rheojax 0.2.2

Unified rheological analysis framework with JAX acceleration

RheoJAX - JAX-Powered Rheological Analysis

JAX-accelerated package for rheological data analysis. Provides 21 rheological models, 5 data transforms, Bayesian inference via NumPyro, and 27 tutorial notebooks.

Features

Rheological analysis toolkit with Bayesian inference and parameter optimization:

Core Capabilities

• 21 Rheological Models: Classical (Maxwell, Zener, SpringPot), Fractional (11 variants), Flow (6 models), Multi-Mode (Generalized Maxwell)
• 5 Data Transforms: FFT, Mastercurve (TTS), Mutation Number, OWChirp (LAOS), Smooth Derivative
• Model-Data Compatibility Checking: Detects when models are inappropriate for data based on physics (exponential vs power-law decay, material type classification)
• Bayesian Inference: All 21 models support NumPyro NUTS sampling with NLSQ warm-start
• Pipeline API: Fluent interface for load → fit → plot → save workflows
• Automatic Initialization: Parameter initialization for fractional models in oscillation mode
• JAX-First Architecture: 5-270x performance improvement with automatic differentiation and GPU support

Data & I/O

• Data Support: Automatic test mode detection (relaxation, creep, oscillation, rotation)
• File Formats: TRIOS, CSV, Excel, Anton Paar with format auto-detection
• Parameter System: Type-safe parameter management with bounds and constraints

Visualization & Diagnostics

• Visualization: Three built-in styles (default, publication, presentation)
• ArviZ Diagnostic Suite: 6 plot types (pair, forest, energy, autocorr, rank, ESS) for MCMC quality
• Plugin System: Support for custom models and transforms

Tutorial Notebooks & Examples

• 27 Tutorial Notebooks: Organized in 4 categories
  • examples/basic/ - 5 notebooks covering fundamental models
  • examples/transforms/ - 7 notebooks for data transforms and analysis
  • examples/bayesian/ - 7 notebooks for Bayesian inference workflows
  • examples/advanced/ - 8 notebooks for production patterns
• I/O Examples: TRIOS complex modulus handling and plotting

Installation

Requirements

• Python 3.12 or later (3.8-3.11 are NOT supported due to JAX 0.8.0 requirements)
• JAX and jaxlib for acceleration
• NLSQ for GPU-accelerated optimization
• NumPyro for Bayesian inference
• ArviZ for Bayesian diagnostics

Basic Installation

pip install rheojax

Development Installation

git clone https://github.com/imewei/rheojax.git
cd rheojax
pip install -e ".[dev]"

GPU Installation (Linux Only)

Performance Impact: 20-100x speedup for large datasets (>10K points)

Option 1: Install via Makefile

From the repository:

git clone https://github.com/imewei/rheojax.git
cd rheojax
make install-jax-gpu  # Handles uninstall + GPU install

This command:

• Uninstalls CPU-only JAX
• Installs GPU-enabled JAX with CUDA 12 support
• Verifies GPU detection

Option 2: Manual Installation

For GPU-accelerated computation on Linux systems with CUDA 12+:

# Step 1: Uninstall CPU-only version
pip uninstall -y jax jaxlib

# Step 2: Install JAX with CUDA support
pip install jax[cuda12-local]==0.8.0 jaxlib==0.8.0

# Step 3: Verify GPU detection
python -c "import jax; print('Devices:', jax.devices())"
# Should show: [cuda(id=0)] instead of [CpuDevice(id=0)]

Why separate installation? JAX with CUDA support is Linux-specific and requires system CUDA 12.1-12.9 pre-installed. Separating the installation avoids dependency conflicts on macOS/Windows.

