Anomaly Classification via Physics-Informed Loss Geometry

We propose using physics loss as a system diagnostic tool rather than a training validation protocol in data sparse systems. We demonstrate the core operating principles by an example of an unsupervised anomaly classification via physics-informed LSTM network in a time-series data.

At inference time, the physics-informed LSTM autoencoder maps each signal window into a 2D loss space, consisting of

• Reconstruction error (log MSE)
• Physics violation (log residual)

We find that this space becomes linearly separable by anomaly type, enabling structured separation of anomaly types in physics-induced loss space.

Key finding

Physics-informed losses induce structured geometry in error space, where different anomaly modes occupy distinct regions. This enables

• unsupervised anomaly detection
• downstream anomaly type classification in the same representation space

Main results

Across 30 seeds and 4 frequencies

• detection improves consistently under physics constraints
• classification benefit is strongest in data sparse regimes

2D loss space

Small vs large dataset

Small dataset	Large dataset

For a more in-depth explanation, see notes.md. These notes contain more quantative information and additional figures.

Tech stack

• PyTorch
• NumPy / SciPy
• scikit-learn (GMM, kNN)
• Optuna (hyperparameter search)
• MLflow (experiment tracking)