Detect structural mismatch in time-series systems that appear identical under conventional metrics such as power spectral density.

SOHM Research Labs develops a spectral-geometry diagnostic basis for comparing time-series signals beyond power spectral density and autocorrelation.

The method operates on delay-embedded representations of signals, capturing the underlying geometry of their dynamics rather than frequency content alone.

From these embeddings, a small set of coordinates is extracted — including spectral gap, concentration (SMK), alignment, and entropy — forming a compact structural signature of the signal.

These coordinates enable detection of structural differences between signals or models, even when conventional metrics indicate agreement.

In controlled experiments across multiple signal classes, different error types produce distinct signatures across this basis, enabling detection and classification of structural mismatch.

The Problem

Modern sensing and simulation systems routinely process signals that are degraded, noisy, or structurally inconsistent with their intended models.

In simulation environments, this often appears as agreement under PSD-based metrics despite underlying dynamical mismatch.

This leads to wasted compute, unreliable outputs, and difficulty diagnosing model or solver failure.

Our Approach

This framework introduces a structure-detection layer upstream of computation.

It answers one question:

Is there real structure here, and does it match what we expect?

This determination is made directly on the signal prior to downstream processing.

No training is required.  

No labels are required.  

No model assumptions are required.

Deployment

The method is designed to integrate into simulation validation workflows, data pipelines, and real-time systems as a lightweight structural comparison layer.

It can be used to compare signals, validate models, or detect structural deviations across runs.

Typical Use Cases:

– Comparing simulation outputs to reference data

– Detecting solver or model drift across runs

– Validating signal integrity prior to downstream processing

Primary Applications

– Digital twin validation  

– Simulation model comparison  

– Solver regression testing  

– Real-time signal integrity monitoring  

Technical References

– Spectral Edge Behavior in Delay-Embedded Systems  

– Koopman Spectral Fingerprints for Time-Series Structure

These works provide the mathematical and experimental foundation for the spectral-geometry approach described above.

Status

Patent pending. Technology available for technical evaluation and integration discussions.