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

TL;DR

This paper introduces a physics-informed neural network framework that accurately infers biophysical parameters and hidden states in complex neuronal models using limited, noisy data, overcoming challenges faced by traditional methods.

Contribution

The authors develop a novel PINN-based approach for joint state and parameter estimation in multiscale neuronal systems, demonstrating robustness and accuracy across various models.

Findings

Effective reconstruction of unobserved states from partial data

Robust parameter estimation despite non-informative initial guesses

Applicable to multiple neuronal regimes with limited observations

Abstract

Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models, where strong nonlinearities, multiscale dynamics, and limited observational data often lead to severe sensitivity to initial parameter guesses and convergence failure in the methods replying on the traditional numerical forward solvers. In this work, we developed a physics-informed neural network (PINN) framework for the joint reconstruction of unobserved state variables and the estimation of unknown biophysical parameters in neuronal models. We demonstrate the effectiveness of the method on biophysical neuron models, including the Morris-Lecar model across multiple spiking and bursting regimes and a respiratory model neuron. The method requires only partial voltage observations over short observation windows and remains robust even when initialized with non-informative parameter guesses. These results suggest that PINN can deliver robust and accurate parameter inference and state reconstruction, providing a promising alternative for inverse problems in multiscale neuronal dynamics, where traditional techniques often struggle.