Related papers: Harnessing physics-informed operators for high-dim…
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…
Constructing first-principles models is usually a challenging and time-consuming task due to the complexity of the real-life processes. On the other hand, data-driven modeling, and in particular neural network models often suffer from…
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…
Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…
This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. The proposed framework learns an operator from the…
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…
The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact…
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…
Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…
Simulating physical systems using Partial Differential Equations (PDEs) has become an indispensible part of modern industrial process optimization. Traditionally, numerical solvers have been used to solve the associated PDEs, however…
Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applications. In such…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Solving partial differential equations with neural operators significantly reduces computational costs but remains bottlenecked by high training data requirements. Active learning offers a natural framework to mitigate this by selectively…
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 a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…
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.…
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…
In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources from observations of system state is vital for attribution…
Learning operators for parametric partial differential equations (PDEs) using neural networks has gained significant attention in recent years. However, standard approaches like Deep Operator Networks (DeepONets) require extensive labeled…
Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require deep domain expertise. Numerical simulations present an…