Related papers: Towards Universal Mesh Movement Networks

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…

We introduce the Universal Manipulation Policy Network (UMPNet) -- a single image-based policy network that infers closed-loop action sequences for manipulating arbitrary articulated objects. To infer a wide range of action trajectories,…

We consider a mesh-based approach for training a neural network to produce field predictions of solutions to parametric partial differential equations (PDEs). This approach contrasts current approaches for "neural PDE solvers" that employ…

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…

Simulating multiscale flows with moving boundaries, such as hypersonic multi-body separation and flows in micro-electro-mechanical systems (MEMS), requires robust numerical methods that couple mesh deformation with complex flow physics.…

Delineating infarcted tissue in ischemic stroke lesions is crucial to determine the extend of damage and optimal treatment for this life-threatening condition. However, this problem remains challenging due to high variability of ischemic…

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…

We propose DriveAnyMesh, a method for driving mesh guided by monocular video. Current 4D generation techniques encounter challenges with modern rendering engines. Implicit methods have low rendering efficiency and are unfriendly to…

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…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful class of mesh-free numerical methods for solving partial differential equations (PDEs), particularly those involving complex geometries. In this work, we present an…

This paper describes Motion Planning Networks (MPNet), a computationally efficient, learning-based neural planner for solving motion planning problems. MPNet uses neural networks to learn general near-optimal heuristics for path planning in…

In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…

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,…

In the field of Maritime Autonomous Surface Ships (MASS), the accurate modeling of ship maneuvering motion for harbor maneuvers is a crucial technology. Non-parametric system identification (SI) methods, which do not require prior knowledge…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

We present a novel, and effective, approach to achieve optimal mesh relocation in finite element methods (FEMs). The cost and accuracy of FEMs is critically dependent on the choice of mesh points. Mesh relocation (r-adaptivity) seeks to…

Modeling dynamics in the form of partial differential equations (PDEs) is an effectual way to understand real-world physics processes. For complex physics systems, analytical solutions are not available and numerical solutions are…

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…

The integration of deep learning in medical imaging has shown great promise for enhancing diagnostic, therapeutic, and research outcomes. However, applying universal models across multiple modalities remains challenging due to the inherent…

Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…