Scientific machine learning
for physical systems.

Abstract. 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.

Abstract. 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 this URL.

Abstract. 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.

Abstract. This study presents a high-performance, fully parallelized computational framework for stationary and non-stationary stochastic wind field simulation that reconciles the conflict between computational efficiency and spectral fidelity. The framework reformulates the classical Shinozuka spectral representation method into a dual-level parallel algorithm that (i) eliminates nested spatial loops for computing pairwise spectral densities with array broadcasting and (ii) parallelizes frequency-wise synthesis via vectorized mapping, transforming the original sequential complexity into fully parallelizable operations. Unlike existing computational acceleration techniques that rely on dimension reduction or frequency interpolation, this reformulation maintains complete spectral fidelity without introducing approximation errors. To bound peak memory use while preserving full spatial coherence, the framework integrates an adaptive frequency batching strategy for large-scale problems. A multi-backend implementation (JAX, PyTorch, NumPy) enables efficient deployment on CPUs and GPUs. Extensive benchmarks show significant performance improvements, achieving speedups of up to several thousand-fold compared with conventional methods and demonstrating superiority over other mainstream algorithms. Practical applications to several engineering case studies, with comparisons to field measurements and theoretical models, validate the accuracy and reliability of the simulated wind fields. This software is released open-source on GitHub to support reproducible research and inspire further innovations in wind engineering.

Abstract. Physics-informed neural networks (PINNs) have emerged as a promising tool for effectively resolving diverse partial differential equations. Despite the numerous recent advances, PINNs often encounter significant challenges when dealing with complex nonlinear systems, such as the coupling Allen-Cahn (AC) and Cahn-Hilliard (CH) equations for phase field interfacial problems. In this work, we present an enhanced PINN framework, termed PF-PINNs, for the robust and efficient resolution of AC-CH coupled PDEs. Key features of the PF-PINNs framework include: (1) a normalisation and de-normalisation method to bridge the disparity in temporal and spatial scales in real-world physical problems, (2) an advanced sampling strategy designed to efficiently diffuse the initial interface and dynamically monitor its evolution throughout the training process, and (3) an NTK-based adaptive weighting strategy with random-batch method to balance the complex loss terms associated with phase field governing equations. We conduct extensive benchmarks on electrochemical corrosion, to showcase the accuracy and efficiency of the proposed PF-PINNs framework. The comparison of our results with reference solutions from FEniCS demonstrates that our PF-PINNs framework is a versatile and powerful tool for a wide range of AC-CH phase field applications.

Abstract. This study presents a comparative analysis of field-measured wind data collected by anemometers positioned on the upstream and downstream sides of the midspan deck of Runyang Suspension Bridge. Considering the intricate aerodynamic interactions between the bridge deck and the wind, the disturbance effects of the bridge deck on the recorded wind data are systematically analyzed. Disturbed wind parameters are identified from the measurements, and their anomalous distribution patterns are investigated. To derive the actual wind parameters, a data-cleaning method is developed for mean wind speed and turbulence intensity. This method employs a statistical model to isolate the disturbance component and establishes empirical relationships linking the disturbed and actual wind parameters. The results demonstrate that the proposed data-cleaning method effectively mitigates the disturbance effects caused by the bridge deck, enabling more accurate evaluation of wind loads acting on the structure.

Abstract. 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.

Abstract. Accurate characterization of wind fields is essential for effectively analyzing wind-induced responses of long-span bridges. However, field measurements often suffer from severe anomalies, compromising their reliability. One significant cause of these anomalies is the disturbances induced by the bridge deck. This study aims to eliminate the effects of such disturbances on the measured data and wind field characteristics. We begin with a comparative analysis of disturbed versus undisturbed wind measurements. To remove the disturbance effects and clean the data, we introduce a novel skip-connected variational autoencoder (SVAE) neural network that can effectively reconstruct undisturbed data from disturbed measurements. The SVAE is trained on a dataset comprising both disturbed and undisturbed measurements collected during strong wind events and is validated against other generative models based on reconstruction accuracy. We then employ the trained SVAE to clean measurements from another event and analyze wind field characteristics such as mean wind speed, turbulence intensity, integral scale of turbulence, and power spectral density from the reconstructed data. Our findings confirm the effectiveness of this approach, suggesting its broader applicability in ensuring the accuracy and reliability of wind field characterizations and subsequent analyses of wind-induced responses on long-span bridges.

