Related papers: Probabilistic operator learning: generative modeli…

Deep neural network models owe their representational power to the high number of learnable parameters. It is often infeasible to run these largely parametrized deep models in limited resource environments, like mobile phones. Network…

We develop a principled framework for discovering causal structure in partial differential equations (PDEs) using physics-informed neural networks and counterfactual perturbations. Unlike classical residual minimization or sparse regression…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…

Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…

We study the problem of learning neural network models for Ordinary Differential Equations (ODEs) with parametric uncertainties. Such neural network models capture the solution to the ODE over a given set of parameters, initial conditions,…

This paper develops a finite-sample statistical theory for in-context learning (ICL), analyzed within a meta-learning framework that accommodates mixtures of diverse task types. We introduce a principled risk decomposition that separates…

Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by…

The infinite-dimensional information operator for the nuisance parameter plays a key role in semiparametric inference, as it is closely related to the regular estimability of the target parameter. Calculation of information operators has…

A framework to learn a multi-modal distribution is proposed, denoted as the Conditional Quantum Generative Adversarial Network (C-qGAN). The neural network structure is strictly within a quantum circuit and, as a consequence, is shown to…

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…

The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…

Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture…

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…

Most existing generative models are limited to learning a single probability distribution from the training data and cannot generalize to novel distributions for unseen data. An architecture that can generate samples from both trained…

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…

Large-scale models trained on broad data have recently become the mainstream architecture in computer vision due to their strong generalization performance. In this paper, the main focus is on an emergent ability in large vision models,…

Understanding why some sequential planning problems are harder than others requires models that go beyond average performance. They should capture the specific pattern of which problems are hard, and ideally fail in the same way people do…