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Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…
In this work, we propose and develop efficient and accurate numerical methods for solving the Kirchhoff-Love plate model in domains with complex geometries. The algorithms proposed here employ curvilinear finite-difference methods for…
Collision detection is essential to virtually all robotics applications. However, traditional geometric collision detection methods generally require pre-existing workspace geometry representations; thus, they are unable to infer the…
This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…
Neural radiance field (NeRF) has shown remarkable performance in generating photo-realistic novel views. Among recent NeRF related research, the approaches that involve the utilization of explicit structures like grids to manage features…
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…
Transformer-based NLP models are powerful but have high computational costs that limit deployment. Finetuned encoder-decoder models are popular in specialized domains and can outperform larger more generalized decoder-only models, such as…
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…
Temporal interpolation often plays a crucial role to learn meaningful representations in dynamic scenes. In this paper, we propose a novel method to train spatiotemporal neural radiance fields of dynamic scenes based on temporal…
Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…
In this paper, we present a powerful differentiable surface fitting technique to derive a compact surface representation for a given dense point cloud or mesh, with application in the domains of graphics and CAD/CAM. We have chosen the Loop…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
Neural fields have become widely used in various fields, from shape representation to neural rendering, and for solving partial differential equations (PDEs). With the advent of hybrid neural field representations like Instant NGP that…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
Large-scale incremental mapping is fundamental to the development of robust and reliable autonomous systems, as it underpins incremental environmental understanding with sequential inputs for navigation and decision-making. LiDAR is widely…
In this paper, we investigate the combination of multigrid methods and neural networks, starting from a Finite Element discretization of an elliptic PDE. Multigrid methods use interpolation operators to transfer information between…
Parametric feature grid encodings have gained significant attention as an encoding approach for neural fields since they allow for much smaller MLPs, which significantly decreases the inference time of the models. In this work, we propose…
Dense reconstruction and differentiable rendering are fundamental tightly connected operations in 3D vision and computer graphics. Recent neural implicit representations demonstrate compelling advantages in reconstruction fidelity and…
We develop efficient and high-order accurate solvers for the Helmholtz equation on complex geometry. The schemes are based on the WaveHoltz algorithm which computes solutions of the Helmholtz equation by time-filtering solutions of the wave…