Publications related to Linear interpolation

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...

Springer International Publishing Ag2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

2024

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Volkan Cevher, Thomas Michaelsen Pethick, Wanyun Xie

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei, Juan Cao

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

Graph Representation Learning with Optimal Transport: Analysis and Applications

Effrosyni Simou

In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph- ...

EPFL2022

On Linear Interpolation in the Latent Space of Deep Generative Models

Quentin Christian Becker, Mike Yan Michelis

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

2021

Remarks on Poincare and interpolation estimates for Truncated Hierarchical B-splines

Annalisa Buffa

This paper should be considered as an addendum to [A. Buffa and C. Giannelli, Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence, Math. Models Methods Appl. Sci. 26 (2016) 1-25] and [A. Buffa and C. Giannelli, Adaptive ...

2021

Computation of "Best" Interpolants in the Lp Sense

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

2020

High-order essentially nonoscillatory methods based on radial basis functions

Fabian Mönkeberg

Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely employed to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well s ...

EPFL2020

Neural BTF Compression and Interpolation

Wenzel Alban Jakob

The Bidirectional Texture Function (BTF) is a data-driven solution to render materials with complex appearance. A typical capture contains tens of thousands of images of a material sample under varying viewing and lighting conditions. While capable of fait ...

WILEY2019

Radar-rain gauge merging and discharge data assimilation for flood forecasting in Alpine catchments

Alain Tommy Foehn

Floods are responsible for one third of the economic losses induced by natural hazards throughout the world. To better protect the population and infrastructures, flood forecasting systems make us of weather forecasts to foresee floods several days in adva ...

EPFL2019

Spatial interpolation of precipitation from multiple rain gauge networks and weather radar data for operational applications in Alpine catchments

Giovanni De Cesare, Javier García Hernández, Bettina Schaefli, Alain Tommy Foehn

Increasing meteorological data availability and quality implies an adaptation of the interpolation methods for data combination. In this paper, we propose a new method to efficiently combine weather radar data with data from two heated rain gauge networks ...

2018

Graph-Based Interpolation for Zooming in 3D Scenes

Pascal Frossard, Pinar Akyazi

In multiview systems, color plus depth format builds 3D representations of scenes within which the users can freely navigate by changing their viewpoints. In this paper we present a framework for view synthesis when the user requests an arbitrary viewpoint ...

2017

Sampling strategies and post-processing methods for increasing the time resolution of organic aerosol measurements requiring long sample-collection times

Satoshi Takahama, Robin Lewis Modini

The composition and properties of atmospheric organic aerosols (OAs) change on timescales of minutes to hours. However, some important OA characterization techniques typically require greater than a few hours of sample-collection time (e.g., Fourier transf ...

Copernicus GmbH2016

Spatial interpolation of experimental raindrop size distribution spectra

Alexis Berne, Timothy Hugh Raupach

We present a new approach for spatial interpolation of experimental raindrop size distribution (DSD) spectra. The DSD is fundamental to the study and understanding of precipitation and its monitoring and modelling. It is measured insitu using disdrometers ...

Wiley-Blackwell2016

An automated baseline correction protocol for infrared spectra of atmospheric aerosols collected on polytetrafluoroethylene (Teflon) filters

Satoshi Takahama, Adela Kuzmiaková

A growing body of research on statistical applications for characterization of atmospheric aerosol Fourier transform infrared (FT-IR) samples collected on polytetrafluoroethylene (PTFE) filters (e.g., Russell et al., 2011; Ruthenburg et al., 2014) and a ri ...

European Geosciences Union2016

Scaling Precipitation Input to Spatially Distributed Hydrological Models by Measured Snow Distribution

Michael Lehning, Nander Wever, Mathias Thierry Pierre Bavay

Accurate knowledge on snow distribution in alpine terrain is crucial for various applications such as flood risk assessment, avalanche warning or managing water supply and hydro-power. To simulate the seasonal snow cover development in alpine terrain, the ...

Frontiers Media Sa2016

Variability of the raindrop size distribution across scales in Mediterranean rainfall : characterisation and stochastic simulation

Timothy Hugh Raupach

Measurement of rain is made difficult by the high variability of the precipitation process, down to raindrop scale. Point measurements are generally accurate, but their lack of spatial representativeness is a significant limitation. Weather radars indirect ...

EPFL2016

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

Michaël Unser, John Paul Ward

Motivated by the interior tomography problem, we propose a method for exact reconstruction of a region of interest of a function from its local Radon transform in any number of dimensions. Our aim is to verify the feasibility of a one-dimensional reconstru ...

Siam Publications2015