Abstract. Wind fields in mountain valleys exhibit pronounced diurnal variability, primarily influenced by topography and temperature fluctuations. A comprehensive understanding of these characteristics is crucial for optimizing the aerodynamic design of long-span bridge structures. This study develops a machine learning framework for recognizing and predicting daily wind speed variation patterns in mountain valleys. First, long-term field measurements of wind speed and temperature are collected from a bridge site in a mountainous valley, providing a comprehensive time-series dataset. Then, we apply Variational Mode Decomposition (VMD) for data processing and train Autoencoders (AE) to extract representative features of diurnal variations in wind speed, temperature, and their combined patterns. Based on the extracted features, we categorize wind-speed–temperature variation patterns using correlation analysis and clustering methods. Finally, a segment-matching algorithm is used to recognize and predict wind speed trends over extended daily timescales. This study provides a structured approach to modeling daily wind speed variations, offering valuable insights into the dynamic wind environment of mountainous valleys and enhancing predictive capabilities for bridge wind-resistant design and operation.

Abstract. Physics-informed neural networks (PINNs) have recently emerged as a promising tool for resolving partial differential equations. However, when confronting complex multi-physics problems, conventional PINNs suffer from substantial challenges. In this study, we present an advanced PINN framework tailored for the phase-field model of pitting corrosion (PC-PINNs), effectively navigating the complexities of the rigidly coupled Allen-Cahn and Cahn-Hilliard equations. The main ingredients of PC-PINNs include: 1) an NTK-based adaptive weighting strategy to balance the multiple loss terms arising from coupled equations, 2) a generalized adaptive sampling scheme complemented by dual criteria to accurately track the corrosion interface, 3) a random-batch technique to accelerate the weight calculation, and 4) a cross-scale sampling technique to ensure the veracity of convergence. We evaluate the PC-PINNs against two phase-field corrosion benchmarks, using various strategy permutations to validate the effectiveness of the proposed theory. Results demonstrate that the PC-PINNs successfully overcome the limitations of the conventional PINNs, delivering simulations with high fidelity.

Abstract. Given the substantial influence of wind loading on the structural performance of long-span bridges, continuous monitoring of wind field characteristics in their vicinity is paramount. PyWindAM is purpose-built web server software meticulously designed to simplify comprehensive wind data analysis and efficient management derived from on-site measurements. The software automates the retrieval of raw data from hardware devices and employs vector decomposition to extract essential wind parameters, including mean wind speed, wind direction, turbulence intensity, and more, from data collected at multiple measurement points. These critical wind parameters are securely stored in the InfluxDB database hosted on the server. In terms of user-friendliness, InfluxDB itself provides an intuitive interface, facilitating convenient data visualization and efficient data management for researchers and technicians engaged in wind field analysis and structural safety assessments.

Abstract. To assess the reliability of wind resistance behavior for long-span cable-stayed bridges, this study establishes a joint probability distribution model for 10-minute mean wind speed and turbulence intensity based on one year of field monitoring data. Firstly, the distribution characteristics of wind parameters at the deck height are investigated. Notably, substantial abnormalities are observed in the anemometer data obtained from the upstream and downstream sides of the mid-span deck. Thus, a novel component-decomposition method is proposed to eliminate these inconsistencies. The decrease in measured mean wind speed and the increase in turbulence intensity resulting from the bridge deck disturbance is considered to restore the actual wind parameters. Finally, the joint probability distribution model is developed using the Gaussian Copula function. The results demonstrate the efficacy of the proposed method in mitigating the bridge deck disturbance on field measurements, thereby establishing accurate and reliable probability distribution models.