Related papers: A near-stationary subspace for ridge approximation
This paper proposes a theoretical framework for modeling and optimizing the bounded functions based on the Fourier series approximation and Ricci flow. Specifically, the initial manifold, $\mathcal{M}_0$ is approximated using Fourier series…
This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building surrogate models of what we call "field amplification",…
Recent developments in surrogate construction predominantly focused on two strategies to improve surrogate accuracy. Firstly, component-wise domain scaling informed by cross-validation. Secondly, regression to construct response surfaces…
In the real world, insufficient information, limited computation resources, and complex problem structures often force an autonomous agent to make a decision in time less than that required to solve the problem at hand completely. Flexible…
Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to…
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represents manifold data accurately while preserving the manifold's…
Motivated by the problem of optimization of force-field systems in physics using large-scale computer simulations, we consider exploration of a deterministic complex multivariate response surface. The objective is to find input combinations…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
The advent of 6G is expected to enable many use cases which may rely on accurate knowledge of the location and orientation of user equipment (UE). The conventional localization methods suffer from limitations such as synchronization and…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of directions in the high-dimensional input…
This works handles the inverse reinforcement learning problem in high-dimensional state spaces, which relies on an efficient solution of model-based high-dimensional reinforcement learning problems. To solve the computationally expensive…
We give a sketching-based iterative algorithm that computes a $1+\varepsilon$ approximate solution for the ridge regression problem $\min_x \|Ax-b\|_2^2 +\lambda\|x\|_2^2$ where $A \in R^{n \times d}$ with $d \ge n$. Our algorithm, for a…
In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a…
We revisit a classical airfoil design problem: the search for shapes that maximize aerodynamic performance metrics, targeting the underexplored intermediate Reynolds-number regime between 1 and 3000, relevant to small animals and miniature…
Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with systems having high input dimensionality, reliability estimation becomes a daunting task. A popular approach to overcome…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…
Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all…