Related papers: Dilated convolution neural operator for multiscale…
Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation,…
The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…
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…
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…
The computational overhead of traditional numerical solvers for partial differential equations (PDEs) remains a critical bottleneck for large-scale parametric studies and design optimization. We introduce a Minimal-Data Parametric Neural…
Recent work in equivariant deep learning bears strong similarities to physics. Fields over a base space are fundamental entities in both subjects, as are equivariant maps between these fields. In deep learning, however, these maps are…
The use of neural operators in a digital twin model of an offshore floating structure can provide a paradigm shift in structural response prediction and health monitoring, providing valuable information for real-time control. In this work,…
Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We…
Recent research has shown that incorporating equivariance into neural network architectures is very helpful, and there have been some works investigating the equivariance of networks under group actions. However, as digital images and…
We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…
We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…
Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…
We address the problem of predicting the next state of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to…
Neural operators have been validated as promising deep surrogate models for solving partial differential equations (PDEs). Despite the critical role of boundary conditions in PDEs, however, only a limited number of neural operators robustly…
Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…
Neural operators learn to map initial conditions to the terminal solution of partial differential equations (PDEs), providing a surrogate for the full operator mapping. This enables rapid prediction across different input configurations.…
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…
Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…