相关论文: Accurate Differential Operators for Hybrid Neural …

Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of…

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Many exact search algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as vertex/edge…

The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…

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…

Neural networks have been employed for a wide range of processing applications like image processing, motor control, object detection and many others. Living neural networks offer advantages of lower power consumption, faster processing,…

Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D…

Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…

Purely MLP-based neural radiance fields (NeRF-based methods) often suffer from underfitting with blurred renderings on large-scale scenes due to limited model capacity. Recent approaches propose to geographically divide the scene and adopt…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…

In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…

Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…

We introduce Differentiable Neural Radiosity, a novel method of representing the solution of the differential rendering equation using a neural network. Inspired by neural radiosity techniques, we minimize the norm of the residual of the…

Neural radiance fields (NeRFs) enable novel view synthesis with unprecedented visual quality. However, to render photorealistic images, NeRFs require hundreds of deep multilayer perceptron (MLP) evaluations - for each pixel. This is…

We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…

Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…