相关论文: Latent Neural Operator for Solving Forward and Inv…

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…

Despite the successes of deep learning in computer vision, difficulties persist in recognizing objects that have undergone group-symmetric transformations rarely seen during training$\unicode{x2013}$for example objects seen in unusual…

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…

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…

We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative…

This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…

Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional…

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate…

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…

We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…

Uncertainty and delayed reactions in human driving behavior lead to stop-and-go traffic congestion on freeways. The freeway traffic dynamics are governed by the Aw-Rascle-Zhang (ARZ) traffic Partial Differential Equation (PDE) models with…

We present the Physics-Informed Low-Rank Neural Operator (PILNO), a neural operator framework for efficiently approximating solution operators of partial differential equations (PDEs) on point cloud data. PILNO combines low-rank kernel…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

The eigendecomposition of the Laplace--Beltrami Operator (LBO) is fundamental to geometric analysis, yet computing its low-frequency eigenmodes remains a significant bottleneck due to the high cost of iterative solvers on large-scale data.…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit…

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a…