Related papers: Compositional Neural Operators for Multi-Dimension…
A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…
Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…
Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon…
Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with…
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For…
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…
Neural operator models for solving partial differential equations (PDEs) often rely on global mixing mechanisms-such as spectral convolutions or attention-which tend to oversmooth sharp local dynamics and introduce high computational cost.…
Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important…
We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…
Artificial intelligence (AI) shows great potential to reduce the huge cost of solving partial differential equations (PDEs). However, it is not fully realized in practice as neural networks are defined and trained on fixed domains and…
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…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…
Convolutional neural operator is a CNN-based architecture recently proposed to enforce structure-preserving continuous-discrete equivalence and enable the genuine, alias-free learning of solution operators of PDEs. This neural operator was…