Related papers: Projection methods for Neural Field equations

Spatial Galerkin projection transfers fields between different meshes. In the area of finite element analysis of electromagnetic fields, it provides great convenience for remeshing, multi-physics, domain decomposition methods, etc. In this…

Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynamics given by Neural Galerkin schemes and propose to…

Neural Radiance Fields (NeRF) have achieved remarkable progress in neural rendering. Extracting geometry from NeRF typically relies on the Marching Cubes algorithm, which uses a hand-crafted threshold to define the level set. However, this…

Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative…

The standard consolidation theory states that short-term memories located in the hippocampus enable the consolidation of long-term memories in the neocortex. In other words, the neocortex slowly learns long-term memories with a transient…

Neural fields (NeFs) have recently emerged as a versatile method for modeling signals of various modalities, including images, shapes, and scenes. Subsequently, a number of works have explored the use of NeFs as representations for…

In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…

Many large scale structure surveys sort their observations into redshift bins and treat every tracer as being located at the mean redshift of its bin, a treatment which we refer to as the equal time approximation. Recently, a new method was…

Neural field equations offer a continuous description of the dynamics of large populations of synaptically coupled neurons. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception,…

Integro-differential equations, analyzed in this work, comprise an important class of models of continuum media with nonlocal interactions. Examples include peridynamics, population and opinion dynamics, the spread of disease models, and…

Reconstructing continuous environmental fields from sparse and irregular observations remains a central challenge in environmental modelling and biodiversity informatics. Many ecological datasets are heterogeneous in space and time, making…

This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the…

We consider a simple neural field model in which the state variable is dendritic voltage, and in which somas form a continuous one-dimensional layer. This neural field model with dendritic processing is formulated as an integro-differential…

Coordinate transformation models often fail to account for nonlinear and spatially dependent distortions, leading to significant residual errors in geospatial applications. Here we propose a residual-based neural correction strategy, in…

Recent advances in modeling density distributions, so-called neural density fields, can accurately describe the density distribution of celestial bodies without, e.g., requiring a shape model - properties of great advantage when designing…

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

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…

A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking…

The proposed method, Neural Radiance Projection (NeRP), addresses the three most fundamental shortages of training such a convolutional neural network on X-ray image segmentation: dealing with missing/limited human-annotated datasets;…

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…