
Personalized Algorithm Generation: A Case Study in MetaLearning ODE Integrators
We study the metalearning of numerical algorithms for scientific comput...
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Initializing LSTM internal states via manifold learning
We present an approach, based on learning an intrinsic data manifold, fo...
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Helmholtzian Eigenmap: Topological feature discovery edge flow learning from point cloud data
The manifold Helmholtzian (1Laplacian) operator Δ_1 elegantly generaliz...
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Learning emergent PDEs in a learned emergent space
We extract datadriven, intrinsic spatial coordinates from observations ...
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Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
We propose the Poisson neural networks (PNNs) to learn Poisson systems a...
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Linking Machine Learning with Multiscale Numerics: DataDriven Discovery of Homogenized Equations
The datadriven discovery of partial differential equations (PDEs) consi...
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Transformations between deep neural networks
We propose to test, and when possible establish, an equivalence between ...
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LOCA: LOcal Conformal Autoencoder for standardized data coordinates
We propose a deeplearning based method for obtaining standardized data ...
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Emergent spaces for coupled oscillators
In this paper we present a systematic, datadriven approach to discoveri...
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Spectral Discovery of Jointly Smooth Features for Multimodal Data
In this paper, we propose a spectral method for deriving functions that ...
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Largescale simulation of shallow water waves with computation only on small staggered patches
The multiscale patch scheme is built from given small microscale simula...
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Coarsescale PDEs from finescale observations via machine learning
Complex spatiotemporal dynamics of physicochemical processes are often m...
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On the Koopman operator of algorithms
A systematic mathematical framework for the study of numerical algorithm...
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A geometric approach to the transport of discontinuous densities
Different observations of a relation between inputs ("sources") and outp...
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Optimal Transport on the Manifold of SPD Matrices for Domain Adaptation
The problem of domain adaptation has become central in many applications...
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Transport map accelerated adaptive importance sampling, and application to inverse problems arising from multiscale stochastic reaction networks
In many applications, Bayesian inverse problems can give rise to probabi...
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Linking Gaussian Process regression with datadriven manifold embeddings for nonlinear data fusion
In statistical modeling with Gaussian Process regression, it has been sh...
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Ioannis G. Kevrekidis
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