Related papers: Projection methods for Neural Field equations

Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…

In neural networks, continual learning results in gradient interference among sequential tasks, leading to catastrophic forgetting of old tasks while learning new ones. This issue is addressed in recent methods by storing the important…

Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…

Deep neural networks have become ubiquitous for applications related to visual recognition and language understanding tasks. However, it is often prohibitive to use typical neural networks on devices like mobile phones or smart watches…

We introduce Einstein Fields, a neural representation designed to compress computationally intensive four-dimensional numerical relativity simulations into compact implicit neural network weights. By modeling the metric, the core tensor…

This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…

We propose and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations. The first projection method is a generalization of the…

How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world…

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…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and…

Neural generative models can be used to learn complex probability distributions from data, to sample from them, and to produce probability density estimates. We propose a computational framework for developing neural generative models…

Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…

We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering…

The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…

This paper addresses the challenge of Neural Field (NeF) generalization, where models must efficiently adapt to new signals given only a few observations. To tackle this, we propose Geometric Neural Process Fields (G-NPF), a probabilistic…

Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks, and the cost functions are taken as the energy minimization…

Many crucial tasks of image processing and computer vision are formulated as inverse problems. Thus, it is of great importance to design fast and robust algorithms to solve these problems. In this paper, we focus on generalized projected…