Data-driven multi-agent modelling of calcium interactions in cell culture: PINN vs Regularized Least-squares
Authors: Aurora Poggi, Giuseppe Alessio D'Inverno, Hjalmar Brismar, Ozan Öktem, Matthieu Barreau, Kateryna Morozovska
Organizations: KTH Royal Institute of Technology, Department of Mathematics, Stockholm, Sweden · International School for Advanced Studies (SISSA), Trieste, Italy · KTH Royal Institute of Technology, Department of Biophysics, Stockholm, Sweden · KTH Royal Institute of Technology, Department of Intelligent Systems, Stockholm, Sweden
Data-driven discovery of dynamics in biological systems allows for better observation and characterization of processes, such as calcium signaling in cell culture. Recent advancements in techniques allow the exploration of previously unattainable insights of dynamical systems, such as the Sparse Identification of Non-Linear Dynamics (SINDy), overcoming the limitations of more classic methodologies. The latter requires some prior knowledge of an effective library of candidate terms, which is not realistic for a real case study. Using inspiration from fields like traffic density estimation and control theory, we propose a methodology for characterization and performance analysis of calcium delivery in a family of cells. In this work, we compare the performance of the Constrained Regularized Least-Squares Method (CRLSM) and Physics-Informed Neural Networks (PINN) for system identification and parameter discovery for governing ordinary differential equations (ODEs). The CRLSM achieves a fairly good parameter estimate and a good data fit when using the learned parameters in the Consensus problem. On the other hand, despite the initial hypothesis, PINNs fail to match the CRLSM performance and, under the current configuration, do not provide fair parameter estimation. However, we have only studied a limited number of PINN architectures, and it is expected that additional hyperparameter tuning, as well as uncertainty quantification, could significantly improve the performance in future works.
Figures & tables
Figure 1: Structure of PINNs for inverse problems.
Figure 2: First frame of cell culture showing calcium signaling.
Figure 3: Frame 145 containing a hot pixel, leading to artifacts in the image.
Figure 4: Before and after median filter is applied to a frame containing a hot pixel.
Figure 5: Results obtained with cellpose segmentation on a selected frame.
Nonlinear system identification must balance physical interpretability with model flexibility. Classical methods yield structured, control-relevant models but rely on rigid parametric forms that often miss complex nonlinearities, whereas Neural ODEs are expressive yet largely black-box. Physics-Informed Neural Networks (PINNs) sit between these extremes, but inverse PINNs typically assume a known governing equation with fixed coefficients, leading to identifiability failures when the true dynamics are unknown or state-dependent. We propose SOLIS, which models unknown dynamics via a state-conditioned second-order surrogate model and recasts identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation, recovering interpretable natural frequency, damping, and gain without presupposing a global equation. SOLIS decouples trajectory reconstruction from parameter estimation and stabilizes training with a cyclic curriculum and Local Physics Hints windowed ridge-regression anchors that mitigate optimization collapse. Experiments on benchmarks show accurate parameter-manifold recovery and coherent physical rollouts from sparse data, including regimes where standard inverse methods fail.
Murat Furkan Mansur, Tufan Kumbasar
AI and Intelligent Systems Laboratory, Istanbul Technical University, 34469, Istanbul, Türkiye
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.
Changliang Wei, Yangyang Wang, Xueyu Zhu
Department of Mathematics, University of Iowa, Iowa City, IA 52246, USA. · Department of Mathematics, Volen National Center for Complex Systems, Brandeis University, Waltham, MA 02453, USA.
A staged physics-informed neural network (PINN) is proposed for identifying the inductance, capacitance and parasitic resistances of a DC buck converter from time-domain data. Gradients are released in the order of L to C to rL to rC, a sequence derived from sensitivity analysis. The five-stage schedule recovers L and C to within 5% and the series ESR to 10%, while a three-stage variant attains the same accuracy 11% faster. An 84 factorial sweep confirms that the trained PINN remains accurate for simultaneous 8% perturbations of all four components, achieving a waveform RMSE of 2.6 x 10-2 over 5 ms-an order-of-magnitude better than a simultaneous-training baseline.