Phase F · Virtual Sensor

Infer hidden parameters (θ)

Paste a measured polarization curve and the Neural Posterior Estimation (NPE) virtual sensor returns the posterior distribution over hidden physical parameters — exchange current density, Tafel slope, biofilm conductivity, and friends — with calibrated credible intervals, a posterior-predictive fit score, and an out-of-distribution flag.

Research preview

This virtual sensor calls the Neural Posterior Estimation inference service. Where that service is not connected, submissions return a graceful “offline” notice instead of results. v1 supports MFC (anodic oxidation) only; other system classes are shown disabled.

Observation

System class

Observation mode

Transfer mode

Polarization curve (CSV)

Reactor conditions (optional)

Temperature (°C)pHAnode area (cm²)Electrode spacing (mm)Biofilm thickness (μm)

Posterior

Paste a polarization curve and submit to see the posterior over hidden θ.

Why these results?

The NPE was trained on simulator draws from the Butler-Volmer + Monod kinetics family (anodic oxidation) with priors over exchange current density, Tafel slope, biofilm conductivity, half-saturation constant, and biofilm thickness. Identifiability is limited under polarization-only observation: Fisher-rank analysis on the simulator showed that D_eff and the Thiele modulus φ are jointly identifiable but individually collapse — the NPE reports the collapsed posterior and flags the affected θ.

The ppc_score is the posterior-predictive fit on the observed curve (0–1; higher is better). The ood_flag uses conformal calibration on a held-out simulator set — when the observed curve's likelihood under the posterior is below the conformal threshold, the flag fires.