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Open access Aug 2026

Boosted training strategy for physics-informed neural networks in modeling non-linear computer virus dynamics with vertical transmission

A Physics-Informed Neural Network based framework for an e-epidemic SI1I2R model of computer-virus spread that incorporates a possibly transmissible class, an amply transmissible class, and direct transmission, allowing nodes to be initially compromised without contact is developed.

Jamshaid Ul Rahman, Shanza Shabeer, Noreen Mustafa et al. · 0 citations
Open access Jul 2026

Physics-Informed Neural Networks (PINNs) for Parameter Estimation in the SIRS-D Epidemiological Model

Infectious diseases exhibit complex and rapidly evolving transmission dynamics, requiring modeling approaches that can accurately capture these mechanisms. The SIRS-D compartmental model provides a suitable framework, as it incorporates temporary immunity and disease-induced mortality within the epidemic process. Accurate parameter estimation is essential for quantifying the transmission rate, recovery rate, waning immunity rate, and mortality rate, which collectively govern the system behavior. Among existing estimation methods, Physics-Informed Neural Networks (PINNs) offer significant advantages by integrating observational data with the underlying structure of differential equations, thereby preserving physical consistency while maintaining robustness under imperfect data conditions. In this study, PINNs are employed to estimate the parameters of the SIRS-D model using synthetic data generated through the fourth-order Runge–Kutta (RK4) method to ensure stable and consistent numerical solutions. To better represent real-world measurement conditions, 5% noise is added to the synthetic data, introducing realistic variability into the training process. The results demonstrate that PINNs successfully reconstruct the trajectories of S(t), I(t), R(t), and D(t) with low prediction errors. The model achieves MAE values of 0.0065 (S), 0.0067 (I), 0.0208 (R), and 0.0043 (D), with corresponding RMSE values of 0.0090, 0.0074, 0.0253, and 0.0058. Moreover, the estimated parameters closely match the true values, yielding ????????=0.5031, ????=0.0996, ????=0.0095, and ????=0.0149, demonstrating strong parameter identification capability. These findings confirm that PINNs constitute a reliable and accurate framework for analyzing infectious disease dynamics and offer promising potential for extension to more complex epidemiological models and real-world datasets.

Fitri Cahyani, Abdurakhman Abdurakhman, Chyntia Meininda Anjanni · 0 citations
Jul 2026

Multi-scale physics-informed neural networks with Fourier features for approximating time-fractional PDEs

Extensive numerical experiments demonstrate that PINNs-MSFF achieves superior accuracy, stability, and convergence, effectively capturing complex fractional dynamics, sharp localized gradients, and dispersive phase transitions where standard PINNs often fail.

Harender Kumar · 0 citations
Aug 2026

SUC–PINNs: A physics-informed neural networks approach to inverse problems in epidemic models with partial observability

Experiments with synthetic data and COVID-19 surveillance data show that SUC–PINN recovers plausible hidden infection trajectories, yields stable parameter estimates, and provides accurate short-term forecasts, support SUC–PINN as a practical computational approach for inverse modeling and prediction in partially observed epidemic dynamics.

U. M. Rifanti, N. Susyanto, Ratinan Boonklurb · 0 citations
Open access Jul 2026

Fractional Physics Informed Neural Networks for Surrogate Modeling of Non-Markovian Discrete-Time Quantum Walks

Predicting anomalous diffusion in quantum walks with non-Markovian environmental noise is computationally demanding. We introduce FracPINN, a fractional physics-informed neural network that embeds a fully differentiable, PyTorch-based Caputo PDE solver into a classical LSTM encoder. Rather than replacing classical predictors, FracPINN acts as a compact physics regularizer that constrains the inference with emergent fractional transport dynamics; every physics-informed loss component is strictly label-free, and the ground-truth exponent enters only through an explicitly supervised regression term. Evaluated on 3709 non-Markovian DTQW simulations with exponentially correlated Gaussian coin noise (filtered from 5000 raw samples to the physically admissible exponent range), FracPINN achieves a mean absolute error of 0.214 and R2=0.682 on held-out test data, outperforming classical baselines by 5.3% in terms of the MAE overall, while adding only four interpretable physical parameters. Notably, gains concentrate in the sub-diffusive regime where memory effects dominate, with a 13.5% MAE improvement over the baseline there, yet the normal and super diffusive accuracy remains intact. Once trained, the surrogate reduces inference from seconds of simulation to fractions of a millisecond per sample. These results show that our fractional PDE networks are most compelling as targeted physics refinements with minimal overhead within stable classical pipelines.

Zhaoyu Zhu, Ming-Xin Liu, Chengtian Liang et al. · 0 citations

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