Physics-informed neural modeling of TiO2 photoanode thickness-dependent electron transport and photovoltaic performance in dye-sensitized solar cells

The thickness of a photoanode in dye-sensitized solar cells (DSSCs) simultaneously influences the dye-accessible volume, optical path length, electron-transport distance and recombination. To estimate this competition, a physics-informed neural network was constructed based on the six compressed TiO 2 photoanodes used by Tsai et al. The spatial state is expressed as a random-feature (RF) neural field u θ (x i , d), with normalized depth, x i = x/d, and film thickness, d. The field is bound by a steady-state diffusion-generation-recombination equation, and extraction and zero-flux boundary conditions. In the 6 devices dataset, the contact-gradient current was mapped with a low-capacity regularized thickness correction, using the PDE result as a fixed value (inverse parameters effective electron diffusion coefficient, electron lifetime, effective photon flux and photon flux). The analytic solution of contact current and relative least square (L 2 ) error of 0.997–1.001 and 0.08–0.68% respectively confirmed the neural field. The last device model resulted in training Mean Absolute Percentage Errors (MAPEs) of 7.03% for J SC , 1.00% for V OC , 1.55% for FF, and 6.44% for algebraically consistent efficiency. The efficiency MAPE of leave-one-thickness-out validation outperformed the results of linear regression (27.76%), quadratic regression (26.08%), natural cubic spline interpolation (78.42%), Gaussian-process regression (19.34%), and a conventional ANN (20.15%). The continuous model gave optimum thickness as 29.72 µm at 8.70% efficiency, while jackknife resampling revealed that the thickness has a significant uncertainty, as only six devices exist. A frozen model transfer to an independent published thickness series yielded the MAPE of 17.10%, indicating a low level of cross-system transfer, and a need for morphology and electrolyte-aware inputs. The study thus presents a physics-regularized small data framework that discriminates between within-system predictive value and universal DSSC generalization, which can be replicated.