arXiv subjects

Rujin Ma

Publications and source records attributed to Rujin Ma.

5 recordsLinked to original sources

arXiv2026

On the training of physics-informed neural operators for solving parametric partial differential equations

Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning. Despite this promise, how to train PINOs efficiently and robustly remains less well-understood than the training of either data-driven neural operators or physics-informed neural networks (PINNs). To bridge this gap, we examine key components of the PINO training pipeline, including architecture design, optimizer choice, loss balancing, and collocation-point sampling strategy. We study three representative operator backbones, Deep Operator Network (DeepONet), Fourier Neural Operator (FNO), and Continuous Vision Transformer (CViT), across five diverse parametric PDE systems. Our results show that CViT provides consistently strong and stable performance across the considered benchmarks. Beyond architecture, we find that several optimization pathologies previously identified in PINN training naturally arise in PINOs, including gradient conflicts and causal violation. We also find that mitigation algorithms developed for PINNs remain effective in the PINO setting. We further compare physics-informed and data-driven training under different data regimes, revealing that a carefully designed physics-informed training pipeline can match, and in some cases, outperform purely data-driven neural operators. Taken together, these findings provide a systematic empirical understanding of the optimization challenges in PINO training and inform a practical pipeline for efficient and robust physics-informed operator learning. Code and data are available at https://github.com/NanxiiChen/PI-CViT.

cs.LG↗

arXiv2026

Physics-informed neural operator for predictive parametric phase-field modelling

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural operator (FNO) show promise in accelerating the solution of parametric partial differential equations (PDEs), the lack of explicit physical constraints, may limit generalisation and long-term accuracy for complex phase-field dynamics. Here, we develop a physics-informed neural operator framework to learn parametric phase-field PDEs, namely PF-PINO. By embedding the residuals of phase-field governing equations into the data-fidelity loss function, our framework effectively enforces physical constraints during training. We validate PF-PINO against benchmark phase-field problems, including electrochemical corrosion, dendritic crystal solidification, and spinodal decomposition. Our results demonstrate that PF-PINO significantly outperforms conventional FNO in accuracy, generalisation capability, and long-term stability. This work provides a robust and efficient computational tool for phase-field modelling and highlights the potential of physics-informed neural operators to advance scientific machine learning for complex interfacial evolution problems.

cs.LG↗

arXiv2025

Enforcing hidden physics in physics-informed neural networks

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully reflect the physical structure embedded in the governing equations remains an open challenge, particularly for maintaining robustness across diverse scientific problems. In this work, we address this issue by introducing a simple, generalized, yet robust irreversibility-regularized strategy that enforces hidden physical laws as soft constraints during training, thereby recovering the missing physics associated with irreversible processes in the conventional PINN. This approach ensures that the learned solutions consistently respect the intrinsic one-way nature of irreversible physical processes. Across a wide range of benchmarks spanning traveling wave propagation, steady combustion, ice melting, corrosion evolution, and crack growth, we observe substantial performance improvements over the conventional PINN, demonstrating that our regularization scheme reduces predictive errors by more than an order of magnitude, while requiring only minimal modification to existing PINN frameworks.

cs.LG↗

arXiv2025

Sharp-PINNs: staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion

Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and strongly coupled solutions. In this work, we present a novel Sharp-PINN framework to tackle complex phase field corrosion problems. Instead of minimizing all governing PDE residuals simultaneously, the Sharp-PINNs introduce a staggered training scheme that alternately minimizes the residuals of Allen-Cahn and Cahn-Hilliard equations, which govern the corrosion system. To further enhance its efficiency and accuracy, we design an advanced neural network architecture that integrates random Fourier features as coordinate embeddings, employs a modified multi-layer perceptron as the primary backbone, and enforces hard constraints in the output layer. This framework is benchmarked through simulations of corrosion problems with multiple pits, where the staggered training scheme and network architecture significantly improve both the efficiency and accuracy of PINNs. Moreover, in three-dimensional cases, our approach is 5-10 times faster than traditional finite element methods while maintaining competitive accuracy, demonstrating its potential for real-world engineering applications in corrosion prediction.

cs.LG↗

arXiv2020

A phase field formulation for dissolution-driven stress corrosion cracking

We present a new theoretical and numerical framework for modelling mechanically-assisted corrosion in elastic-plastic solids. Both pitting and stress corrosion cracking (SCC) can be captured, as well as the pit-to-crack transition. Localised corrosion is assumed to be dissolution-driven and a formulation grounded upon the film rupture-dissolution-repassivation mechanism is presented to incorporate the influence of film passivation. The model incorporates, for the first time, the role of mechanical straining as the electrochemical driving force, accelerating corrosion kinetics. The computational complexities associated with tracking the evolving metal-electrolyte interface are resolved by making use of a phase field paradigm, enabling an accurate approximation of complex SCC morphologies. The coupled electro-chemo-mechanical formulation is numerically implemented using the finite element method and an implicit time integration scheme; displacements, phase field order parameter and concentration are the primary variables. Five case studies of particular interest are addressed to showcase the predictive capabilities of the model, revealing an excellent agreement with analytical solutions and experimental measurements. By modelling these paradigmatic 2D and 3D boundary value problems we show that our formulation can capture: (i) the transition from activation-controlled corrosion to diffusion-controlled corrosion, (ii) the sensitivity of interface kinetics to mechanical stresses and strains, (iii) the role of film passivation in reducing corrosion rates, and (iv) the dependence of the stability of the passive film to local strain rates. The influence of these factors in driving the shape change of SCC defects, including the pit-to-crack transition, is a natural outcome of the model, laying the foundations for a mechanistic assessment of engineering materials and structures.

physics.app-ph↗