PHYSICS-INFORMED MACHINE LEARNING • POWER SYSTEMS • REPRODUCIBLE

Physics-Informed AI
for Power Systems,
Proven by Reproduction.

An open-source library that solves power flow with neural networks constrained by the governing physics — validated against exact solvers on the IEEE 9-bus benchmark, with every number reproducible by a single command.

OPEN SOURCE (MIT)
25 TESTS PASSING
DC + AC POWER FLOW · N-1 CONTINGENCY
THE PROBLEM

Power systems can't trust a black box

A model whose predictions can violate Kirchhoff's laws is hard to trust in critical infrastructure. Embedding the physics as a loss term makes compliance measurable.

Black-box predictions are hard to verify

If a forecast can quietly break the power-balance equations, an operator has no principled way to bound its error. That is a real barrier to adoption.

Physics is free supervision

The governing equations act as a strong inductive bias: faster convergence, better generalization from limited data, and a residual you can actually measure.

Residuals make trust quantitative

A physics-violation residual is a number you can check. We report it, and we show a controlled ablation where the physics-informed model violates it far less than a black box.

EXPLORE

Interactive DC Power-Flow Explorer

An honest, in-browser tool that runs the exact DC power-flow solve on the real IEEE 9-bus network — the same physics the validated PINN learns to respect. A teaching aid, distinct from the reproducible results below.

Open the explorer
OPEN-SOURCE PINN LIBRARY

A Power-Flow Library You Can Run Today

DC and AC power flow on the IEEE 9-bus benchmark, validated against analytical and Newton-Raphson ground truth • N-1 contingency • a controlled PINN-vs-black-box ablation • 25 passing tests • reproducible reports in Markdown / JSON / TXT / PDF. PyTorch.

Run It Yourself in One Command

Install the open-source library and regenerate every validated number locally — the PINN training, the analytical comparison, the N-1 sweep, and the full report. Nothing hidden, nothing hosted required.

See the reproducible results
RELATED ACADEMIC BACKGROUND

Cited Research Background

We cite related academic work on ontologies for smart-grid cyber intelligence. It is background — distinct from, and not a claim of, the reproducible power-flow validation in this repository, which is our own work.

MASTER THESIS • RWTH AACHEN • 2025

Data Modeling in a Cross-domain Ontology for Cyber Intelligence in Smart-Grids Using Reinforcement Learning

Vincenzo Grimaldi · RWTH Aachen University · Institute for Automation of Complex Power Systems

The thesis develops a methodology mapping the Common Information Model (CIM) to a cybersecurity framework for smart grids. Its results are the author's own contribution. We reference it as related background; it is not implemented in, or validated by, this repository.

Request the publication reference
OUR OWN VALIDATION — REPRODUCIBLE

We Don't Just Claim Physics-Informed. We Prove It.

Our open-core PINN solves DC and AC power flow on the standard IEEE 9-bus benchmark, validated against the exact analytical and Newton-Raphson solutions. Every number below is reproducible with a single command.

RMSE VS ANALYTICAL TRUTH
0.0124°
bus voltage angle error
AC PINN (NONLINEAR)
0.0035°
angle RMSE vs Newton-Raphson
GROUND-TRUTH RESIDUAL
1e-16
analytical solve, machine precision
PINN VS BLACK-BOX
2.9M×
lower physics violation (controlled ablation)
VALIDATION TESTS
25
automated tests passing
Live results visualization
Loading validated results…
Reproduce it yourself
pip install -e . && python -m physics_informed_grid.validate_ieee9

The command trains the PINN on the IEEE 9-bus system, compares every bus angle against the exact DC power-flow solution, and regenerates the full validation report and convergence plot. Deterministic, seed-fixed, auditable.

Download report:PDFJSONTXTMarkdown
View the full validation report on GitHub
WHAT YOU GET

A Validation Report on Your System

A pilot produces one concrete deliverable: the same rigorous, reproducible report you see below — run on your network instead of the benchmark. Here is the exact format, so there are no surprises.

Inside the report

  • 01 Ground-truth solution for your case (analytical / Newton-Raphson), verified to machine precision
  • 02 Physics-informed model trained and measured against that ground truth, with per-bus error
  • 03 N-1 contingency findings: which single-element losses your network survives
  • 04 A controlled physics-violation comparison vs. an unconstrained baseline
  • 05 The code to regenerate every number yourself — you keep it
Scope a pilot on your system

See the sample

The IEEE 9-bus benchmark report — the exact deliverable format, in four open formats. Inspect it before you ever talk to us.

typical first pilot: a fixed-scope engagement, invoiced — see Pricing
HOW TO ENGAGE

From Open-Source Library to a Scoped Pilot

Open Core + Python Library

  • • PyTorch physics-residual training loops (DC and AC power flow)
  • • Analytical DC solver + Newton-Raphson AC solver as exact ground truth
  • • N-1 single-line-outage contingency sweep on IEEE 9-bus
  • • Controlled PINN-vs-black-box ablation (physics-violation metric)
  • • One-command reproducible reports: Markdown / JSON / TXT / PDF + convergence plot
View full repository on GitHub

Why a Physics-Informed Approach Earns Trust

Verifiability first
A measurable physics-violation residual gives a quantitative trust signal — the kind of evidence engineers, auditors, and reviewers can check rather than take on faith.
Data efficiency
Embedding the governing equations as a loss term lets the model generalize from limited data, which matters where labeled operational data is scarce or expensive.
Reproducible by design
Every published number is seed-fixed and regenerated by a single command, so a reviewer can confirm the claims independently before any conversation.
Start a pilot on your own data

What a Pilot Actually Involves

We run the methodology against your system data and produce a validation report on your case
Python-first; you keep the code and can reproduce every result yourself
Scoped individually, invoiced per engagement — no lock-in, no hosted dependency
Clear, honest boundaries on what is validated today vs. on the roadmap
Pilots are scoped after a short technical conversation and invoiced per engagement.

Reproducible physics-informed
power flow. See it for yourself.

Start with the open-source library and the validation report. When you want it run on your own system, we scope a pilot.

OPEN CORE AVAILABLE NOW • PILOTS SCOPED INDIVIDUALLY

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