Two-phase flow involves the simultaneous dynamics of two distinct phases, with numerous important implications in the industrial field. However, accurately modeling these flows, whether through experiments or numerical simulations, requires substantial computational resources to capture the complex interfacial dynamics. In this study, we tested three different neural operators—the Fourier neural operator (FNO), physics-aware recurrent convolutions (PARC), and the deep operator network (DeepONet), with the aim of accelerating the simulation of dynamics in two-phase flows. We employed two benchmark problems of single bubble rising (140 cases) to bubble condensation (50 cases) for predicting the volume fraction, pressure, velocity fields, and more. Our framework considers only initial and boundary conditions to predict the entire temporal evolution, where physical parameters such as fluid density, fluid dynamic viscosity, and surface tension coefficient are set to the initial conditions. As a result, in the single bubble rising case, FNO achieved the best accuracy, yielding a root mean square error (RMSE) of 0.0154 in predicting the volume fraction field. On the other hand, for the bubble condensation case, DeepONet exhibited the lowest RMSE value of 0.0123. Additionally, we examined the computational efficiency and distinctive characteristics of each technique, as well as its applicability to modeling two-phase flows. Overall, this study offered practical insights into utilizing neural operators for solving fundamental benchmark problems, further demonstrating the potential of neural operators as efficient surrogate models for a wide range of physical phenomena at significantly reduced computational costs.

Federated learning (FL) enables multiple clients with distributed data sources to collaboratively train a shared model without compromising data privacy. However, existing FL paradigms face challenges due to heterogeneity in client data distributions and system capabilities. Personalized federated learning (pFL) has been proposed to mitigate these problems, but often requires a shared model architecture and a central entity for parameter aggregation, resulting in scalability and communication issues. More recently, model-heterogeneous FL has gained attention due to its ability to support diverse client models, but existing methods are limited by their dependence on a centralized framework, synchronized training, and publicly available datasets. To address these limitations, we introduce Federated Peer-Adaptive Ensemble Learning (FedPAE), a fully decentralized pFL algorithm that supports model heterogeneity and asynchronous learning. Our approach utilizes a peer-to-peer model sharing mechanism and ensemble selection to achieve a more refined balance between local and global information. Experimental results show that FedPAE outperforms existing state-of-the-art pFL algorithms, effectively managing diverse client capabilities and demonstrating robustness against statistical heterogeneity.

Modeling unsteady, fast transient, and advection-dominated physics problems is a pressing challenge for physics-aware deep learning (PADL). The physics of complex systems is governed by large systems of partial differential equations (PDEs) and ancillary constitutive models with nonlinear structures, as well as evolving state fields exhibiting sharp gradients and rapidly deforming material interfaces. Here, we investigate an inductive bias approach that is versatile and generalizable to model generic nonlinear field evolution problems. Our study focuses on the recent physics-aware recurrent convolutions (PARC), which incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. We extend the capabilities of PARC to simulate unsteady, transient, and advection-dominant systems. The extended model, referred to as PARCv2, is equipped with differential operators to model advection-reaction-diffusion equations, as well as a hybrid integral solver for stable, long-time predictions. PARCv2 is tested on both standard benchmark problems in fluid dynamics, namely Burgers and Navier-Stokes equations, and then applied to more complex shock-induced reaction problems in energetic materials. We evaluate the behavior of PARCv2 in comparison to other physics-informed and learning bias models and demonstrate its potential to model unsteady and advection-dominant dynamics regimes.

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints. These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.

We propose a novel interpretable deep neural network for text classification, called ProtoryNet, based on a new concept of prototype trajectories. Motivated by the prototype theory in modern linguistics, ProtoryNet makes a prediction by finding the most similar prototype for each sentence in a text sequence and feeding an RNN backbone with the proximity of each sentence to the corresponding active prototype. The RNN backbone then captures the temporal pattern of the prototypes, which we refer to as prototype trajectories. Prototype trajectories enable intuitive and fine-grained interpretation of the reasoning process of the RNN model, in resemblance to how humans analyze texts. We also design a prototype pruning procedure to reduce the total number of prototypes used by the model for better interpretability. Experiments on multiple public datasets demonstrate that ProtoryNet achieves higher accuracy than the baseline prototype-based deep neural net and narrows the performance gap when compared to state-of-the-art black-box models. In addition, after prototype pruning, the resulting ProtoryNet models only need less than or around 20 prototypes for all datasets, which significantly benefits interpretability. Furthermore, we report survey results indicating that human users find ProtoryNet more intuitive and easier to understand compared to other prototype-based methods.

Abstract In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two‐dimensional manifolds using orthogonal basis functions called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific trends and phenomena, where accurate numerical quantification of geometric features is critical. Recently, CNNs have demonstrated a substantial improvement in extracting and codifying geometric features. However, the progress is mostly centred around computer vision and its applications where an inherent grid‐like data representation is naturally present. In contrast, many geometry processing problems deal with curved surfaces and the application of CNNs is not trivial due to the lack of canonical grid‐like representation, the absence of globally consistent orientation and the incompatible local discretizations. In this paper, we show that the Zernike polynomials allow rigourous yet practical mathematical generalization of CNNs to arbitrary surfaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike coefficients and the rotation of a convolution kernel is essentially a set of 2 × 2 rotation matrices applied to the coefficients. The key contribution of this work is in such a computationally efficient but rigorous generalization of the major CNN building blocks.

This paper presents an improvement of the ELMVIS+ method that is proposed for fast nonlinear dimensionality reduction. The ELMVIS++C has an additional supervised learning component compared to ELMVIS+, which is originally an unsupervised method as like the majority of the other dimensionality reduction method. This component prevents samples under the same class being separated apart from each other. In this improved method, the importance of the supervised component can be further tuned to have different level of influence. The test results on four datasets indicate that the proposed improvement not only maintains the performance of ELMVIS+, but also is extremely beneficial for certain applications where the visualization of the data in relation with the class becomes an important issue.