Parameter Recovery and Noise Sensitivity of Physics-Informed Neural Networks for Michaelis–Menten Kinetics: A Benchmark Against Classical Nonlinear Least Squares
Abstract
This study evaluates a physics-informed neural network (PINN) for estimating Michaelis–Menten kinetic parameters from sparse and noisy concentration–time observations. The investigated system follows the ordinary differential equation , with a true maximum reaction rate of , Michaelis constant , initial substrate concentration , and a simulation duration of 10 time units. Synthetic observations were generated using numerical integration and additive Gaussian noise at 1% and 5% levels. The PINN consisted of a fully connected neural network with three hidden layers, 32 hidden units, and hyperbolic tangent activation functions. Its trainable kinetic parameters were constrained to positive values using the softplus transformation. Training minimized a weighted combination of data error, initial-condition error, and differential-equation residual error. To address optimization instability, the study used an increased training budget of up to 8000 epochs, early stopping, multiple initialization seeds, and cross-validation for selecting the physics-loss weight. A classical nonlinear least-squares estimator was used as a comparison method. In a diagnostic example, the corrected PINN produced errors of 1.04% for and 5.10% for , compared with 2.99% and 19.32% for the classical method. However, across the small benchmark of 18 replicates, the classical method generally achieved lower median errors and lower prediction RMSE, especially under 5% noise. The results show that the PINN can recover kinetic parameters accurately in favorable conditions, but its performance remains sensitive to data quantity, noise, optimization, and experimental design.
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BibTeX
@misc{rehman2026parameter,
title = {{Parameter Recovery and Noise Sensitivity of Physics-Informed Neural Networks for Michaelis–Menten Kinetics: A Benchmark Against Classical Nonlinear Least Squares}},
author = {Mateen Ur Rehman},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15009723/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009723/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Parameter Recovery and Noise Sensitivity of Physics-Informed Neural Networks for Michaelis–Menten Kinetics: A Benchmark Against Classical Nonlinear Least Squares
AU - Mateen Ur Rehman
PY - 2026
DA - 2026/10/01
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009723/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009723/v1
AB - This study evaluates a physics-informed neural network (PINN) for estimating Michaelis–Menten kinetic parameters from sparse and noisy concentration–time observations. The investigated system follows the ordinary differential equation , with a true maximum reaction rate of , Michaelis constant , initial substrate concentration , and a simulation duration of 10 time units. Synthetic observations were generated using numerical integration and additive Gaussian noise at 1% and 5% levels. The PINN consisted of a fully connected neural network with three hidden layers, 32 hidden units, and hyperbolic tangent activation functions. Its trainable kinetic parameters were constrained to positive values using the softplus transformation. Training minimized a weighted combination of data error, initial-condition error, and differential-equation residual error. To address optimization instability, the study used an increased training budget of up to 8000 epochs, early stopping, multiple initialization seeds, and cross-validation for selecting the physics-loss weight. A classical nonlinear least-squares estimator was used as a comparison method. In a diagnostic example, the corrected PINN produced errors of 1.04% for and 5.10% for , compared with 2.99% and 19.32% for the classical method. However, across the small benchmark of 18 replicates, the classical method generally achieved lower median errors and lower prediction RMSE, especially under 5% noise. The results show that the PINN can recover kinetic parameters accurately in favorable conditions, but its performance remains sensitive to data quantity, noise, optimization, and experimental design.
ER -