相关论文: StEik: Stabilizing the Optimization of Neural Sign…

Implicit Neural Representations (INRs) that learn Signed Distance Functions (SDFs) from point cloud data represent the state-of-the-art for geometrically accurate 3D scene reconstruction. However, training these Neural SDFs often requires…

Implicit Neural Representations (INRs) have emerged as a powerful tool for geometric representation, yet their suitability for physics-based simulation remains underexplored. While metrics like Hausdorff distance quantify surface…

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Implicit Neural Representations have gained prominence as a powerful framework for capturing complex data modalities, encompassing a wide range from 3D shapes to images and audio. Within the realm of 3D shape representation, Neural Signed…

We present STITCH, a novel approach for neural implicit surface reconstruction of a sparse and irregularly spaced point cloud while enforcing topological constraints (such as having a single connected component). We develop a new…

We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, and inversion. Several numerical…

Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to…

\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating…

Optimization-based PDE solvers that minimize scalar loss functions have gained increasing attention in recent years. These methods either define the loss directly over discrete variables, as in Optimizing a Discrete Loss (ODIL), or…

Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained…

We study the optimization landscape and the stability properties of training problems with squared loss for neural networks and general nonlinear conic approximation schemes. It is demonstrated that, if a nonlinear conic approximation…

Representing surfaces as zero level sets of neural networks recently emerged as a powerful modeling paradigm, named Implicit Neural Representations (INRs), serving numerous downstream applications in geometric deep learning and 3D vision.…

Physics-Informed Neural Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit within the training domain, leading to…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs), yet they often fail to achieve accurate convergence in the H1 norm, especially in the presence of boundary…

This paper proposes a rank inspired neural network (RINN) to tackle the initialization sensitivity issue of physics informed extreme learning machines (PIELM) when numerically solving partial differential equations (PDEs). Unlike PIELM…

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…