Related papers: Deep neural operators can predict the real-time re…

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error…

Recent research on deep learning, a set of machine learning techniques able to learn deep architectures, has shown how robotic perception and action greatly benefits from these techniques. In terms of spacecraft navigation and control…

This study aims to develop surrogate models for accelerating decision making processes associated with carbon capture and storage (CCS) technologies. Selection of sub-surface $CO_2$ storage sites often necessitates expensive and involved…

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…

Dirichlet-Neumann Operators (DNOs) are important to the formulation, analysis, and simulation of many crucial models found in engineering and the sciences. For instance, these operators permit moving-boundary problems, such as the classical…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

In climate simulations, small-scale processes shape ocean dynamics but remain computationally expensive to resolve directly. For this reason, their contributions are commonly approximated using empirical parameterizations, which lead to…

Increased demands for high-performance materials have led to advanced composite materials with complex hierarchical designs. However, designing a tailored material microstructure with targeted properties and performance is extremely…

Infusing deep learning with structural engineering has received widespread attention for both forward problems (structural simulation) and inverse problems (structural health monitoring). Based on Fourier Neural Operator, this study…

In time-varying fading channels, channel coefficients are estimated using pilot symbols that are transmitted every coherence interval. For channels with high Doppler spread, the rapid channel variations over time will require considerable…

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…

This study presents OceanCastNet (OCN), a machine learning approach for wave forecasting that incorporates wind and wave fields to predict significant wave height, mean wave period, and mean wave direction.We evaluate OCN's performance…

Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical…

Neural operators have emerged as powerful tools for learning nonlinear mappings between function spaces, enabling real-time prediction of complex dynamics in diverse scientific and engineering applications. With their growing adoption in…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically…

Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…

Modeling the recovery of interdependent critical infrastructure is a key component of quantifying and optimizing societal resilience to disruptive events. However, simulating the recovery of large-scale interdependent systems under random…

We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As emission norms become more stringent, the need for fast and…