Related papers: Spectral methods for Neural Integral Equations
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
In this review, we survey the latest approaches and techniques developed to overcome the spectral bias towards low frequency of deep neural network learning methods in learning multiple-frequency solutions of partial differential equations.…
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of these methods often depend on traditional eigensolvers, which…
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…
With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
Deep learning computer vision techniques have achieved many successes in recent years across numerous imaging domains. However, the application of deep learning to spectral data remains a complex task due to the need for augmentation…
Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal…
Accurately predicting infrared (IR) spectra in computational chemistry using ab initio methods remains a challenge. Current approaches often rely on an empirical approach or on tedious anharmonic calculations, mainly adapted to semi-rigid…
Deep learning frameworks have become powerful tools for approaching scientific problems such as turbulent flow, which has wide-ranging applications. In practice, however, existing scientific machine learning approaches have difficulty…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…
We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely…
We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which…
Deep representation learning is a crucial procedure in multimedia analysis and attracts increasing attention. Most of the popular techniques rely on convolutional neural network and require a large amount of labeled data in the training…