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Documentation

Difflow Documentation
Getting Started
Chemical Unit Operations
Bio-Manufacturing Unit Operations
Rare Earth Element (REE) Unit Operations
Carbon Capture Unit Operations
Gas Transmission Network Unit Operations
Electrical Grid Unit Operations
Refinery Unit Operations
Refinery Units at a Glance
Thermodynamics
Technoeconomic Analysis
Parameter Estimation
Experiment Design and Identifiability
Data Reconciliation
Delta-Base Planning
Design: Aspen PIMS, and delta-base planning beyond refining
Operability and Controllability Screening
Flexibility Analysis
Stochastic Programming (difflow.stochastic)
Streams and Flowsheets
Convergence and Initialization
Dynamic Modeling
Moving-Horizon Estimation
Solvers and Utilities
External solvers: pounce and discopt
Equation-Oriented (EO) Solver
Ask: the in-browser docs assistant
Agents: the difflow mcp server

About Flowsheets

What is a Flowsheet? (Basic)
What is a Flowsheet? (Intermediate)
What is a Flowsheet? (Advanced)
Single Unit: The CSTR (Continuous Stirred-Tank Reactor)
Single Unit: Energy Balances
Single Unit: The PFR (Plug Flow Reactor)
Single Unit: Separators (Flash Drums)
Connecting Units in Series
Parallel and Bypass Configurations
Recycle Streams
Why Differentiable Flowsheets?

JAX Tutorials

JAX Fundamentals: Differentiable Programming
Inverse Hessian-Vector Products and Newton Optimization
Optimization with JAX
Differential Equations with JAX
Custom Derivatives in JAX
Machine Learning with JAX
JAX Gotchas and Common Pitfalls
When Automatic Differentiation Goes Wrong
Optax: Gradient-Based Optimization in JAX
Diffrax: Differential Equation Solvers in JAX
Optimistix: Nonlinear Solvers in JAX
Neural Networks in JAX: Equinox and Flax
Gaussian Processes in JAX with GPJax
Lineax: Linear Equation Solvers in JAX
Gradient Checkpointing in JAX
Bayesian Inference with BlackJAX
Sparse Jacobians in JAX
Discrete Decisions and Differentiable Relaxations
Control and Trajectory Optimization
Differentiable Data Structures in JAX
Differentiable Programming Patterns
Tutorial 21: Sensitivity Analysis and Uncertainty Quantification
Tutorial 22: Distributed and Parallel Differentiation
Tutorial 23: Multi-Objective Optimization
Tutorial 24: Debugging Gradients
Tutorial 25: Accessing Intermediate Derivatives
Tutorial 26: GPU Acceleration for Differentiable Programming

Literature

Literature Review: Differentiable Flowsheets and Related Work

Examples

CSTR and PFR Basics: Conventional vs Difflow
CSTR + Flash Separator with Recycle
Differentiable CSTR: Sensitivity Analysis
Optimization with Differentiable Flowsheets
Rare Earth Extraction: Liquid-Liquid Separation
Technoeconomic Analysis with Differentiable Flowsheets
Uncertainty Propagation in Differentiable Flowsheets
Heat Exchanger Examples
Cantera Integration for Thermodynamic and Kinetic Data
REE Separation for NdFeB Magnet Production
REE Separation from Bastnasite Concentrate
Dynamic Modeling with difflow
Interactive Flowsheet Visualization
Surrogate Models for Unit Operations: Pump Example
Parameter Estimation from Process Data
PFR with Multiple Reactions: Validation Against Analytical Solution
Convergence Strategies and Debugging Flowsheets
Superstructure Optimization with Differentiable Flowsheets
Equation-Oriented (EO) Solver
EO vs SM Solver Benchmarks
Gas transmission networks as differentiable flowsheets (difflow_gas)
REE Extraction Basics: Using the difflow_ree Module
Custom Extractants: Defining and Using Novel REE Extractants
Parameter Estimation with difflow.estimation
Parameter Estimation for REE Distribution Coefficients
Bootstrap Uncertainty and Cross-Validation
Custom REE Elements: Adding New Elements to the Database
NASA Glenn (pyglenn) Thermodynamic Import
DWSIM Thermodynamic Import (prototype)
Flowsheet Optimization with pounce and asdex
Data Reconciliation of a Gas Transmission Network
Updating a Model from Plant Data
Delta-Base Planning from Differentiable Flowsheets
AC Optimal Power Flow with difflow_power
Stochastic Programming: Nd/Dy Separation with Uncertain Distribution Coefficients
Refinery Gasoline Blending: Nonlinear Pool vs. Linear LP with Back-off
Vacuum Distillation with difflow_refinery
The Crude Unit as a Planning Block
Crude to Vacuum on One Characterization
Crude Preheat Train in Front of the CDU
The Saturated Gas Plant
C5/C6 Light Naphtha Isomerization
A Small Whole Refinery

Bio Manufacturing Examples

Bioreactor Unit Operations
Downstream Processing Unit Operations
Monoclonal Antibody (mAb) Process Optimization
mAb Downstream Purification Process

Carbon Capture Examples

Amine-Based CO2 Capture: Fundamentals and Simulation
Membrane-Based CO2 Separation
Adsorption-Based CO2 Capture
Gradient-Based Optimization for Carbon Capture
Integrated Carbon Capture Plant Design

Index

By Differentiable Flowsheets Contributors