PI-VIB-ResNet: Technical Overview

Background

The KTBIX project transitions from the published AE-BPNN baseline (Güneşer et al., Scientific Reports 2025, DOI: 10.1038/s41598-025-12771-4) to a significantly more powerful architecture: the Physics-Informed Variational Information Bottleneck with Residual Neural Network (PI-VIB-ResNet).

The core limitation of the AE-BPNN approach — and of purely data-driven EIS models generally — is noise entanglement: measurement noise in the EIS spectrum is encoded alongside structural aging features, degrading SOH prediction accuracy under real-world operating conditions.

The PI-VIB Encoder

The Variational Information Bottleneck (VIB) [Alemi et al., ICLR 2017] learns a latent representation Z of the input X (the impedance spectrum) that maximally compresses irrelevant information while preserving what is predictive of the label Y (SOH).

The information-theoretic objective is:

$\min_{p(z|x)} \; I(X; Z) - \beta \cdot I(Z; Y)$

where $\beta$ controls the compression–accuracy trade-off.

Physics Loss Term

KTBIX adds a novel physics consistency loss $\mathcal{L}_{\text{physics}}$ that penalizes latent representations inconsistent with known electrochemical constraints derived from the Randles equivalent circuit:

$\mathcal{L}_{\text{total}} = \mathcal{L}_{\text{MSE}} + \lambda_{\text{KL}} \cdot D_{KL}(q(Z|X) \| p(Z)) + \lambda_{\text{phys}} \cdot \mathcal{L}_{\text{physics}}$

The physics loss enforces:

• Monotonic degradation of charge-transfer resistance $R_{ct}$ with cycling
• Warburg diffusion element consistency with electrolyte conductivity
• CPE exponent bounds from validated battery models

The ResNet-BPNN Regressor

The latent vector extracted by the VIB encoder feeds into a Residual Backpropagation Neural Network (ResNet-BPNN):

• Residual skip connections every 2 layers prevent gradient vanishing
• Enables 12–18 layer depth without performance degradation
• Trained end-to-end with the VIB encoder using the combined loss

# Simplified PI-VIB-ResNet forward pass
def forward(self, eis_spectrum):
    # VIB encoding
    mu, log_var = self.encoder(eis_spectrum)
    z = self.reparameterize(mu, log_var)
    
    # Physics constraint check
    phys_loss = self.physics_loss(z, eis_spectrum)
    
    # ResNet-BPNN regression
    soh = self.resnet_bpnn(z)
    
    return soh, mu, log_var, phys_loss

Pipeline

Raw EIS Data
    │  (Nyquist spectra from EIS analyzer)
    ▼
Wavelet Denoising
    │  (DWT multi-level noise suppression)
    ▼
Feature Scaling
    │  (min-max normalization + impedance mapping)
    ▼
VIB Latent Extraction  ←── Physics Loss (Randles circuit)
    │  (μ, σ → z via reparameterization trick)
    ▼
ResNet-BPNN
    │  (12–18 residual layers)
    ▼
SOH Estimate (%)
    │  RMSE ≤1.2% target
    ▼
BMS Integration

Expected Performance

Metric	AE-BPNN (Baseline)	PI-VIB-ResNet (Target)
RMSE	~1.8%	≤1.2%
MAE	~1.4%	≤0.9%
R²	~0.96	≥0.98
Cross-chemistry generalization	Limited	Strong (via physics loss)
Noise robustness	Moderate	High (VIB disentanglement)

Key Innovations

1. Noise Disentanglement — VIB compression separates measurement noise from aging signatures
2. Physics Consistency — $\mathcal{L}_{\text{physics}}$ prevents physically impossible predictions
3. Residual Depth — ResNet skip connections enable complex capacity-impedance mappings
4. Industrial Validation — Tested on real T-EV and TOGG field data (not just lab batteries)

References

• Alemi et al. (2017). Deep Variational Information Bottleneck. ICLR 2017
• Güneşer et al. (2025). AE-BPNN for Battery SOH via EIS. Scientific Reports. DOI: 10.1038/s41598-025-12771-4
• Randles (1947). Kinetics of rapid electrode reactions. Discuss. Faraday Soc.