GPU Troubleshooting

Issue: Warning "An NVIDIA GPU may be present... but a CUDA-enabled jaxlib is not installed"

Solution:

# 1. Check GPU hardware
nvidia-smi  # Should show your GPU

# 2. Check CUDA version
nvcc --version  # Should show CUDA 12.1-12.9

# 3. Reinstall JAX with GPU support
pip uninstall -y jax jaxlib
pip install jax[cuda12-local]==0.8.0 jaxlib==0.8.0

# 4. Verify JAX detects GPU
python -c "import jax; print(jax.devices())"
# Expected: [cuda(id=0)]
# If still showing [CpuDevice(id=0)], check CUDA installation

Issue: ImportError or CUDA library not found

Solution:

# Set CUDA library path (add to ~/.bashrc for permanent fix)
export LD_LIBRARY_PATH=/usr/local/cuda/lib64:$LD_LIBRARY_PATH

Platform Support

• Linux + NVIDIA GPU + CUDA 12.1-12.9: Full GPU acceleration (20-100x speedup)
• macOS: CPU-only (Apple Silicon/Intel, no NVIDIA GPU support)
• Windows: CPU-only (CUDA support experimental/unstable)

Requirements (Linux GPU):

• System CUDA 12.1-12.9 pre-installed
• NVIDIA driver >= 525
• Linux x86_64 or aarch64

Conda/Mamba Users

The package works in conda environments using pip:

conda create -n rheojax python=3.12
conda activate rheojax
pip install rheojax

# For GPU acceleration (Linux only)
git clone https://github.com/imewei/rheojax.git
cd rheojax
make install-jax-gpu

Note: Conda extras syntax (conda install rheojax[gpu]) is not supported. Use the Makefile or manual pip installation method above.

Quick Start

Loading and Visualizing Data

from rheojax.io.readers import auto_read
from rheojax.visualization import plot_rheo_data
import matplotlib.pyplot as plt

# Load data (auto-detect format)
data = auto_read("stress_relaxation.txt")

# Check detected test mode
print(f"Test mode: {data.test_mode}")  # Output: relaxation

# Visualize
fig, ax = plot_rheo_data(data, style='publication')
plt.show()

Basic Model Fitting

from rheojax.models.maxwell import Maxwell
import numpy as np

# Generate or load data
t = np.logspace(-2, 2, 50)
G_data = 1e5 * np.exp(-t / 0.01) + np.random.normal(0, 1e3, 50)

# Fit with NLSQ (5-270x faster than scipy)
model = Maxwell()
model.fit(t, G_data)

print(f"G0 = {model.parameters.get_value('G0'):.3e} Pa")
print(f"eta = {model.parameters.get_value('eta'):.3e} Pa·s")

Bayesian Inference Workflow

from rheojax.models.maxwell import Maxwell
import numpy as np

# Create model and data
model = Maxwell()
t = np.logspace(-2, 2, 50)
G_data = 1e5 * np.exp(-t / 0.01) + np.random.normal(0, 1e3, 50)

# Step 1: NLSQ optimization (fast point estimate)
model.fit(t, G_data)
print(f"NLSQ: G0={model.parameters.get_value('G0'):.3e}")

# Step 2: Bayesian inference with warm-start
result = model.fit_bayesian(
    t, G_data,
    num_warmup=1000,
    num_samples=2000
)

# Step 3: Analyze results
print(f"Posterior mean: G0={result.summary['G0']['mean']:.3e} ± {result.summary['G0']['std']:.3e}")
print(f"Convergence: R-hat={result.diagnostics['r_hat']['G0']:.4f}, ESS={result.diagnostics['ess']['G0']:.0f}")

# Get credible intervals
intervals = model.get_credible_intervals(result.posterior_samples, credibility=0.95)
print(f"G0 95% CI: [{intervals['G0'][0]:.3e}, {intervals['G0'][1]:.3e}]")

Bayesian Pipeline with ArviZ Diagnostics

from rheojax.pipeline.bayesian import BayesianPipeline

pipeline = BayesianPipeline()

# Fluent API: load → fit_nlsq → fit_bayesian → plot → save
(pipeline
    .load('data.csv', x_col='time', y_col='stress')
    .fit_nlsq('maxwell')
    .fit_bayesian(num_samples=2000, num_warmup=1000)
    .plot_posterior()
    .plot_trace()
    .save('results.hdf5'))

