hyper-surrogate 0.2.0

Hyperelastic Surrogates

hyper-surrogate

Data-driven surrogates for hyperelastic constitutive models in finite element analysis.

• Github repository: https://github.com/jpsferreira/hyper-surrogate/
• Documentation: https://jpsferreira.github.io/hyper-surrogate/

Table of Contents

• Why hyper-surrogate?
• Architecture
• Features
• Quick Start
• Installation
• Examples
• Contributing

Why hyper-surrogate?

Finite element solvers need constitutive models (stress-strain relationships) to simulate materials. Writing and maintaining these models — especially user-defined material subroutines (UMATs) for Abaqus/LS-DYNA — is tedious, error-prone, and tightly coupled to the solver.

hyper-surrogate provides an end-to-end pipeline that:

1. Generates training data from symbolic material definitions (NeoHooke, Mooney-Rivlin, etc.)
2. Trains neural network surrogates (MLP or Input-Convex NN) that learn the strain energy function
3. Exports to standalone Fortran 90 with baked-in weights — no Python or external dependencies at runtime

This gives you solver portability (one training, any Fortran-capable solver), thermodynamic consistency (energy-based formulation with automatic stress/tangent derivation), and speed (the exported Fortran is a pure forward pass).

Architecture

Material ─> DeformationGenerator ─> Dataset ─> MLP / ICNN ─> FortranEmitter ─> .f90
   │                                              │
   │         (symbolic SEF)                        │  (trained NN weights)
   │                                              │
   └──── UMATHandler ─────────────────────────────┘
         (analytical Fortran via SymPy CSE)     HybridUMATEmitter
                                                (NN SEF + analytical mechanics)

Features

• Symbolic mechanics -- Automatic PK2 stress and stiffness tensor derivation via SymPy
• ML surrogates -- MLP and Input-Convex Neural Network (ICNN) models for constitutive response approximation
• Hybrid UMAT -- NN-based strain energy with analytical kinematics, stress push-forward, and tangent computation
• Energy-stress loss -- Joint energy + stress gradient loss for thermodynamic consistency via autograd
• ICNN convexity -- Input-Convex Neural Networks guarantee convexity of the predicted strain energy
• Fortran export -- Transpile trained models to standalone Fortran 90 subroutines with baked-in weights
• Analytical UMAT -- Generate optimized Fortran UMAT subroutines from symbolic expressions via CSE

Quick Start

MLP surrogate (stress-based)

import hyper_surrogate as hs

# Define material and generate training data
material = hs.NeoHooke({"C10": 0.5, "KBULK": 1000.0})
train_ds, val_ds, in_norm, out_norm = hs.create_datasets(
    material, n_samples=5000, input_type="invariants", target_type="pk2_voigt",
)

# Train an MLP surrogate
model = hs.MLP(input_dim=3, output_dim=6, hidden_dims=[32, 32], activation="tanh")
result = hs.Trainer(model, train_ds, val_ds, loss_fn=hs.StressLoss(), max_epochs=500).fit()

# Export to Fortran 90
exported = hs.extract_weights(result.model, in_norm, out_norm)
hs.FortranEmitter(exported).write("nn_surrogate.f90")

ICNN surrogate (energy-based)

import hyper_surrogate as hs

material = hs.NeoHooke({"C10": 0.5, "KBULK": 1000.0})
train_ds, val_ds, in_norm, out_norm = hs.create_datasets(
    material, n_samples=5000, input_type="invariants", target_type="energy",
)

# ICNN guarantees convexity of the predicted strain energy
model = hs.ICNN(input_dim=3, hidden_dims=[32, 32])
result = hs.Trainer(
    model, train_ds, val_ds,
    loss_fn=hs.EnergyStressLoss(alpha=1.0, beta=1.0),
    max_epochs=500,
).fit()

exported = hs.extract_weights(result.model, in_norm, out_norm)
exported.save("icnn_surrogate.npz")

See the examples for more usage patterns, including hybrid UMAT export and analytical Fortran generation.

Installation

pip install hyper-surrogate        # core (NumPy, SymPy)
pip install hyper-surrogate[ml]    # with PyTorch for ML surrogates

From source with uv:

git clone https://github.com/jpsferreira/hyper-surrogate.git
cd hyper-surrogate
uv sync --all-groups --extra ml

Examples

Runnable scripts are in the examples/ directory:

Script	Description
train_neohooke_sef.py	Train MLP on NeoHooke SEF with hybrid inference
train_neohooke_stress.py	Train MLP on PK2 stress with StressLoss
train_icnn_energy.py	Train ICNN with EnergyStressLoss
export_hybrid_umat.py	End-to-end train + HybridUMATEmitter export
analytical_umat.py	Symbolic material to Fortran via UMATHandler

Run any example with:

uv run python examples/<script>.py

Contributing

Contributions are welcome! See CONTRIBUTING.md for setup instructions and guidelines.