Accelerating Multiscale Modeling with Hybrid Solvers: Coupling FEM and Neural Operators with Domain Decomposition

Numerical solvers for partial differential equations (PDEs) face challenges balancing computational cost and accuracy, especially in multiscale and dynamic systems. Neural operators can significantly speed up simulations; however, they often face challenges such as error accumulation and limited generalization in multiphysics problems. This work introduces a novel hybrid framework that integrates physics-informed DeepONet with FEM through domain decomposition. The core innovation lies in adaptively coupling FEM and DeepONet subdomains via a Schwarz alternating method. This methodology strategically allocates computationally demanding regions to a pre-trained Deep Operator Network, while the remaining computational domain is solved through FEM. To address dynamic systems, we integrate the Newmark time-stepping scheme directly into the DeepONet, significantly mitigating error accumulation in long-term simulations. Furthermore, an adaptive subdomain evolution enables the ML-resolved region to expand dynamically, capturing emerging fine-scale features without remeshing. The framework's efficacy has been validated across a range of solid mechanics problems, including static, quasi-static, and dynamic regimes, demonstrating accelerated convergence rates (up to 20% improvement compared to FE-FE approaches), while preserving solution fidelity with error < 1%. Our case studies show that our proposed hybrid solver: (1) maintains solution continuity across subdomain interfaces, (2) reduces computational costs by eliminating fine mesh requirements, (3) mitigates error accumulation in time-dependent simulations, and (4) enables automatic adaptation to evolving physical phenomena. This work bridges the gap between numerical methods and AI-driven surrogates, offering a scalable pathway for high-fidelity simulations in engineering and scientific applications.

A Multiple Transferable Neural Network Method with Domain Decomposition for Elliptic Interface Problems

The transferable neural network (TransNet) is a two-layer shallow neural network with pre-determined and uniformly distributed neurons in the hidden layer, and the least-squares solvers can be particularly used to compute the parameters of its output layer when applied to the solution of partial differential equations. In this paper, we integrate the TransNet technique with the nonoverlapping domain decomposition and the interface conditions to develop a novel multiple transferable neural network (Multi-TransNet) method for solving elliptic interface problems, which typically contain discontinuities in both solutions and their derivatives across interfaces. We first propose an empirical formula for the TransNet to characterize the relationship between the radius of the domain-covering ball, the number of hidden-layer neurons, and the optimal neuron shape. In the Multi-TransNet method, we assign each subdomain one distinct TransNet with an adaptively determined number of hidden-layer neurons to maintain the globally uniform neuron distribution across the entire computational domain, and then unite all the subdomain TransNets together by incorporating the interface condition terms into the loss function. The empirical formula is also extended to the Multi-TransNet and further employed to estimate appropriate neuron shapes for the subdomain TransNets, greatly reducing the parameter tuning cost. Additionally, we propose a normalization approach to adaptively select the weighting parameters for the terms in the loss function. Ablation studies and extensive experiments with comparison tests on different types of elliptic interface problems with low to high contrast diffusion coefficients in two and three dimensions are carried out to numerically demonstrate the superior accuracy, efficiency, and robustness of the proposed Multi-TransNet method.

Scalable Signature Kernel Computations for Long Time Series via Local Neumann Series Expansions

The signature kernel is a recent state-of-the-art tool for analyzing high-dimensional sequential data, valued for its theoretical guarantees and strong empirical performance. In this paper, we present a novel method for efficiently computing the signature kernel of long, high-dimensional time series via dynamically truncated recursive local power series expansions. Building on the characterization of the signature kernel as the solution of a Goursat PDE, our approach employs tilewise Neumann-series expansions to derive rapidly converging power series approximations of the signature kernel that are locally defined on subdomains and propagated iteratively across the entire domain of the Goursat solution by exploiting the geometry of the time series. Algorithmically, this involves solving a system of interdependent local Goursat PDEs by recursively propagating boundary conditions along a directed graph via topological ordering, with dynamic truncation adaptively terminating each local power series expansion when coefficients fall below machine precision, striking an effective balance between computational cost and accuracy. This method achieves substantial performance improvements over state-of-the-art approaches for computing the signature kernel, providing (a) adjustable and superior accuracy, even for time series with very high roughness; (b) drastically reduced memory requirements; and (c) scalability to efficiently handle very long time series (e.g., with up to half a million points or more) on a single GPU. These advantages make our method particularly well-suited for rough-path-assisted machine learning, financial modeling, and signal processing applications that involve very long and highly volatile data.

