相关论文: Operator Learning Using Weak Supervision from Walk…

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…

Weakly supervised object detection(WSOD) task uses only image-level annotations to train object detection task. WSOD does not require time-consuming instance-level annotations, so the study of this task has attracted more and more…

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the inherent complexity and diversity, such as long…

Accurately quantifying long-term risk probabilities in diverse stochastic systems is essential for safety-critical control. However, existing sampling-based and partial differential equation (PDE)-based methods often struggle to handle…

Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…

Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure to train a single neural network on data from multiple…

We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and…

We introduce a framework for eliminating the computation of controller gain functions in PDE control. We learn the nonlinear operator from the plant parameters to the control gains with a (deep) neural network. We provide closed-loop…

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we…

Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the…

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…

For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a large dataset of geometry-solution pairs in order to obtain a…

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…

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…

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…

In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value…

Self-supervised learning (SSL) is a powerful paradigm for learning from unlabeled time-series data. However, popular methods such as masked autoencoders (MAEs) rely on reconstructing inputs from a fixed, predetermined masking ratio. Instead…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…