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Neural fields are evolving towards a general-purpose continuous representation for visual computing. Yet, despite their numerous appealing properties, they are hardly amenable to signal processing. As a remedy, we present a method to…

Computer Vision and Pattern Recognition · Computer Science 2024-04-08 Ntumba Elie Nsampi , Adarsh Djeacoumar , Hans-Peter Seidel , Tobias Ritschel , Thomas Leimkühler

We present a novel method for using Neural Networks (NNs) for finding solutions to a class of Partial Differential Equations (PDEs). Our method builds on recent advances in Neural Radiance Field research (NeRFs) and allows for a NN to…

Machine Learning · Computer Science 2022-05-31 Jaroslaw Rzepecki , Daniel Bates , Chris Doran

The reconstruction of indoor scenes from multi-view RGB images is challenging due to the coexistence of flat and texture-less regions alongside delicate and fine-grained regions. Recent methods leverage neural radiance fields aided by…

Computer Vision and Pattern Recognition · Computer Science 2024-08-14 Sheng Ye , Yubin Hu , Matthieu Lin , Yu-Hui Wen , Wang Zhao , Yong-Jin Liu , Wenping Wang

Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these…

Numerical Analysis · Mathematics 2026-01-21 Maxime Bouchereau

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…

Machine Learning · Computer Science 2023-05-30 Haixu Wu , Tengge Hu , Huakun Luo , Jianmin Wang , Mingsheng Long

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…

Quantum Physics · Physics 2026-04-17 Nils Klement , Veronika Eyring , Mierk Schwabe

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

Machine Learning · Computer Science 2021-02-23 Qunxi Zhu , Yao Guo , Wei Lin

Differentiable rendering aims to compute the derivative of the image rendering function with respect to the rendering parameters. This paper presents a novel algorithm for 6-DoF pose estimation through gradient-based optimization using a…

Computer Vision and Pattern Recognition · Computer Science 2022-12-27 Ramchander Rao Bhaskara , Roshan Thomas Eapen , Manoranjan Majji

We present a method to automatically compute correct gradients with respect to geometric scene parameters in neural SDF renderers. Recent physically-based differentiable rendering techniques for meshes have used edge-sampling to handle…

We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

Machine Learning · Computer Science 2020-11-16 Maysum Panju , Kourosh Parand , Ali Ghodsi

Partial differential equations (PDEs) are crucial in modeling diverse phenomena across scientific disciplines, including seismic and medical imaging, computational fluid dynamics, image processing, and neural networks. Solving these PDEs at…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-01-07 George Bisbas , Rhodri Nelson , Mathias Louboutin , Fabio Luporini , Paul H. J. Kelly , Gerard Gorman

Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…

Machine Learning · Computer Science 2024-09-24 Jaouad Dabounou

Recent progress in large-scale scene rendering has yielded Neural Radiance Fields (NeRF)-based models with an impressive ability to synthesize scenes across small objects and indoor scenes. Nevertheless, extending this idea to large-scale…

Computer Vision and Pattern Recognition · Computer Science 2024-05-13 Xiaohan Zhang , Yukui Qiu , Zhenyu Sun , Qi Liu

The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…

Numerical Analysis · Mathematics 2024-08-26 Lukas Gonon , Arnulf Jentzen , Benno Kuckuck , Siyu Liang , Adrian Riekert , Philippe von Wurstemberger

This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…

Machine Learning · Computer Science 2024-01-09 Lars Ruthotto

Photo-realistic rendering and novel view synthesis play a crucial role in human-computer interaction tasks, from gaming to path planning. Neural Radiance Fields (NeRFs) model scenes as continuous volumetric functions and achieve remarkable…

Computer Vision and Pattern Recognition · Computer Science 2025-03-19 Iryna Repinetska , Anna Hilsmann , Peter Eisert

Semantic segmentation of overhead remote sensing imagery enables applications in mapping, urban planning, and disaster response. State-of-the-art segmentation networks are typically developed and tuned on ground-perspective photographs and…

Computer Vision and Pattern Recognition · Computer Science 2025-09-05 David Huangal , J. Alex Hurt

Implicit radiance functions emerged as a powerful scene representation for reconstructing and rendering photo-realistic views of a 3D scene. These representations, however, suffer from poor editability. On the other hand, explicit…

Computer Vision and Pattern Recognition · Computer Science 2022-10-28 Li Ma , Xiaoyu Li , Jing Liao , Xuan Wang , Qi Zhang , Jue Wang , Pedro Sander

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…

Numerical Analysis · Mathematics 2023-01-30 Zezhong Zhang , Feng Bao , Lili Ju , Guannan Zhang

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Machine Learning · Computer Science 2021-06-11 Sifan Wang , Paris Perdikaris