Related papers: M2N: Mesh Movement Networks for PDE Solvers
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…
Neural Controlled Differential Equations (Neural CDEs) provide a powerful continuous-time framework for sequence modeling, yet the roughness of the driving control path often restricts their efficiency. Standard splines introduce…
In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…
In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…
Meshfree particle methods, such as Smoothed Particle Hydrodynamics (SPH) and the Moving Particle Semi-Implicit (MPS) method, are widely used to simulate complex free-surface and multiphase flows. A key challenge in these methods is the…
In this paper, we propose a novel method for monocular depth estimation in dynamic scenes. We first explore the arbitrariness of object's movement trajectory in dynamic scenes theoretically. To overcome the arbitrariness, we use assume that…
The solution of a PDE over varying initial/boundary conditions on multiple domains is needed in a wide variety of applications, but it is computationally expensive if the solution is computed de novo whenever the initial/boundary conditions…
Motion boundary detection is a crucial yet challenging problem. Prior methods focus on analyzing the gradients and distributions of optical flow fields, or use hand-crafted features for motion boundary learning. In this paper, we propose…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
The multi-modality and stochastic characteristics of human behavior make motion prediction a highly challenging task, which is critical for autonomous driving. While deep learning approaches have demonstrated their great potential in this…
The concept of the path-dependent partial differential equation (PPDE) was first introduced in the context of path-dependent derivatives in financial markets. Its semilinear form was later identified as a non-Markovian backward stochastic…
This article presents an introduction to MMPDElab, a package written in MATLAB for adaptive mesh movement and adaptive moving mesh P1 finite element solution of second-order partial different equations having continuous solutions in one,…
We propose a new method for the construction of layer-adapted meshes for singularly perturbed differential equations (SPDEs), based on mesh partial differential equations (MPDEs) that incorporate \emph{a posteriori} solution information.…
Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
Motion estimation (ME) and motion compensation (MC) have been widely used for classical video frame interpolation systems over the past decades. Recently, a number of data-driven frame interpolation methods based on convolutional neural…
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…
Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…