Related papers: DeepONet prediction of linear instability waves in…

Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior…

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…

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…

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…

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…

Full Waveform Inversion (FWI) is an important geophysical technique considered in subsurface property prediction. It solves the inverse problem of predicting high-resolution Earth interior models from seismic data. Traditional FWI methods…

Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein,…

Current groundwater models face a significant challenge in their implementation due to heavy computational burdens. To overcome this, our work proposes a cost-effective emulator that efficiently and accurately forecasts the impact of…

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be…

Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

The Deep Operator Network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…

We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

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…

Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis. Herein, we employ neural operators to solve…

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…

A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under…