Related papers: Manifold Learning for Accelerating Coarse-Grained …

Branch and bound methods which are based on the principle "divide and conquer" are a well established solution approach in single-objective integer programming. In multi-objective optimization branch and bound algorithms are increasingly…

Manifold alignment is a type of data fusion technique that creates a shared low-dimensional representation of data collected from multiple domains, enabling cross-domain learning and improved performance in downstream tasks. This paper…

Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…

In robotics, methods and softwares usually require optimizations of hyperparameters in order to be efficient for specific tasks, for instance industrial bin-picking from homogeneous heaps of different objects. We present a developmental…

The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by…

Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…

Most decentralized optimization algorithms are handcrafted. While endowed with strong theoretical guarantees, these algorithms generally target a broad class of problems, thereby not being adaptive or customized to specific problem…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large…

Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than…

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…

Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…

We propose a novel algorithm for combined unit and layer pruning of deep neural networks that functions during training and without requiring a pre-trained network to apply. Our algorithm optimally trades-off learning accuracy and pruning…

Finding Minimal Unsatisfiable Subsets (MUSes) of binary constraints is a common problem in infeasibility analysis of over-constrained systems. However, because of the exponential search space of the problem, enumerating MUSes is extremely…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…

This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…

Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…