相关论文: Accurate Differential Operators for Hybrid Neural …

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

Dynamic imaging is essential for analyzing various biological systems and behaviors but faces two main challenges: data incompleteness and computational burden. For many imaging systems, high frame rates and short acquisition times require…

We propose a simple yet effective neural network-based framework for global illumination rendering. Recently, rendering techniques that learn neural radiance caches by minimizing the difference (i.e., residual) between the left and right…

Recently, neural fields, also known as coordinate-based MLPs, have achieved impressive results in representing low-dimensional data. Unlike CNN, MLPs are globally connected and lack local control; adjusting a local region leads to global…

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…

Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these…

Depth of Field (DoF) in games is usually achieved as a post-process effect by blurring pixels in the sharp rasterized image based on the defined focus plane. This paper describes a novel real-time DoF technique that uses ray tracing with…

Faster rendering of synthetic images is a core problem in the field of computer graphics. Rendering algorithms, such as path-tracing is dependent on parameters like size of the image, number of light bounces, number of samples per pixel,…

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…

Neural Radiance Fields (NeRFs) can be dramatically accelerated by spatial grid representations. However, they do not explicitly reason about scale and so introduce aliasing artifacts when reconstructing scenes captured at different camera…

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…

Neural fields, coordinate-based neural networks, have recently gained popularity for implicitly representing a scene. In contrast to classical methods that are based on explicit representations such as point clouds, neural fields provide a…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…

This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines…

Solving partial differential equations (PDEs) has been a fundamental problem in computational science and of wide applications for both scientific and engineering research. Due to its universal approximation property, neural network is…

PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key…

We introduce a new approach for reconstruction and novel view synthesis of unbounded real-world scenes. In contrast to previous methods using either volumetric fields, grid-based models, or discrete point cloud proxies, we propose a hybrid…

Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…

Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…

Current differentiable renderers provide light transport gradients with respect to arbitrary scene parameters. However, the mere existence of these gradients does not guarantee useful update steps in an optimization. Instead, inverse…