
-
Learning emergent PDEs in a learned emergent space
We extract data-driven, intrinsic spatial coordinates from observations ...
read it
-
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
We propose the Poisson neural networks (PNNs) to learn Poisson systems a...
read it
-
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
The data-driven discovery of partial differential equations (PDEs) consi...
read it
-
Transformations between deep neural networks
We propose to test, and when possible establish, an equivalence between ...
read it
-
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
We propose a deep-learning based method for obtaining standardized data ...
read it
-
Emergent spaces for coupled oscillators
In this paper we present a systematic, data-driven approach to discoveri...
read it
-
Spectral Discovery of Jointly Smooth Features for Multimodal Data
In this paper, we propose a spectral method for deriving functions that ...
read it
-
Large-scale simulation of shallow water waves with computation only on small staggered patches
The multiscale patch scheme is built from given small micro-scale simula...
read it
-
Coarse-scale PDEs from fine-scale observations via machine learning
Complex spatiotemporal dynamics of physicochemical processes are often m...
read it
-
On the Koopman operator of algorithms
A systematic mathematical framework for the study of numerical algorithm...
read it
-
A geometric approach to the transport of discontinuous densities
Different observations of a relation between inputs ("sources") and outp...
read it
-
Optimal Transport on the Manifold of SPD Matrices for Domain Adaptation
The problem of domain adaptation has become central in many applications...
read it
-
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...
read it
-
Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion
In statistical modeling with Gaussian Process regression, it has been sh...
read it