# Physics-Informed Neural Network Surrogate for Oxygen Vacancy Dynamics in epitaxial SrTiO3 on Si memristors via Dynamic Spectral Optimization

arXiv: https://arxiv.org/abs/2609.02966 · HTML: https://mlsanity.com/paper/2609.02966/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Error estimates for physics informed neural networks approximating the Navier-Stokes equations](https://mlsanity.com/paper/2203.09346/) (2022)
- [The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton](https://mlsanity.com/paper/2510.09378/) (2025)
- [Residual-based error bound for physics-informed neural networks](https://mlsanity.com/paper/2306.03786/) (2023)
- [Towards Practical Second-Order Optimizers in Deep Learning: Insights from Fisher Information Analysis](https://mlsanity.com/paper/2504.20096/) (2025)
- [Blockwise Stabilized Adaptive Cubic Regularization with Subsolvers via Recurrence](https://mlsanity.com/paper/2608.22129/) (2026)
- [Loss Landscape Features That Make Adam Stall: Definitions, Estimators, and the Preconditioned Hessian View](https://mlsanity.com/paper/2608.22145/) (2026)

## Abstract (arXiv)

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.