Related papers: Projection methods for Neural Field equations
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
The ability to learn continually without forgetting the past tasks is a desired attribute for artificial learning systems. Existing approaches to enable such learning in artificial neural networks usually rely on network growth, importance…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
Recent neural networks based surface reconstruction can be roughly divided into two categories, one warping templates explicitly and the other representing 3D surfaces implicitly. To enjoy the advantages of both, we propose a novel 3D…
Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes' rule to find the best explanation for available data. Understanding the neural mechanisms underlying…
This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear parametrizations such as deep networks. The proposed…
Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to…
In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…
After the tremendous development of neural networks trained by backpropagation, it is a good time to develop other algorithms for training neural networks to gain more insights into networks. In this paper, we propose a new algorithm for…
We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…
This paper is concerned with numerical analysis of two fully discrete Chorin-type projection methods for the stochastic Stokes equations with general non-solenoidal multiplicative noise. The first scheme is the standard Chorin scheme and…
Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
This paper presents a data driven universal ball trajectory prediction method integrated with physics equations. Existing methods are designed for specific ball types and struggle to generalize. This challenge arises from three key factors.…
Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…
Simulation of extracellular fields is one of the substantial methods used in the area of computational neuroscience. Its most common usage is validation of experimental methods as EEG and extracellular spike recordings or modeling of…
Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…
We propose a method for extending the technique of equilibrium propagation for estimating gradients in fixed-point neural networks to the more general setting of directed, time-varying neural networks by modeling them as electrical…
Notions of depth in regression have been introduced and studied in the literature. The most famous example is Regression Depth (RD), which is a direct extension of location depth to regression. The projection regression depth (PRD) is the…
In many so-called "beyond-mean-field" many-body methods, one creates symmetry-breaking states and then projects out states with good quantum number(s); the most important example is angular momentum. Motivated by the computational intensity…