Related papers: Multifidelity Deep Operator Networks For Data-Driv…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Traditional 2D hydraulic models face significant computational challenges that limit their applications that are time-sensitive or require many model evaluations. This study presents a physics-informed Deep Operator Network (DeepONet)…

Deep neural operators (DNOs) have been utilized to approximate nonlinear mappings between function spaces. However, DNOs face the challenge of increased dimensionality and computational cost associated with unaligned observation data. In…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

FNO and DeepONet are by far the most popular neural operator learning algorithms. FNO seems to enjoy an edge in popularity due to its ease of use, especially with high dimensional data. However, a lesser-acknowledged feature of DeepONet is…

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…

Effective real-time monitoring is a foundation of digital twin technology, crucial for detecting material degradation and maintaining the structural integrity of nuclear systems to ensure both safety and operational efficiency. Traditional…

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies,…

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…

In this work, we propose a network which can utilize computational cheap low-fidelity data together with limited high-fidelity data to train surrogate models, where the multi-fidelity data are generated from multiple underlying models. The…

Seismic forward and inverse problems are significant research areas in geophysics. However, the time burden of traditional numerical methods hinders their applications in scenarios that require fast predictions. Machine learning-based…

For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory…

Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution…

Time-dependent flow fields are typically generated by a computational fluid dynamics (CFD) method, which is an extremely time-consuming process. However, the latent relationship between the flow fields is governed by the Navier-Stokes…

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Physics-constrained neural networks are commonly employed to enhance prediction robustness compared to purely data-driven models, achieved through the inclusion of physical constraint losses during the model training process. However, one…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…

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…