Related papers: Accelerate Neural Subspace-Based Reduced-Order Sol…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
Motion planning is a mature area of research in robotics with many well-established methods based on optimization or sampling the state space, suitable for solving kinematic motion planning. However, when dynamic motions under constraints…
Current trends in the computer graphics community propose leveraging the massive parallel computational power of GPUs to accelerate physically based simulations. Collision detection and solving is a fundamental part of this process. It is…
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While…
Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
We propose a model order reduction approach to speed up the computation of seismograms, i.e. the solution of the seismic wave equation evaluated at a receiver location, for different model parameters. Our approach achieves a reduction of…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective…
MR Fingerprinting is a novel quantitative MR technique that could simultaneously provide multiple tissue property maps. When optimizing MRF scans, modeling undersampling errors and field imperfections in cost functions will make the…
Computer simulations are invaluable tools for scientific discovery. However, accurate simulations are often slow to execute, which limits their applicability to extensive parameter exploration, large-scale data analysis, and uncertainty…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…
To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the…
Recent methods for neural surface representation and rendering, for example NeuS, have demonstrated the remarkably high-quality reconstruction of static scenes. However, the training of NeuS takes an extremely long time (8 hours), which…
We develop a proxy model based on deep learning methods to accelerate the simulations of oil reservoirs--by three orders of magnitude--compared to industry-strength physics-based PDE solvers. This paper describes a new architectural…