Related papers: FreqMoE: Dynamic Frequency Enhancement for Neural …

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important…

Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propose an invertible…

Preference-based reinforcement learning offers a scalable alternative to manual reward engineering by learning reward structures from comparative feedback. However, large-scale preference datasets, whether collected from crowdsourced…

The popular VQ-VAE models reconstruct images through learning a discrete codebook but suffer from a significant issue in the rapid quality degradation of image reconstruction as the compression rate rises. One major reason is that a higher…

Learning solution operators for partial differential equations (PDEs) has become a foundational task in scientific machine learning. However, existing neural operator methods require abundant training data for each specific PDE and lack the…

Ultrasound image segmentation is pivotal for clinical diagnosis, yet challenged by speckle noise and imaging artifacts. Recently, DINOv3 has shown remarkable promise in medical image segmentation with its powerful representation…

Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically…

Many real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles. However, modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a…

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…

Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, such as uncertainty…

It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to solve nonlinear elliptic partial differential equations…

Federated learning (FL) is a collaborative machine learning approach that enables multiple clients to train models without sharing their private data. With the rise of deep learning, large-scale models have garnered significant attention…

As revealed by the scaling law of fine-grained MoE, model performance ceases to be improved once the granularity of the intermediate dimension exceeds the optimal threshold, limiting further gains from single-dimension fine-grained design.…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

Training large language models (LLMs) for different inference constraints is computationally expensive, limiting control over efficiency-accuracy trade-offs. Moreover, once trained, these models typically process tokens uniformly,…

Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based…

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…