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In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…

This paper introduces the Descriptive Variational Autoencoder (DVAE), an unsupervised and end-to-end trainable neural network for predicting vehicle trajectories that provides partial interpretability. The novel approach is based on the…

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The model is a version of a conditional variational auto-encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty…

Auto-encoder is a special kind of neural network based on reconstruction. De-noising auto-encoder (DAE) is an improved auto-encoder which is robust to the input by corrupting the original data first and then reconstructing the original…

This study explores the application of Convolutional Autoencoders (CAEs) for analyzing and reconstructing Scanning Tunneling Microscopy (STM) images of various crystalline lattice structures. We developed two distinct CAE architectures to…

Is there really much more to say about sparse autoencoders (SAEs)? Autoencoders in general, and SAEs in particular, represent deep architectures that are capable of modeling low-dimensional latent structure in data. Such structure could…

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

We develop a convolutional regularized least squares ($\texttt{CRLS}$) framework for reduced-order modeling of transonic flows with shocks. Conventional proper orthogonal decomposition (POD) based reduced models are attractive because of…

We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demonstrative application, we pursue the modeling of cathodic…

With the integration of image modality, the semantic space of multimodal large language models (MLLMs) is more complex than text-only models, making their interpretability more challenging and their alignment less stable, particularly…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Understanding how generative models represent and transform data is a foundational problem in deep learning interpretability. While mechanistic interpretability of discriminative architectures has yielded substantial insights, relatively…

Layout design with complex constraints is a challenging problem to solve due to the non-uniqueness of the solution and the difficulties in incorporating the constraints into the conventional optimization-based methods. In this paper, we…

Representation learning seeks to expose certain aspects of observed data in a learned representation that's amenable to downstream tasks like classification. For instance, a good representation for 2D images might be one that describes only…

Sparse Autoencoders (SAEs) are a powerful dictionary learning technique for decomposing neural network activations, translating the hidden state into human ideas with high semantic value despite no external intervention or guidance.…

The need for interpretable models has fostered the development of self-explainable classifiers. Prior approaches are either based on multi-stage optimization schemes, impacting the predictive performance of the model, or produce…

Deep learning models for medical image classification usually achieve promising results but typically rely on large, annotated datasets or standard transfer learning from ImageNet. Self-Supervised Learning (SSL) has emerged as a powerful…

Data-driven fault diagnostics of safety-critical systems often faces the challenge of a complete lack of labeled data associated with faulty system conditions (i.e., fault types) at training time. Since an unknown number and nature of fault…