Md Sadik Yasir Tauki - Physics-Informed Neural Network Model

Physics-Informed Neural Network for Ferroelectric Capacitor Modeling and Parameter Extraction
Combining ferroelectric device physics with neural networks to accelerate compact-model calibration, reconstruct hidden polarization states, and predict device response under previously unseen waveforms.

Project Overview
This project develops a physics-informed neural network, or PINN, for modeling the history-dependent electrical response of metal–ferroelectric–metal capacitors. Ferroelectric parameter extraction is challenging because polarization depends not only on the instantaneous voltage but also on voltage history, sweep direction, frequency, pulse duration, domain configuration, and previous switching events.

A purely data-driven neural network may reproduce measured curves but can violate physical constraints, fail under unseen waveforms, or predict nonphysical polarization states. The proposed PINN embeds the governing equations of irreversible domain switching and reversible dielectric response directly into the training objective.

The network receives electrical excitation and history-related variables as inputs and predicts internal ferroelectric states such as switched-domain fraction, irreversible polarization, reversible domain-wall response, and total terminal charge. Experimental measurements are combined with physical residual losses so that the learned model remains consistent with ferroelectric switching kinetics, charge conservation, bounded state variables, and domain-wall dynamics.

Key Features

🧠 Physics-Informed Learning: Trains the neural network using both experimental data and ferroelectric governing equations.

🔁 History-Dependent Inputs: Includes voltage, time, waveform frequency, amplitude, sweep direction, and previous polarization state.

🧲 Hidden-State Reconstruction: Estimates internal states such as switched-domain fraction and domain-wall activity that are not directly measurable.

📉 Joint P–V and C–V Learning: Learns large-signal polarization and small-signal capacitance within one state-space framework.

⚡ Fast Surrogate Simulation: Replaces computationally expensive multidomain calculations with rapid neural-network inference.

🔍 Inverse Parameter Extraction: Determines compact-model parameters from measured electrical characteristics.

🌊 Arbitrary Waveform Prediction: Supports triangular sweeps, sinusoidal signals, write pulses, read pulses, minor loops, and mixed waveform sequences.

🧪 Limited-Data Training: Uses physical equations to reduce the amount of experimental data needed for reliable fitting.

Research Contributions

Developed a PINN that combines measured ferroelectric data with governing physical equations.
Predicted hidden states such as domain fraction, irreversible polarization, and domain-wall response.
Enabled joint learning of large-signal P–V and small-signal C–V behavior.
Created an inverse-modeling approach for compact-model parameter extraction.

Technical Achievements

Included voltage history, sweep direction, frequency, and signal amplitude as model inputs.
Enforced switching dynamics, domain-wall motion, charge conservation, and physical state bounds.
Used automatic differentiation to calculate polarization, current, and capacitance.
Built a fast surrogate model for unseen waveforms, minor loops, and pulse sequences.

Tools and Software Used

Python for model development and data preprocessing.
PyTorch / TensorFlow for neural-network training and automatic differentiation.
MATLAB for comparison with the original multidomain compact model.
NumPy and SciPy for numerical processing and parameter optimization.
Experimental P–V and C–V Data for supervised training.
GPU Computing for accelerated PINN training.
Verilog-A / SPICE for transferring extracted parameters into circuit-compatible compact models.
Optimization and Sensitivity Analysis for identifying influential physical parameters.

Applications

Automatic Compact-Model Calibration: Extracting model parameters from measured P–V and C–V datasets with reduced manual tuning.
Fast Ferroelectric Simulation: Providing a computationally efficient surrogate for multidomain transient simulations.
Hidden-State Estimation: Reconstructing domain fraction, reversible polarization, and domain-wall activity from terminal measurements.
Waveform Optimization: Identifying write and read pulses that maximize switching or capacitance contrast while minimizing disturbance.
Non-Destructive Read Design: Predicting operating regions where capacitive-state sensing avoids unwanted polarization reversal.
Device Variability Analysis: Learning distributions of switching barriers and dynamic parameters across devices.
Circuit-Aware Modeling: Generating differentiable device models that can be integrated into circuit and system optimization workflows.
Digital-Twin Development: Creating an adaptive model that can be updated as new device measurements become available.

Impact and Recognition

This project connects physics-based ferroelectric modeling with modern machine learning. Instead of treating the neural network as a black-box curve-fitting tool, the PINN is constrained by the same equations that govern domain switching, reversible wall displacement, and terminal charge.

The resulting model is intended to provide three capabilities simultaneously: physically meaningful hidden-state prediction, rapid forward simulation, and automated inverse parameter extraction. This makes the approach valuable for compact-model development, experimental characterization, waveform design, and device–circuit co-optimization.

Together, the unified analytical model and the PINN form a complementary workflow: the compact model provides interpretability and SPICE compatibility, while the PINN accelerates calibration and captures complex multidimensional dependencies that are difficult to fit manually.