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

TL;DR

A physics-informed neural network framework for the joint reconstruction of unobserved state variables and the estimation of unknown biophysical parameters in neuronal models is developed, suggesting that PINN can deliver robust and accurate parameter inference and state reconstruction.

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.

Figures (15)

• Figure 2.1: Comparison of the signal filtering results under different parameter choices. The left panel corresponds to $p=95$, while the right panel corresponds to $p=99$. In each subplot, the observed noisy signal is filtered and compared against the ground-truth signal.
• Figure 2.2: Illustration of the architecture of the proposed PINN, using model \ref{['eq:ex_model_de1']}--\ref{['eq:ex_model_de3']} with state variables $(V, n, \mathrm{Ca})$ as an illustrative example.
• Figure 3.1: Time trajectories of the solution of the spiking Morris–Lecar model under three distinct bifurcation regimes: Hopf (first column), SNIC (second column) and Homoclinic (third column). Each row corresponds to one state variable: voltage $V$, gating variable $n$.
• Figure 3.2: Comparison between the ground-truth trajectories and the PINN-reconstructed trajectories for the Hopf regime under two noise levels based on the non-informative initial guess. PINN predictions are shown as dashed blue lines, while the observation voltage $V$ and ground-truth gating $n$ trajectories are shown as solid yellow lines.
• Figure 3.3: Comparison between the ground-truth trajectories and the PINN-reconstructed solutions for the SNIC regime under two noise levels based on the non-informative initial guess, where the PINN predictions are shown as dashed blue lines and the observation voltage $V$ and ground-truth gating $n$ trajectories are shown as solid yellow lines.