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Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…

In this paper, we propose a non-negative representation based discriminative dictionary learning algorithm (NRDL) for multicategory face classification. In contrast to traditional dictionary learning methods, NRDL investigates the use of…

The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…

A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…

In developing data-driven modeling methodologies, there is an ongoing need to reconcile the strong predictive performance of opaque black-box models with the transparency required for critical applications. This work introduces an…

Causal representation learning seeks to recover latent factors that generate observational data through a mixing function. Needing assumptions on latent structures or relationships to achieve identifiability in general, prior works often…

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…

We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean…

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…

This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different…

Humans develop world models that capture the underlying generation process of data. Whether neural networks can learn similar world models remains an open problem. In this work, we present the first theoretical results for this problem,…

Deep neural networks have proven to be quite effective in a wide variety of machine learning tasks, ranging from improved speech recognition systems to advancing the development of autonomous vehicles. However, despite their superior…

Variational data assimilation in ocean models depends on the ability to model general correlation operators in the presence of coastlines. Grid-point filters based on diffusion operators are widely used for this purpose, but come with a…

This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…

Learning the differential statistical dependency network between two contexts is essential for many real-life applications, mostly in the high dimensional low sample regime. In this paper, we propose a novel differential network estimator…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

We present a novel Deep Neural Network (DNN) architecture for non-linear system identification. We foster generalization by constraining DNN representational power. To do so, inspired by fading memory systems, we introduce inductive bias…

One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that…