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We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

Variational autoencoders (VAEs) are a popular class of deep generative models with many variants and a wide range of applications. Improvements upon the standard VAE mostly focus on the modelling of the posterior distribution over the…

Sparse autoencoders (SAEs) have received considerable recent attention as tools for mechanistic interpretability, showing success at extracting interpretable features even from very large LLMs. However, this research has been largely…

The cosmic microwave background power spectra are a primary window into the early universe. However, achieving interpretable, likelihood-compatible compression and fast inference under weak model assumptions remains challenging. We propose…

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…

With the development of generative-based self-supervised learning (SSL) approaches like BeiT and MAE, how to learn good representations by masking random patches of the input image and reconstructing the missing information has grown in…

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…

Inverse problems are paramount in Science and Engineering. In this paper, we consider the setup of Statistical Inverse Problem (SIP) and demonstrate how Stochastic Gradient Descent (SGD) algorithms can be used in the linear SIP setting. We…

Optical spectra contain a wealth of information about the physical properties and formation histories of galaxies. Often though, spectra are too noisy for this information to be accurately retrieved. In this study, we explore how machine…

The symmetric inclusion process (SIP) models particles diffusing on a graph with mutual attraction. We recently showed that, in the log-concave regime (where diffusivity dominates interaction), the spectral gap of the conservative SIP…

Sparse Autoencoders (SAEs) have emerged as a powerful tool for interpreting the internal representations of CLIP vision encoders, yet existing analyses largely focus on the semantic meaning of individual features. We introduce information…

Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on…

Ground deformation measured from Interferometric Synthetic Aperture Radar (InSAR) data is considered a sign of volcanic unrest, statistically linked to a volcanic eruption. Recent studies have shown the potential of using Sentinel-1 InSAR…

The spatio-temporal interpolation of large geophysical datasets has historically been addressed by Optimal Interpolation (OI) and more sophisticated equation-based or data-driven Data Assimilation (DA) techniques. Recent advances in the…

Dynamic state estimation (DSE) is becoming increasingly important for monitoring inverter-dominated power systems. Due to their cascading control structures, inverter-based resources (IBRs) exhibit multi-timescale dynamics, leading to stiff…

Discriminative features extracted from the sparse coding model have been shown to perform well for classification. Recent deep learning architectures have further improved reconstruction in inverse problems by considering new dense priors…

Conflicting objectives present a considerable challenge in interleaving multi-task learning, necessitating the need for meticulous design and balance to ensure effective learning of a representative latent data space across all tasks…

Probabilistic generative models are attractive for scientific modeling because their inferred parameters can be used to generate hypotheses and design experiments. This requires that the learned model provide an accurate representation of…

We explore the use of deep neural networks for nonlinear dimensionality reduction in climate applications. We train convolutional autoencoders (CAEs) to encode two temperature field datasets from pre-industrial control runs in the CMIP5…

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…