Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

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This work develops new algorithms with rigorous efficiency guarantees for infinite horizon imitation learning (IL) with linear function approximation without restrictive coherence assumptions. We begin with the minimax formulation of the problem and then o ...

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we g ...

A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low-dimensional representation o ...

In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the ...

We propose an adaptive variance-reduction method, called AdaSpider, for minimization of L-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fai ...

A new approach is presented to obtain a convex set of robust D—stabilizing fixed structure controllers, relying on Cauchy's argument principle. A convex set of D—stabilizing controllers around an initial D—stabilizing controller for a multi-model set is re ...

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

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Proximal Point Imitation Learning

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Structure-preserving approaches and data-driven closure modeling for model order reduction

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

A convex set of robust D—stabilizing controllers using Cauchy's argument principle

Dynamical low rank approximation for uncertainty quantification of time-dependent problems