Knowledge Distillation and Enhanced Subdomain Adaptation Using Graph Convolutional Network for Resource-Constrained Bearing Fault Diagnosis

Bearing fault diagnosis under varying working conditions faces challenges, including a lack of labeled data, distribution discrepancies, and resource constraints. To address these issues, we propose a progressive knowledge distillation framework that transfers knowledge from a complex teacher model, utilizing a Graph Convolutional Network (GCN) with Autoregressive moving average (ARMA) filters, to a compact and efficient student model. To mitigate distribution discrepancies and labeling uncertainty, we introduce Enhanced Local Maximum Mean Squared Discrepancy (ELMMSD), which leverages mean and variance statistics in the Reproducing Kernel Hilbert Space (RKHS) and incorporates a priori probability distributions between labels. This approach increases the distance between clustering centers, bridges subdomain gaps, and enhances subdomain alignment reliability. Experimental results on benchmark datasets (CWRU and JNU) demonstrate that the proposed method achieves superior diagnostic accuracy while significantly reducing computational costs. Comprehensive ablation studies validate the effectiveness of each component, highlighting the robustness and adaptability of the approach across diverse working conditions.

IQA-Adapter: Exploring Knowledge Transfer from Image Quality Assessment to Diffusion-based Generative Models

Diffusion-based models have recently transformed conditional image generation, achieving unprecedented fidelity in generating photorealistic and semantically accurate images. However, consistently generating high-quality images remains challenging, partly due to the lack of mechanisms for conditioning outputs on perceptual quality. In this work, we propose methods to integrate image quality assessment (IQA) models into diffusion-based generators, enabling quality-aware image generation. First, we experiment with gradient-based guidance to optimize image quality directly and show this approach has limited generalizability. To address this, we introduce IQA-Adapter, a novel architecture that conditions generation on target quality levels by learning the relationship between images and quality scores. When conditioned on high target quality, IQA-Adapter shifts the distribution of generated images towards a higher-quality subdomain. This approach achieves up to a 10% improvement across multiple objective metrics, as confirmed by a subjective study, while preserving generative diversity and content. Additionally, IQA-Adapter can be used inversely as a degradation model, generating progressively more distorted images when conditioned on lower quality scores. Our quality-aware methods also provide insights into the adversarial robustness of IQA models, underscoring the potential of quality conditioning in generative modeling and the importance of robust IQA methods.

Speed-enhanced Subdomain Adaptation Regression for Long-term Stable Neural Decoding in Brain-computer Interfaces

Brain-computer interfaces (BCIs) offer a means to convert neural signals into control signals, providing a potential restoration of movement for people with paralysis. Despite their promise, BCIs face a significant challenge in maintaining decoding accuracy over time due to neural nonstationarities. However, the decoding accuracy of BCI drops severely across days due to the neural data drift. While current recalibration techniques address this issue to a degree, they often fail to leverage the limited labeled data, to consider the signal correlation between two days, or to perform conditional alignment in regression tasks. This paper introduces a novel approach to enhance recalibration performance. We begin with preliminary experiments that reveal the temporal patterns of neural signal changes and identify three critical elements for effective recalibration: global alignment, conditional speed alignment, and feature-label consistency. Building on these insights, we propose the Speed-enhanced Subdomain Adaptation Regression (SSAR) framework, integrating semi-supervised learning with domain adaptation techniques in regression neural decoding. SSAR employs Speed-enhanced Subdomain Alignment (SeSA) for global and speed conditional alignment of similarly labeled data, with Contrastive Consistency Constraint (CCC) to enhance the alignment of SeSA by reinforcing feature-label consistency through contrastive learning. Our comprehensive set of experiments, both qualitative and quantitative, substantiate the superior recalibration performance and robustness of SSAR.

