Related papers: Spectral-inspired Operator Learning with Limited D…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Neural operators for time-dependent PDEs face a structural tension: spectral architectures (FNO and descendants) inherit exponential rollout-error growth from their one-step Lipschitz constant, while hierarchical U-Net operators trade…

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…

In this paper, we introduce the Spectral Coefficient Learning via Operator Network (SCLON), a novel operator learning-based approach for solving parametric partial differential equations (PDEs) without the need for data harnessing. The…

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…

Solving partial differential equations remains a central challenge in scientific machine learning. Neural operators offer a promising route by learning mappings between function spaces and enabling resolution-independent inference, yet they…

We consider optimal experimental design (OED) problems in selecting the most informative observation sensors to estimate model parameters in a Bayesian framework. Such problems are computationally prohibitive when the…

Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…

Spectral super-resolution (SSR) aims to reconstruct hyperspectral images (HSIs) from multispectral observations, with broad applications in computer vision and remote sensing. Deep learning-based methods have been widely used, but they…

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While…

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Many physical systems exhibit nonlocal spatiotemporal behaviors described by integro-differential equations (IDEs). Classical methods for solving IDEs require repeatedly evaluating convolution integrals, whose cost increases quickly with…

Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of…

In this work, we describe a novel approach to building a neural PDE solver leveraging recent advances in transformer based neural network architectures. Our model can provide solutions for different values of PDE parameters without any need…

Training neural PDE solvers is often bottlenecked by expensive data generation or unstable physics-informed neural network (PINN) involving challenging optimization landscapes due to higher-order derivatives. To tackle this issue, we…

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed…