Related papers: An Advanced Physics-Informed Neural Operator for C…
Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…
Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire…
Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational…
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…
Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires…
We propose to take a novel approach to robot system design where each building block of a larger system is represented as a differentiable program, i.e. a deep neural network. This representation allows for integrating algorithmic planning…
The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…
Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by…
This study focuses on addressing the challenges of solving analytically intractable differential equations that arise in scientific and engineering fields such as Hamilton-Jacobi-Bellman. Traditional numerical methods and neural network…
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…
Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning…
Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…
Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase…
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…
This paper proposes a new data-driven method for the reliable prediction of power system post-fault trajectories. The proposed method is based on the fundamentally new concept of Deep Operator Networks (DeepONets). Compared to traditional…
Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…
Recent advances in modeling large-scale complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources.…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…
The Li-ion battery is a complex physicochemical system that generally takes applied current as input and terminal voltage as output. The mappings from current to voltage can be described by several kinds of models, such as accurate but…