Related papers: Learning filtered discretization operators: non-in…

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…

Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…

This paper develops a deep learning method for linear and nonlinear filtering. The idea is to start with a nominal dynamic model and generate Monte Carlo sample paths. Then these samples are used to train a deep neutral network. A least…

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…

On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the…

Deep learning often faces the challenge of efficiently processing dynamic inputs, such as sensor data or user inputs. For example, an AI writing assistant is required to update its suggestions in real time as a document is edited.…

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…

Most existing federated learning methods are unable to estimate model/predictive uncertainty since the client models are trained using the standard loss function minimization approach which ignores such uncertainties. In many situations,…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…

We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for input and output function distributions. We introduce the concepts of \textit{numerical operator…

Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…

Traditional fluid flow predictions require large computational resources. Despite recent progress in parallel and GPU computing, the ability to run fluid flow predictions in real-time is often infeasible. Recently developed machine learning…

Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer…

This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…

Stable partitioned techniques for simulating unsteady fluid-structure interaction (FSI) are known to be computationally expensive when high added-mass is involved. Multiple coupling strategies have been developed to accelerate these…