相关论文: Data-Efficient Time-Dependent PDE Surrogates: Grap…

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…

Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss function during training. Current approaches allow to…

Current simulation of metal forging processes use advanced finite element methods. Such methods consist of solving mathematical equations, which takes a significant amount of time for the simulation to complete. Computational time can be…

Reservoir simulations are computationally expensive in the well control and well placement optimization. Generally, numerous simulation runs (realizations) are needed in order to achieve the optimal well locations. In this paper, we propose…

Researchers train neural simulators on uniformly sampled numerical simulation data. But under the same budget, does systematically sampled data provide the most effective information? A fundamental yet unformalized problem is how to sample…

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude…

Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important…

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…

One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE…

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…

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…

Hyperbolic conservation laws govern a wide range of transport-driven dynamics featuring shocks, contact discontinuities, and complex wave interactions, posing distinct challenges for deep-learning-based surrogate modeling. While classical…

The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…

Scientific machine learning is increasingly being spoken of as universal emulators for classical numerical solvers for multi-scale partial differential equations, but most apparent successes can be explained by facts that also define their…

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation into the finite-dimensional algebraic system solved by computers. Due to complicated nature of the…

Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible computational cost of such surrogates renders them an attractive…

High-performance scientific simulations, important for comprehension of complex systems, encounter computational challenges especially when exploring extensive parameter spaces. There has been an increasing interest in developing deep…

Accurate and scalable surrogate models for AC power flow are essential for real-time grid monitoring, contingency analysis, and decision support in increasingly dynamic and inverter-dominated power systems. However, most existing surrogates…