Related papers: Learning nonlinear level sets for dimensionality r…

In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward…

Deep metric learning (DML) aims to learn a discriminative high-dimensional embedding space for downstream tasks like classification, clustering, and retrieval. Prior literature predominantly focuses on pair-based and proxy-based methods to…

Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general…

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

We consider the problem of linear classification under general loss functions in the limited-data setting. Overfitting is a common problem here. The standard approaches to prevent overfitting are dimensionality reduction and regularization.…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

We address the problem of accelerating thin-shell deformable object simulations by dimension reduction. We present a new algorithm to embed a high-dimensional configuration space of deformable objects in a low-dimensional feature space,…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…

We present a computational method for empirically characterizing the training loss level-sets of deep neural networks. Our method numerically constructs a path in parameter space that is constrained to a set with a fixed near-zero training…

In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling…

Training reinforcement learning (RL) agents often requires significant computational resources and prolonged training durations. To address this challenge, we build upon prior work that introduced a neural architecture with…

We present a machine learning framework that blends image super-resolution technologies with passive, scalar transport in the level-set method. Here, we investigate whether we can compute on-the-fly, data-driven corrections to minimize…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

Immersive novel view generation is an important technology in the field of graphics and has recently also received attention for operator-based human-robot interaction. However, the involved training is time-consuming, and thus the current…

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…

Current end-to-end deep Reinforcement Learning (RL) approaches require jointly learning perception, decision-making and low-level control from very sparse reward signals and high-dimensional inputs, with little capability of incorporating…

Large language models (LLMs) are trained for downstream tasks by updating their parameters (e.g., via RL). However, updating parameters forces them to absorb task-specific information, which can result in catastrophic forgetting and loss of…