TY - EJOU AU - Idrees, Hassaan AU - Budarapu, Pattabhi Ramaiah AU - Paggi, Marco TI - Physics-Informed Neural Networks for Hail-Impact Dynamics of Photovoltaic Panels: Multi-Condition Forward Modeling and Inverse Identification of Contact Stiffness T2 - Computers, Materials \& Continua PY - VL - IS - SN - 1546-2226 AB - Hail impacts on photovoltaic laminates generate strongly nonlinear contact forces whose polynomial restoring form and coefficients govern the resulting damage pattern. Predicting the dynamic response across a range of impact velocities, and inferring substrate properties from post-event vibration measurements, are two tasks that classical time-integration schemes do not address in a unified manner. This work develops a physics-informed neural network (PINN) framework that handles both. For the forward problem, the network is conditioned on the initial velocity and trained simultaneously at four representative hail-impact speeds, i.e.,

v_{0} \in {2, 3, 4, 6}

m/s, so that it learns a solution operator rather than a single trajectory; relative

L^{2}

errors against Newmark-

β

reference solutions reach

10^{- 3}

for the soft and medium substrate regimes and

10^{- 4}

for the hard regime, in both undamped and damped configurations. The predictive performance of the PINN was evaluated across both interpolation and extrapolation scenarios. For interpolation at an initial velocity of 5 m/s, the model achieved computational speed-ups of approximately 30×, 19×, and 4× for soft, medium, and hard undamped stiffness, respectively. Furthermore, in an extrapolation scenario at 7 m/s, the model demonstrated a 40× speed-up for the soft undamped case. For the inverse problem, a two-phase algorithm alternates network refinement with an analytical least-squares update under gradient-balanced physics regularization and an exponential loss ramp. All polynomial stiffness coefficients are recovered within 6% of their true values from as few as 300 sparse displacement–velocity samples, and the damping coefficient with an error below 1%. Benchmark verification on the Duffing and belt–mass oscillators yields parameter errors below 0.4%, confirming that the strategy is not tied to the polynomial restoring-force structure. The inverse methodology was then evaluated using data corrupted by Gaussian noise, demonstrating robust noise insensitivity. Although the coefficients for the soft, medium, and hard substrates differ by one to two orders of magnitude, the achieved identification accuracy is sufficient to discriminate substrate type and, by extension, to flag mechanical degradation of a PV backing layer from data obtained through numerical simulation. For future work, the proposed model should be evaluated using similar experimental data. KW - Physics-informed neural networks; hail impact dynamics; photovoltaic panel structural integrity; inverse parameter identification; nonlinear contact stiffness; multi-condition training DO - 10.32604/cmc.2026.085634