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We investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of a convolutional neural network and multi-layer perceptrons is considered in…

Variational Autoencoders (VAEs) are powerful generative models for learning latent representations. Standard VAEs generate dispersed and unstructured latent spaces by utilizing all dimensions, which limits their interpretability, especially…

Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…

A new deep-learning-based reduced-order modeling (ROM) framework is proposed for application in subsurface flow simulation. The reduced-order model is based on an existing embed-to-control (E2C) framework and includes an auto-encoder, which…

In this thesis, we develop methods to enhance the interpretability of recent representation learning techniques in natural language processing (NLP) while accounting for the unavailability of annotated data. We choose to leverage…

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A…

We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…

Despite the superior performance in modeling complex patterns to address challenging problems, the black-box nature of Deep Learning (DL) methods impose limitations to their application in real-world critical domains. The lack of a smooth…

In this paper, we present two deep learning-based hybrid data-driven reduced order models for the prediction of unsteady fluid flows. The first model projects the high-fidelity time series data from a finite element Navier-Stokes solver to…

As large language models (LLMs) grow in scale and capability, understanding their internal mechanisms becomes increasingly critical. Sparse autoencoders (SAEs) have emerged as a key tool in mechanistic interpretability, enabling the…

Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational…

Explainability is a critical factor influencing the wide deployment of deep vision models (DVMs). Concept-based post-hoc explanation methods can provide both global and local insights into model decisions. However, current methods in this…

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

Learning rich data representations from unlabeled data is a key challenge towards applying deep learning algorithms in downstream tasks. Several variants of variational autoencoders (VAEs) have been proposed to learn compact data…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…

To truly understand vision models, we must not only interpret their learned features but also validate these interpretations through controlled experiments. While earlier work offers either rich semantics or direct control, few post-hoc…

Sparse autoencoders (SAEs) emerged as a promising tool for mechanistic interpretability of transformer-based foundation models. Very recently, SAEs were also adopted for the visual domain, enabling the discovery of visual concepts and their…

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…