Introduction to PEM Electrolyzer PINNs

Objectives

• Understand what Physics-Informed Neural Networks (PINNs) are

• Learn about PEM electrolyzers and why voltage prediction matters

• Know the project objectives and repository structure

• Understand the 6-model comparison framework and the 12-number equation takeaway

Why This Matters

The Scenario: An operator at a green hydrogen plant notices the cell voltage climbing during a high-demand shift. She needs to know: is it safe to increase pressure to boost hydrogen output, or will the membrane degrade? A fast, accurate voltage model — one that works even at conditions the plant has never operated at — could answer that question in milliseconds.

The Research Question: Can a 12-parameter physics model, trained through knowledge distillation from a larger teacher network, predict cell voltage accurately enough to replace expensive CFD simulations — and generalize reliably to operating conditions never seen during training?

What This Episode Gives You: The big picture — how 6 models are compared, why physics-informed approaches win, and why the final model fits in a single equation with 12 numbers.

Overview

This repository provides a complete framework for training physics-informed neural networks (PINNs) to predict PEM electrolyzer cell voltage from operating conditions (current, pressure, temperature).

PEM (Proton Exchange Membrane) electrolyzers split water into hydrogen and oxygen using electricity. Accurate voltage prediction is critical for optimizing efficiency, monitoring degradation, and designing control systems.

Why Physics-Informed Neural Networks?

Traditional approaches have limitations:

• First-principles models require detailed knowledge of all physical processes, which is often incomplete

• Pure ML models fit training data well but fail on out-of-distribution (OOD) conditions

PINNs combine both: they encode electrochemical physics (Nernst equation, Butler-Volmer kinetics, Ohmic losses) while learning residual corrections from data.

6-Model Comparison Framework

The notebook trains 6 models from scratch on the same data and compares their OOD generalization:

Model	Type	Parameters	Physics?
PureMLP	Standard neural network	~2,000	No
BigMLP	Large neural network	~50,000	No
Transformer	Self-attention network	~50,000	No
Teacher (HybridPhysicsMLP)	Physics + MLP hybrid	~9,000	Partial
Pure Physics	12-param electrochemistry (alpha=1.0)	12	Full
Distilled Student	12-param electrochemistry (alpha=0.1)	12	Full

The key finding: the 12-parameter distilled student achieves the best OOD generalization, beating neural networks with 50,000+ parameters.

Left: Out-of-distribution performance (lower is better). The 12-parameter student (17 mV) beats all neural networks. Right: Parameters vs OOD accuracy — the student sits in the ideal lower-left corner.

Teacher-Student Architecture

This project uses a two-stage approach:

1. Teacher Model (HybridPhysicsMLP): 8 physics parameters + MLP residual (~9,354 parameters)

2. Student Model (PhysicsHybrid12Param): 12-parameter pure physics model, trained via knowledge distillation

The student learns from both real data and teacher predictions, achieving better OOD generalization with only 12 parameters.

The Biggest Takeaway: A 12-Number Equation

After training, the distilled student is not a neural network. It is a deterministic algebraic equation defined by exactly 12 scalar constants:

• 6 physics parameters (exchange currents, resistance, transfer coefficients, limiting current)

• 6 hybrid correction parameters (logistic curve + pressure/temperature modulation)

Anyone with these 12 numbers can reproduce the model’s predictions in any language (Python, MATLAB, Excel) without PyTorch or any ML framework. The notebook verifies this by implementing the full equation in pure NumPy and confirming it matches the PyTorch model to micro-volt precision.

Self-Contained Repository

Component	Location
NORCE experimental data	dataset/ (3 test datasets)
ML training scripts	scripts/pem_electrolyzer/
Interactive notebook	demonstrator-v1.orchestrator.ipynb
Sample results	results/
Dependencies	requirements.txt

Using AI Coding Assistants

If you’re using an AI coding assistant, the repository includes an AGENT.md file with setup instructions. Tell your assistant:

“Read AGENT.md and help me run the PEM electrolyzer PINN demonstrator on my NAIC VM.”

What You Will Learn

Episode	Topic
02	Provisioning a NAIC VM
03	Setting up the environment
04	Understanding PEM electrolyzer data
05	PINN methodology and electrochemistry
06	Running experiments
07	Analyzing results
08	FAQ

Notebook Structure (11 Parts)

The interactive notebook covers the full pipeline:

Part	Topic
1	Environment Setup
2	Data Exploration
3	PINN Methodology
4	Training the Teacher
5	Baseline Models & Comparison (PureMLP, BigMLP, Transformer, Pure Physics)
6	Knowledge Distillation
7	Full 6-Model Comparison
8	Interactive Exploration (widgets)
9	Batch Ablation Study
10	Summary & Next Steps
11	The Biggest Takeaway: 12-Number Equation

Resources

• NAIC Portal: https://orchestrator.naic.no

• Repository: https://github.com/NAICNO/wp7-UC2-pem-electrolyzer-digital-twin

Keypoints

• PINNs combine electrochemical physics with ML for better generalization

• 6 models are compared: 3 pure-ML baselines + teacher + pure physics + distilled student

• The distilled student (12 params) beats 50,000-parameter neural networks on OOD

• After training, the student is a deterministic equation — reproducible from 12 numbers

• Knowledge distillation with alpha=0.1 transfers physics understanding from teacher to student

• All code and data are included in this repository