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Found 20 papers, 6 papers with code
Multi-fidelity Gaussian process surrogate modeling for regression problems in physics
One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations.
Systematic construction of continuous-time neural networks for linear dynamical systems
Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space.
Gappy local conformal auto-encoders for heterogeneous data fusion: in praise of rigidity
Fusing measurements from multiple, heterogeneous, partial sources, observing a common object or process, poses challenges due to the increasing availability of numbers and types of sensors.
Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operator
Importantly, we show that the proposed Koopman operator approach provides, for any practical purposes, equivalent results to the FNN-GH approach, thus bypassing the need to train a non-linear map and to use GH to extrapolate predictions in the ambient fMRI space; one can use instead the low-frequency truncation of the DMs function space of L^2-integrable functions, to predict the entire list of coordinate functions in the fMRI space and to solve the pre-image problem.
A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms
Meta-learning of numerical algorithms for a given task consists of the data-driven identification and adaptation of an algorithmic structure and the associated hyperparameters.
Safe Policy Improvement Approaches and their Limitations
Based on this finding, we develop adaptations, the Adv-Soft-SPIBB algorithms, and show that they are provably safe.
Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles
We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian Dynamics Simulations.
Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space
A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models.
Safe Policy Improvement Approaches on Discrete Markov Decision Processes
Safe Policy Improvement (SPI) aims at provable guarantees that a learned policy is at least approximately as good as a given baseline policy.
On the Parameter Combinations That Matter and on Those That do Not
We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models.
On the Correspondence between Gaussian Processes and Geometric Harmonics
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts.
Learning the temporal evolution of multivariate densities via normalizing flows
Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time.
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.
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.
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.
Spectral Discovery of Jointly Smooth Features for Multimodal Data
We show analytically that our method is guaranteed to provide a set of orthogonal functions that are as jointly smooth as possible, ordered by increasing Dirichlet energy from the smoothest to the least smooth.
Domain Adaptation with Optimal Transport on the Manifold of SPD matrices
We model the difference between two domains by a diffeomorphism and use the polar factorization theorem to claim that OT is indeed optimal for DA in a well-defined sense, up to a volume preserving map.
Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion
In this paper, we will explore mathematical algorithms for multifidelity information fusion that use such an approach towards improving the representation of the high-fidelity function with only a few training data points.
