Related papers: PCENet: High Dimensional Surrogate Modeling for Le…

Biophysical neural system simulations are among the most computationally demanding scientific applications, and their optimization requires navigating high-dimensional parameter spaces under numerous constraints that impose a binary…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications…

Representation learning is a widely adopted framework for learning in data-scarce environments, aiming to extract common features from related tasks. While centralized approaches have been extensively studied, decentralized methods remain…

In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…

The increasing adoption of Deep Neural Networks (DNNs) has led to their application in many challenging scientific visualization tasks. While advanced DNNs offer impressive generalization capabilities, understanding factors such as model…

Despite tremendous progress over the past decade, deep learning methods generally fall short of human-level systematic generalization. It has been argued that explicitly capturing the underlying structure of data should allow connectionist…

We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

High-fidelity electromagnetic (EM) simulations are indispensable for the design of microwave and wave devices, yet repeated full-wave evaluations over high-dimensional design spaces are often computationally prohibitive. While neural…

We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Machine learning classification techniques have been used widely to recognize the feasible design domain and discover hidden patterns in engineering design. An accurate classification model needs a large dataset; however, generating a large…

Robust control of mechanical systems with multiple uncertainties remains a fundamental challenge, particularly when nonlinear dynamics and operating-condition variations are intricately intertwined. Although deep reinforcement learning…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However,…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…