A Practitioner's Guide to Continual Multimodal Pretraining

Multimodal foundation models serve numerous applications at the intersection of vision and language. Still, despite being pretrained on extensive data, they become outdated over time. To keep models updated, research into continual pretraining mainly explores scenarios with either (1) infrequent, indiscriminate updates on large-scale new data, or (2) frequent, sample-level updates. However, practical model deployment often operates in the gap between these two limit cases, as real-world applications often demand adaptation to specific subdomains, tasks or concepts -- spread over the entire, varying life cycle of a model. In this work, we complement current perspectives on continual pretraining through a research test bed as well as provide comprehensive guidance for effective continual model updates in such scenarios. We first introduce FoMo-in-Flux, a continual multimodal pretraining benchmark with realistic compute constraints and practical deployment requirements, constructed over 63 datasets with diverse visual and semantic coverage. Using FoMo-in-Flux, we explore the complex landscape of practical continual pretraining through multiple perspectives: (1) A data-centric investigation of data mixtures and stream orderings that emulate real-world deployment situations, (2) a method-centric investigation ranging from simple fine-tuning and traditional continual learning strategies to parameter-efficient updates and model merging, (3) meta learning rate schedules and mechanistic design choices, and (4) the influence of model and compute scaling. Together, our insights provide a practitioner's guide to continual multimodal pretraining for real-world deployment. Our benchmark and code is here: https://github.com/ExplainableML/fomo_in_flux.

Progressive Domain Adaptation for Thermal Infrared Object Tracking

Due to the lack of large-scale labeled Thermal InfraRed (TIR) training datasets, most existing TIR trackers are trained directly on RGB datasets. However, tracking methods trained on RGB datasets suffer a significant drop-off in TIR data due to the domain shift issue. To this end, in this work, we propose a Progressive Domain Adaptation framework for TIR Tracking (PDAT), which transfers useful knowledge learned from RGB tracking to TIR tracking. The framework makes full use of large-scale labeled RGB datasets without requiring time-consuming and labor-intensive labeling of large-scale TIR data. Specifically, we first propose an adversarial-based global domain adaptation module to reduce domain gap on the feature level coarsely. Second, we design a clustering-based subdomain adaptation method to further align the feature distributions of the RGB and TIR datasets finely. These two domain adaptation modules gradually eliminate the discrepancy between the two domains, and thus learn domain-invariant fine-grained features through progressive training. Additionally, we collect a largescale TIR dataset with over 1.48 million unlabeled TIR images for training the proposed domain adaptation framework. Experimental results on five TIR tracking benchmarks show that the proposed method gains a nearly 6% success rate, demonstrating its effectiveness.

ADLDA: A Method to Reduce the Harm of Data Distribution Shift in Data Augmentation

This study introduces a novel data augmentation technique, ADLDA, aimed at mitigating the negative impact of data distribution shifts caused by the data augmentation process in computer vision task. ADLDA partitions augmented data into distinct subdomains and incorporates domain labels, combined with domain adaptation techniques, to optimize data representation in the model's feature space. Experimental results demonstrate that ADLDA significantly enhances model performance across multiple datasets, particularly in neural network architectures with complex feature extraction layers. Furthermore, ADLDA improves the model's ability to locate and recognize key features, showcasing potential in object recognition and image segmentation tasks. This paper's contribution provides an effective data augmentation regularization method for the field of computer vision aiding in the enhancement of robustness and accuracy in deep learning models.

Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems

We present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://dx.doi.org/10.2139/ssrn.4766623), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.