相关论文: Merging Memory and Space: A State Space Neural Ope…

We study the approximation-theoretic implications of mixture-of-experts architectures for operator learning, where the complexity of a single large neural operator is distributed across many small neural operators (NOs), and each input is…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning…

Scientific machine learning is increasingly used to build surrogate models, yet most models are trained under a restrictive assumption in which future data follow the same distribution as the training set. In practice, new experimental…

Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical…

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model,…

Simulating the dynamics of open quantum systems with spatial structure and external control is an important challenge in quantum information science. Classical numerical solvers for such systems require integrating coupled master and field…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

Neural operators (NOs) excel at learning mappings between function spaces, serving as efficient forward solution approximators for PDE-governed systems. However, as black-box solvers, they offer limited insight into the underlying physical…

The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear…

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While…

Data-driven methods have emerged as powerful tools for modeling the responses of complex nonlinear materials directly from experimental measurements. Among these methods, the data-driven constitutive models present advantages in physical…

Selection of perefect parameters for low-pass filters can sometimes be an expensive problem with no analytical solution or differentiability of cost function. In this paper, we introduce a new PSO-inspired algorithm, that incorporates the…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

Physics-Informed Neural Networks (PINNs) are a kind of deep-learning-based numerical solvers for partial differential equations (PDEs). Existing PINNs often suffer from failure modes of being unable to propagate patterns of initial…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…

Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with…

Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…