Related papers: Neural Shape Operator Surrogates -- Expression Rat…
For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a large dataset of geometry-solution pairs in order to obtain a…
Recent experiments have shown that deep networks can approximate solutions to high-dimensional PDEs, seemingly escaping the curse of dimensionality. However, questions regarding the theoretical basis for such approximations, including the…
This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…
Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional function spaces using conventional neural architectures, have…
Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…
Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…
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,…
We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solution of partial differential equations (PDEs), and are used in…
Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…
Neural surrogates for Partial Differential Equations (PDEs) often suffer significant performance degradation when evaluated on problem configurations outside their training distribution, such as new initial conditions or structural…
This work presents an interpretable parametric surrogate model motivated by the need to identify a hydrodynamic model for resolving the trajectory of an object in real-time. The surrogate is formulated as a reduced-order model for a…
Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…
Neural operators have emerged as a powerful, discretization-invariant framework for solving partial differential equations (PDEs). Although established approaches like the Deep Operator Network (DeepONet) have successfully achieved…
We consider the point evaluation of the solution to interface problems with geometric uncertainties, where the uncertainty in the obstacle is described by a high-dimensional parameter $\boldsymbol{y}\in[-1,1]^d$, $d\in\mathbb{N}$. We focus…
Metasurfaces, typically realized as arrays of nanopillars, transform electromagnetic (EM) fields depending on their geometry and spatial arrangement. For solving the inverse problem of designing new metasurfaces that transform EM fields in…
A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of…
Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…
Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained…
Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only apply to rectilinear domains, and do not systematically…
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order model, such as a deep neural network, to approximate the…