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Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the…

Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…

Data-based inference of directed interactions in complex dynamical systems is a problem common to many disciplines of science. In this work, we study networks of spatially separate dynamical entities, which could represent physical systems…

Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies…

We explore a case example of networks of classical electronic oscillators evolving towards the solution of complex optimization problems. We show that when driven into subharmonic response, a network of such nonlinear electrical resonators…

Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is…

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…

Analysis of human affect plays a vital role in human-computer interaction (HCI) systems. Due to the difficulty in capturing large amounts of real-life data, most of the current methods have mainly focused on controlled environments, which…

We address the problem of building theoretical models that help elucidate the function of the visual brain at computational/algorithmic and structural/mechanistic levels. We seek to understand how the receptive fields and topographic maps…

Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear…

The large majority of inferences drawn in empirical political research follow from model-based associations (e.g. regression). Here, we articulate the benefits of predictive modeling as a complement to this approach. Predictive models aim…

We consider scenarios where a very accurate (often small) predictive model using restricted features is available when training a full-featured (often larger) model. This restricted model may be thought of as side-information'', and can…

Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…

We investigate a class of binary choice models with social interactions. We propose a unifying perspective that integrates economic models using a utility function and psychological models using an impact function. A general approach for…

Neural Network Potentials (NNPs) have emerged as a powerful tool for modelling atomic interactions with high accuracy and computational efficiency. Recently, denoising diffusion models have shown promise in NNPs by training networks to…

Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…

Logistic regression is key method for modeling the probability of a binary outcome based on a collection of covariates. However, the classical formulation of logistic regression relies on the independent sampling assumption, which is often…

We build simple models for the distribution of voting patterns in a group, using the Supreme Court of the United States as an example. The least structured, or maximum entropy, model that is consistent with the observed pairwise…

Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem - the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined…