Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks

2026-03-11 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Computational Neuroscience · Depth: Expert, extended

Summary

This work introduces a Physics-Informed Neural Network (PINN) framework for robustly estimating biophysical parameters and reconstructing hidden state variables in multiscale neuronal models from partial and noisy observations. The method addresses challenges like strong nonlinearities, multiscale dynamics, and limited data that hinder traditional numerical forward solvers. The PINN framework incorporates Fourier feature embeddings, random weight factorization, a two-stage training strategy, adaptive loss balancing with residual scaling, and separate learning rate schedules. It was tested on the Morris-Lecar model (spiking and bursting regimes) and a pre-Bötzinger complex respiratory neuron model, demonstrating accurate parameter inference and state reconstruction even with non-informative initial guesses and short observation windows. The framework consistently outperformed traditional methods like Unscented Kalman Filter (UKF) and 4D-Var, particularly under high noise and poor initialization, and successfully reproduced complex bifurcation diagrams.

Key takeaway

For AI Researchers and Computational Neuroscientists developing models of complex biological systems, this PINN framework offers a robust alternative to traditional data assimilation. You should consider adopting its two-stage training and advanced regularization techniques to achieve accurate parameter inference and state reconstruction, especially when dealing with noisy, partial observations and a lack of informative initial parameter guesses. This approach can significantly improve model reliability and reduce sensitivity to initialization challenges.

Key insights

PINNs offer robust parameter and state estimation in multiscale neuronal systems, overcoming limitations of traditional methods.

Principles

• Embed governing equations directly into the training loss.
• Approximate system dynamics as global functions over observation windows.
• Decouple scale and direction of neural network weights for stability.

Method

A two-stage PINN training strategy: initial data-driven pre-training for observed variables, followed by physics-informed training for unobserved states and parameters, enhanced by Fourier features and adaptive loss balancing.

In practice

• Use Fourier feature embeddings for oscillatory signals.
• Implement a two-stage training for observed vs. unobserved variables.
• Apply separate learning rates for network and biophysical parameters.

Topics

• Physics-Informed Neural Networks
• Neuronal Dynamics
• Parameter Estimation
• State Reconstruction
• Multiscale Systems

Best for: AI Researcher, AI Scientist, Research Scientist

Related on AIssential

• Physics-Informed Neural Network with Squeeze-Excitation-like Attention — SEA-PINN uses Squeeze-Excitation-like attention for dynamic neuron recalibration and stable initialization in physics-informed neural networks.
• Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle — This guide demystifies PINN training by exposing the full algebraic cycle, from forward pass to gradient descent.
• Statistical Learning Analysis of Physics-Informed Neural Networks — PINNs can be understood as a statistical learning problem minimizing KL divergence with physics as indirect data.
• Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks — Curvature-aware optimization using secant information significantly improves PINN training stability and accuracy.
• Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential--Algebraic Systems — An extended Newton implicit layer enables simulation-free, accurate operator learning for stiff DAEs by enforcing constraints and reducing dimensions.
• Evolutionary Two-Stage Hyperparameter Optimization Strategies for Physics-Informed Neural Networks — Evolutionary two-stage hyperparameter optimization significantly enhances PINN accuracy and robustness under fixed computational budgets.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.