# ArviZ diagnostic plots (MCMC quality assessment)
(pipeline
    .plot_pair(divergences=True)        # Parameter correlations with divergences
    .plot_forest(hdi_prob=0.95)         # Credible intervals comparison
    .plot_energy()                       # NUTS energy diagnostic
    .plot_autocorr()                     # Mixing diagnostic
    .plot_rank()                         # Convergence diagnostic
    .plot_ess(kind='local'))            # Effective sample size

Reference: See Bayesian Quick Start Guide for:

• When and why to use Bayesian inference
• NLSQ → NUTS → ArviZ workflow walkthrough
• Troubleshooting convergence issues
• Best practices checklist
• Runnable demo: python examples/bayesian_workflow_demo.py

Model-Data Compatibility Checking

RheoJAX detects when models are inappropriate for data based on physics:

from rheojax.models.fractional_zener_ss import FractionalZenerSolidSolid
from rheojax.utils.compatibility import check_model_compatibility, format_compatibility_message
import numpy as np

# Generate exponential decay data
t = np.logspace(-2, 2, 50)
G_t = 1e5 * np.exp(-t / 1.0)

# Check compatibility before fitting
model = FractionalZenerSolidSolid()
compat = check_model_compatibility(
    model, t=t, G_t=G_t, test_mode='relaxation'
)

# Get report
print(format_compatibility_message(compat))
# Output:
# ⚠ Model may not be appropriate for this data
#   Confidence: 90%
#   Detected decay: exponential
#   Material type: viscoelastic_liquid
#
# Warnings:
#   • FZSS model expects Mittag-Leffler (power-law) relaxation,
#     but data shows exponential decay.
#
# Recommended alternative models:
#   • Maxwell
#   • Zener

# Or enable checking during fit
model.fit(t, G_t, check_compatibility=True)  # Warns if incompatible

Features:

• Detects decay type (exponential, power-law, stretched, Mittag-Leffler)
• Classifies material type (solid, liquid, gel, viscoelastic)
• Provides model recommendations when incompatible
• Error messages explain physics mismatches

Reference: Model Selection Guide for decision flowcharts and model characteristics.

Working with Parameters

from rheojax.core import ParameterSet

# Create parameter set
params = ParameterSet()
params.add("E", value=1000.0, bounds=(100, 10000), units="Pa")
params.add("tau", value=1.0, bounds=(0.1, 100), units="s")

# Get/set values
E = params.get_value("E")
params.set_value("tau", 2.5)

Data Transforms

from rheojax.transforms import FFTAnalysis, Mastercurve, MutationNumber

# FFT analysis for frequency spectrum
fft = FFTAnalysis(window='hann', detrend=True)
freq_data = fft.transform(data)
tau_char = fft.get_characteristic_time(freq_data)

# Time-temperature superposition (mastercurves)
mc = Mastercurve(reference_temp=298.15, method='wlf')

# Option 1: Create mastercurve (basic)
mastercurve = mc.create_mastercurve(datasets)

# Option 2: Transform with shift factors (for plotting)
mastercurve, shift_factors = mc.transform(datasets)

# Get parameters and arrays for analysis
wlf_params = mc.get_wlf_parameters()
temps, shifts = mc.get_shift_factors_array()

# Mutation number (viscoelastic character)
mn = MutationNumber()
delta = mn.calculate(data)  # 0=elastic, 1=viscous

Tutorial Notebooks

27 tutorial notebooks organized by topic:

examples/
├── basic/                       # 5 notebooks: Fundamental models
│   ├── 01-maxwell-fitting.ipynb
│   ├── 02-zener-fitting.ipynb
│   ├── 03-springpot-fitting.ipynb
│   ├── 04-bingham-fitting.ipynb
│   └── 05-power-law-fitting.ipynb
├── transforms/                  # 7 notebooks: Data analysis workflows
│   ├── 01-fft-analysis.ipynb
│   ├── 02-mastercurve-tts.ipynb
│   ├── 02b-mastercurve-wlf-validation.ipynb
│   ├── 03-mutation-number.ipynb
│   ├── 04-owchirp-laos-analysis.ipynb
│   ├── 05-smooth-derivative.ipynb
│   └── 07-mastercurve_auto_shift.ipynb
├── bayesian/                    # 7 notebooks: Bayesian inference
│   ├── 01-bayesian-basics.ipynb
│   ├── 02-prior-selection.ipynb
│   ├── 03-convergence-diagnostics.ipynb
│   ├── 04-model-comparison.ipynb
│   ├── 05-uncertainty-propagation.ipynb
│   ├── 06-bayesian_workflow_demo.ipynb
│   └── 07-gmm_bayesian_workflow.ipynb
├── advanced/                    # 8 notebooks: Production patterns
│   ├── 01-multi-technique-fitting.ipynb
│   ├── 02-batch-processing.ipynb
│   ├── 03-custom-models.ipynb
│   ├── 04-fractional-models-deep-dive.ipynb
│   ├── 05-performance-optimization.ipynb
│   ├── 06-frequentist-model-selection.ipynb
│   ├── 07-trios_chunked_reading_example.ipynb
│   └── 08-generalized_maxwell_fitting.ipynb
└── io/                          # I/O demonstrations
    └── plot_trios_complex_modulus.ipynb

See examples/README.md for learning path guide.

Documentation

Documentation: https://rheojax.readthedocs.io

Key Topics

• Getting Started - Installation and basic usage
• Core Concepts - RheoData, Parameters, Test Modes
• Bayesian Inference - NLSQ → NUTS workflow, ArviZ diagnostics
• Pipeline API - High-level workflows
• I/O Guide - Reading and writing data
• Visualization Guide - Creating plots
• API Reference - API documentation

Performance

NLSQ Optimization Performance

NLSQ performance compared to scipy:

Dataset Size	scipy (Powell)	NLSQ (JAX)	Speedup
50 points	180 ms	35 ms	5x
500 points	920 ms	48 ms	19x
5000 points	8.2 s	95 ms	86x
50000 points	94 s	350 ms	270x

Bayesian Warm-Start Performance

NLSQ → NUTS warm-start improves MCMC convergence:

Method	Convergence Time	Divergences	ESS/sec
Cold start (random init)	45s	15%	44
NLSQ warm-start	18s	0.2%	111
Improvement	2.5x faster	75x fewer	2.5x higher

Benchmarks on M1 MacBook Pro. GPU acceleration provides additional 5-20x speedups for large datasets.

Contributing

Contributions are accepted. See Contributing Guide for details.

Development Setup

# Clone repository
git clone https://github.com/imewei/rheojax.git
cd rheojax

# Install development dependencies
pip install -e ".[dev]"

# Install pre-commit hooks
pre-commit install

# Run tests
pytest

License

This project is licensed under the MIT License - see the LICENSE file for details.

Citation

If you use rheo in your research, please cite:

@software{rheo2024,
  title = {Rheo: JAX-Powered Unified Rheology Package with Bayesian Inference},
  year = {2024},
  author = {Wei Chen},
  url = {https://github.com/imewei/rheojax},
  version = {0.2.2}
}

Acknowledgments

Built on open-source software:

• JAX for automatic differentiation and acceleration
• NLSQ for GPU-accelerated nonlinear least squares
• NumPyro for probabilistic programming
• ArviZ for Bayesian visualization
• NumPy and SciPy for numerical computing
• matplotlib for visualization

Support

• Documentation: https://rheojax.readthedocs.io
• Discussions: GitHub Discussions
• Issues: GitHub Issues
• Email: [e-mail]

Roadmap

See CHANGELOG.md for development history and examples/ for tutorial notebooks.

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Wei Chen