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Sparse autoencoders are a promising new approach for decomposing language model activations for interpretation and control. They have been applied successfully to vision transformer image encoders and to small-scale diffusion models.…

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…

Three-dimensional (3D) medical image enhancement, including denoising and super-resolution, is critical for clinical diagnosis in CT, PET, and MRI. Although diffusion models have shown remarkable success in 2D medical imaging, scaling them…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

Test-Time Adaptation (TTA) adjusts models using unlabeled test data to handle dynamic distribution shifts. However, existing methods rely on frequent adaptation and high computational cost, making them unsuitable for resource-constrained…

State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…

High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Dictionary learning is a challenge topic in many image processing areas. The basic goal is to learn a sparse representation from an overcomplete basis set. Due to combining the advantages of generic multiscale representations with learning…

Physics-informed methods have gained a great success in analyzing data with partial differential equation (PDE) constraints, which are ubiquitous when modeling dynamical systems. Different from the common penalty-based approach, this work…

Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…

Spatio-temporal feature encoding is essential for encoding facial expression dynamics in video sequences. At test time, most spatio-temporal encoding methods assume that a temporally segmented sequence is fed to a learned model, which could…

In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…

This study presents a framework for predicting unsteady transonic wing pressure distributions, integrating an autoencoder architecture with graph convolutional networks and graph-based temporal layers to model time dependencies. The…

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

Multivariate long-term time series forecasting is of great application across many domains, such as energy consumption and weather forecasting. With the development of transformer-based methods, the performance of multivariate long-term…