pycse - Python Computations in Science and Engineering

pycse is a comprehensive library for scientific computing, data analysis, and uncertainty quantification in Python.

Core Capabilities

1. Nonlinear Regression and Curve Fitting

• nlinfit: Nonlinear least squares fitting with uncertainty quantification
• regress: Linear regression with statistics
• Supports parameter uncertainty estimation and confidence intervals

2. Design of Experiments (DOE)

• Latin Hypercube Sampling (LHC): Space-filling designs for efficient parameter exploration
• Surface Response Modeling: Fit polynomial response surfaces to experimental data
• Useful for optimizing experimental conditions with minimal trials

3. Uncertainty Quantification with DPOSE

• DPOSE (Direct Propagation of Shallow Ensembles): Neural network ensemble for UQ
• Provides per-sample uncertainty estimates (heteroscedastic)
• Handles gaps, extrapolation, and nonlinear relationships
• Trained using CRPS or NLL loss for calibrated uncertainties

4. Numerical Methods

• Root finding and optimization
• Integration and differentiation
• ODE solvers
• Statistical analysis tools

When to Use pycse

Use this skill when the user asks about:

• Fitting experimental data to nonlinear models
• Estimating parameter uncertainties
• Designing experiments or sampling parameter spaces
• Latin squares or Latin hypercube designs
• Surface response methodology
• Uncertainty quantification in predictions
• Neural network-based surrogate models with uncertainty
• Scientific data analysis in Python

Key Functions

nlinfit

from pycse import nlinfit

# Fit data to a model with uncertainty quantification
pars, pint, se = nlinfit(model_func, x0, x, y)

Latin Hypercube Design

from pycse.sklearn.lhc import LatinSquare

# Create a Latin hypercube design
factors = {'Temperature': [20, 40, 60], 'Pressure': [1, 2, 3]}
ls = LatinSquare(factors)
design = ls.design()

Surface Response

from pycse.sklearn.surface_response import SurfaceResponse

# Design and fit a surface response model
sr = SurfaceResponse(
    inputs=['red', 'green', 'blue'],
    outputs=['intensity'],
    bounds=[[0, 1], [0, 1], [0, 1]]
)
design = sr.design()
# ... run experiments ...
sr.set_output(results)
sr.fit()

DPOSE (Uncertainty Quantification)

from pycse.sklearn.dpose import DPOSE
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler

# Create DPOSE model with uncertainty estimates
model = Pipeline([
    ('scaler', StandardScaler()),
    ('dpose', DPOSE(
        layers=(n_features, 50, 32),  # (input, hidden, ensemble)
        loss_type='crps',              # CRPS loss (recommended)
        activation='tanh',             # Smooth activation
        maxiter=500
    ))
])

model.fit(X_train, y_train)

# Get predictions with uncertainty
y_pred, y_std = model.named_steps['dpose'].predict(
    X_test_scaled,
    return_std=True
)

MCP Server

pycse provides an MCP server for Claude Desktop with tools for:

• Design of experiments (Latin squares, surface response)
• Function documentation lookup
• DPOSE model information and examples
• Python documentation search

To install the MCP server:

pycse mcp install

Docker-based Jupyter Lab

pycse includes a CLI for launching Jupyter Lab in a Docker container:

pycse launch              # Launch Jupyter Lab
pycse pull                # Update Docker image
pycse rm                  # Remove stuck container

Documentation

For detailed documentation, see the pycse repository at: https://github.com/jkitchin/pycse

Tips for Using pycse

1. Always use StandardScaler with DPOSE for better convergence
2. CRPS loss is recommended for DPOSE - more robust than NLL
3. Latin hypercube designs are more efficient than grid searches
4. Surface response models are useful when experiments are expensive
5. For uncertainty propagation, use predict_ensemble() to get all ensemble members

Common Workflows

Fitting Data with Uncertainty

1. Define your model function
2. Use nlinfit with initial parameter guesses
3. Examine parameter confidence intervals and standard errors

Designing Experiments

1. Define factors and their levels
2. Create a LatinSquare or SurfaceResponse design
3. Run experiments according to the design
4. Analyze results with ANOVA or response surface fitting

Uncertainty Quantification

1. Prepare and scale your training data
2. Create a DPOSE model with appropriate architecture
3. Train the model
4. Get predictions with uncertainty estimates
5. Visualize uncertainty intervals