Related papers: Structure-Preserving Operator Learning
The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs).…
Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…
We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…
Boundary conditions (BCs) are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations (PDEs) to satisfy at specific spatial locations. These constraints carry important physical…
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…
Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…
Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…
The Transformer architecture has revolutionized artificial intelligence, yet a principled theoretical understanding of its internal mechanisms remains elusive. This paper introduces a novel analytical framework that reconceptualizes the…
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…
Weakly supervised object localization(WSOL) remains an open problem given the deficiency of finding object extent information using a classification network. Although prior works struggled to localize objects through various spatial…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…
Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal fields for new initial conditions or forcing functions.…
Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…
Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…