Physics-informed neural networks (PINNs) offer a promising framework for modeling semiconductor devices, yet standard architectures struggle with severe numerical stiffness and multiscale spatial discrepancies inherent to oxide heterostructures. Here, we demonstrate a cascaded PINN architecture coupled with a custom second-order Chebyshev second kind polynomial spectral optimizer (DSO V2 Hybrid) to model ion-electronic drift-diffusion transport in Pt/SrTiO3/Si memristive heterostructures across a 20 nm STO film on a 380 μm Si substrate. By isolating potential, carrier density, and vacancy transport into four sequentially trained sub-neural-networks, our model circumvents condition numbers exceeding 1016 without operator splitting. The trained surrogate reproduces experimental conductive-AFM current-voltage hysteresis (R2>0.96) while ensuring strict Poisson consistency across continuous space. Compared to conventional finite-element solvers (e.g., COMSOL), the PINN surrogate enables differentiable inverse parameter estimation and linear time inference.
This study develops a dimensionless multi-domain physics-informed neural network (PINN) framework for electro-osmotic radial consolidation considering smear effects and combined vacuum and surcharge loading. Three PINN-based models are investigated: a standard soft-constrained PINN (Std-PINN), a modified gated PINN (Mod-PINN), and a modified gated PINN with hard-constraint boundary encoding (Mod-HC-PINN). The models are evaluated against FEM reference solutions under four loading cases, including constant vacuum, exponential vacuum, exponential vacuum with ramp surcharge, and exponential vacuum with cyclic haversine surcharge. The results indicate that the gated architecture applied in Mod-PINN improves the resolution of steep pressure gradients near the cathode and smear-zone interface under constant vacuum loading. Under time-dependent loading, the soft-constrained Mod-PINN shows reduced accuracy because it must learn multiple competing objectives simultaneously. The Mod-HC-PINN mitigates this issue by embedding the cathode boundary and initial conditions into the output structure, thereby reducing the optimization burden and improving physical consistency. The Mod-HC-PINN achieves MAE values of 0.43, 0.41, and 0.27 kPa for the exponential vacuum, ramp surcharge, and cyclic surcharge cases, respectively. Sensitivity analyses further demonstrate that the proposed framework remains robust across practical ranges of network architecture, collocation density, and permeability contrast.
In this work, we develop an inverse Physics-Informed Neural Network (PINN) framework to infer the dependence of the scrape-off layer (SOL) perpendicular heat conductivity on plasma density and temperature, κ⊥(n,T). The method combines radial profile measurements of electron density and temperature with the residual of a reduced one-dimensional SOL transport equation, so that the inferred conductivity is constrained by both the measurements and the underlying transport model. Three neural networks are trained simultaneously: two reconstruct the temperature and density profiles as functions of the radial coordinate and transported power, while a third represents the effective conductivity as a function of the local density and temperature. The framework is first validated using synthetic data generated from a prescribed conductivity function, allowing the inferred κ⊥(n,T) to be compared directly with the ground truth. The model recovers the imposed functional dependence with errors below 10% in the data-constrained region. Bootstrap resampling is shown to provide a practical indicator of prediction reliability and consistency. A scan in the number of plasma profiles used for training and the number of radial measurement positions per profile identifies a practical trade-off between reconstruction accuracy and data availability. Finally, the method is applied to an experimental dataset from the TJ-II stellarator obtained with the helium-beam diagnostic. This exploratory application provides an initial estimate of the effective SOL conductivity and illustrates the potential of inverse PINNs for extracting transport information from plasma edge measurements.
J. Gallego (Departamento de Tecnología, CIEMAT, Spain) +23
Physics-Informed Neural Networks (PINNs) are a common class of machine learning-based partial differential equation (PDE) solvers which train a network to represent a solution by minimizing a residual loss that encodes the PDE. Despite their successes, they are known to fail on certain simple equations, converging to an incorrect solution despite low loss. These failure modes have garnered significant attention in the literature over the past several years, motivating both architectural and optimization based solutions. By directly visualizing the residual, we show that failure modes are the result of overfitting: the loss is minimized on the collocation points, but not elsewhere. Applying regularization causes the failure modes to vanish. Finally, we extend double backpropagation over the full set of residuals, and use it to achieve state-of-the-art performance on four standard failure mode equations with up to 23× fewer collocation points and a vanilla architecture.