Search Results for author:
Found 8 papers, 2 papers with code
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss.
Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics.
Personalized Algorithm Generation: A Case Study in Learning ODE Integrators
As a case study, we develop a machine learning approach that automatically learns effective solvers for initial value problems in the form of ordinary differential equations (ODEs), based on the Runge-Kutta (RK) integrator architecture.
Initializing LSTM internal states via manifold learning
We present an approach, based on learning an intrinsic data manifold, for the initialization of the internal state values of LSTM recurrent neural networks, ensuring consistency with the initial observed input data.
Learning emergent PDEs in a learned emergent space
These coordinates then serve as an emergent space in which to learn predictive models in the form of partial differential equations (PDEs) for the collective description of the coupled-agent system.
Coarse-grained and emergent distributed parameter systems from data
We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) from spatiotemporal data.
Transformations between deep neural networks
We propose to test, and when possible establish, an equivalence between two different artificial neural networks by attempting to construct a data-driven transformation between them, using manifold-learning techniques.
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized latent variables.
