) 
def compute_constraint_2(y2: float) -> float:
    """Constraint formulation: y2 - 24.0 <= 0"""
    return y2 - 24.0

# ==============================================================================
# PART 3: Bridge the Pipeline to an Optimizer-Agnostic Problem
# ==============================================================================
evaluator = PipelineEvaluator(
    pipeline=pipeline,
    design_vars=["z1", "z2", "x1"],
    constants={"y2": 1.0} # Initial guess to kick off the cycle
)

# Both backends expect h(x) >= 0; Sellar's constraints are naturally written
# as g(x) <= 0, so we flip the sign with multiplier=-1.0.
problem = OptimizationProblem(
    evaluator=evaluator,
    initial_guess=[1.0, 1.0, 1.0],
    bounds=[(-10.0, 10.0), (0.0, 10.0), (0.0, 10.0)],
    objective="objective",
    constraints=[
        ConstraintSpec(name="constraint_1", multiplier=-1.0),
        ConstraintSpec(name="constraint_2", multiplier=-1.0),
    ],
)

# ==============================================================================
# PART 4: Run the *same* problem through two different backends
# ==============================================================================
for backend_name in ("scipy", "openturns"):
    result = optimize(problem, backend=backend_name)
    print(f"[{backend_name:>9}] objective={result.objective_value:.4f}")

🧠 Advanced Examples

The Quick Start above just scratches the surface! Notably:

• readme_quick_start.py — the complete version of the Quick Start above, including SciPy's raw minimize() call, full state extraction, and pipeline visualization.
• optimizer_backends_demo.py — define one OptimizationProblem and run the exact same Sellar problem through scipy, openturns, and a custom registered backend, just by swapping a string.
• type_validation_demo.py — static and runtime type validation, Optional/Union support, and writing a custom TypeChecker.
• non_numeric_convergence_demo.py — two full non-numeric convergence cases: a single-discipline dependency closure over a frozenset, and a two-discipline negotiation over a shared Plan dataclass with an auto-detected HybridSolver cycle.

For deeper nesting, custom convergence solvers, or more complex multidisciplinary systems, check out the scripts folder in our GitHub repository.

📦 Installation

SmartMDAO is available on PyPI. We recommend using uv for lightning-fast installation, but standard pip works perfectly.

Using uv:

uv add smartmdao

Using pip:

pip install smartmdao

(Note: Visualization features require the graphviz system binary to be installed on your OS).

Installing Graphviz (Optional System Requirement)

While smartmdao works perfectly on its own, generating pipeline diagrams requires the graphviz system binary to be installed on your OS.

macOS (Homebrew):

brew install graphviz

Linux (Ubuntu/Debian):

sudo apt-get install graphviz

Windows (winget):

winget install graphviz

(Alternatively, you can download the Windows installer directly from the official Graphviz website)

🤝 Contributing & License

Contributions are welcome! Please feel free to submit a Pull Request.This project is licensed under the MIT License - see the LICENSE file for details.