Physics-Informed Machine Learning

A neural network that cannot leave physical reality.

DeCoN-PINN models how open quantum systems lose coherence — and guarantees every prediction is a valid quantum state by construction, not by penalty. The result is a drift detector you can actually trust.

Physical validity · 100 trials
Penalty baseline
67%
Constraints enforced by tuned loss penalties — and still drift negative.
DeCoN-PINN
99%
Gram-matrix construction. Valid by architecture, every step.
Success criterion: |Tr(ρ)−1| < 10⁻¹², λ_min(ρ) ≥ −10⁻¹⁰, residual < 10⁻⁵.

Most methods discretize a quantum trajectory. We made the network the solution.

Open quantum systems evolve continuously, governed by the Lindblad master equation. Classical solvers chop that evolution into a grid; a physics-informed neural network instead represents the density matrix as a continuous function of time that satisfies the equation everywhere.

The catch: a generic network output is almost never a valid quantum state. DeCoN-PINN closes that gap by changing what the network outputs — building the density matrix from a Gram factorization so that Hermiticity, positivity, and unit trace hold automatically, at every point, throughout training.

01 — Architecture

Valid by construction

The network predicts an auxiliary matrix A; the state is built as AA† ⁄ Tr(AA†). A Gram matrix is always Hermitian, positive, and unit-trace — no penalty terms required.

02 — Evaluation

Rigorously measured

100 independent trials under formally defined physical-validity criteria. 99% success against 67% for the penalty-based baseline, same hyperparameters throughout.

03 — Toward SNAP ADS

Scored anomaly detection

The same constraint-aware foundation generalizes into SNAP ADS — scored neural activation patterns for continuous-confidence anomaly detection beyond the quantum lab.

What constraint preservation buys you.

Across 100 seeds with identical hyperparameters, the architecture holds machine precision where penalty-based training drifts off the manifold of valid quantum states entirely.

99%
Trials producing a fully valid quantum state, vs 67% for the baseline.
10⁻¹⁵
Trace error held at machine precision throughout evolution.
0
Constraint-violation failures — the lone miss was a numerical edge case.
Figure — trace error & minimum eigenvalue vs time
Fig.Baseline (drifts, dips below zero) versus DeCoN-PINN (flat at machine precision, always non-negative).

Understand the why behind the result.

Fifty short lessons take you from a single qubit to the architecture — no prior quantum background assumed.