┌─────────────────────────────────────────┐
│  BMS Signals (11 features)              │
│  V, I, T, R, Q_charge, Q_discharge,    │
│  charge_time, η_energy, η_coulombic,   │
│  dQ/dV, dV/dQ                           │
└──────────────┬──────────────────────────┘
               │
┌──────────────▼──────────────────────────┐
│  STAGE 1: Physics-Informed Degradation  │
│  Estimator (Deep Neural Network)        │
│  ├─ Arrhenius temperature gating        │
│  ├─ Cycle positional embedding          │
│  ├─ Monotonicity constraint loss        │
│  └─ Outputs: 7 degradation features     │
│     • SEI layer thickness               │
│     • Lithium inventory loss             │
│     • Active material loss (an/ca)       │
│     • Resistance growth                  │
│     • Electrolyte decomposition          │
│     • Lithium plating                    │
└──────────────┬──────────────────────────┘
               │
┌──────────────▼──────────────────────────┐
│  STAGE 2: RUL Predictor Ensemble        │
│  ├─ Gradient Boosted Trees (GBT)        │
│  ├─ Neural Network                       │
│  └─ Weighted ensemble                    │
│  Input: BMS + Predicted Degradation      │
│  Output: Remaining Useful Life (cycles)  │
└─────────────────────────────────────────┘

Results

Metric	Value
MAE	111.72 cycles
RMSE	140.22 cycles
R²	0.9215
MAPE	50.41%

Physics-Informed Design

Stage 1: Degradation Estimator

Based on electrochemical battery degradation models from the literature:

SEI Growth: Arrhenius kinetics with diffusion-limited square-root scaling (Wang et al.)
Lithium Inventory Loss: Proportional to SEI thickness + power-law cycling
Active Material Loss: Stress-based fatigue model with temperature dependence
Electrolyte Decomposition: First-order reaction kinetics
Lithium Plating: Temperature and C-rate dependent nucleation

Key physics constraints in the loss function:

Monotonicity: Degradation features must increase with cycling
Arrhenius Gating: Temperature modulates hidden layer activations
Softplus Output: Ensures non-negative degradation predictions

Stage 2: RUL Predictor

Combines BMS signals with predicted degradation features using an ensemble:

Gradient Boosted Trees for robust non-linear feature interactions
Neural Network for pattern recognition
Optimized ensemble weights via validation-set grid search

Input Features

BMS Observable Signals

Feature	Description	Unit
voltage	Terminal voltage	V
current	Charge/discharge current	A
temperature_measured	Cell temperature	°C
internal_resistance	Measured via pulse test	mΩ
charge_capacity	Charge capacity	Ah
discharge_capacity	Discharge capacity	Ah
charge_time	Time to full charge	s
energy_efficiency	Round-trip energy efficiency	-
coulombic_efficiency	Charge/discharge ratio	-
dqdv_peak_height	Differential capacity peak	Ah/V
dvdq_peak_height	Incremental capacity peak	V/Ah

Operating Conditions

Feature	Description	Unit
cycle	Cycle number	-
c_rate	Charging C-rate	C
depth_of_discharge	Depth of discharge	-

Based on Research

Hassanaly et al. (2023) — PINN surrogate of Li-ion battery models (arXiv:2312.17329)
Nicolae et al. (2024) — Physics-informed cycle life prediction (arXiv:2404.17174)
Wang et al. — Arrhenius-based capacity fade model for SEI formation
Microsoft BatteryML — Open-source battery degradation platform

Usage

python

import torch
import numpy as np
import joblib
import json

# Load model components
config = json.load(open('config.json'))
# ... (see repository for full loading code)

dikshant1103/battery-rul-predictor

Battery RUL Predictor — Two-Stage Physics-Informed ML Model

Architecture

Results

Physics-Informed Design

Stage 1: Degradation Estimator

Stage 2: RUL Predictor

Input Features

BMS Observable Signals

Operating Conditions

Based on Research

Usage

dikshant1103/
battery-rul-predictor