Related papers: Probabilistic operator learning: generative modeli…

We develop a class of data-driven generative models that approximate the solution operator for parameter-dependent partial differential equations (PDE). We propose a novel probabilistic formulation of the operator learning problem based on…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…

Understanding the mechanism of generative adversarial networks (GANs) helps us better use GANs for downstream applications. Existing efforts mainly target interpreting unconditional models, leaving it less explored how a conditional GAN…

We introduce the Probabilistic Generative Adversarial Network (PGAN), a new GAN variant based on a new kind of objective function. The central idea is to integrate a probabilistic model (a Gaussian Mixture Model, in our case) into the GAN…

Probabilistic models often use neural networks to control their predictive uncertainty. However, when making out-of-distribution (OOD)} predictions, the often-uncontrollable extrapolation properties of neural networks yield poor uncertainty…

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…

In-context learning (ICL) refers to a remarkable capability of pretrained large language models, which can learn a new task given a few examples during inference. However, theoretical understanding of ICL is largely under-explored,…

Generative Adversarial Networks (GANs) can generate near photo realistic images in narrow domains such as human faces. Yet, modeling complex distributions of datasets such as ImageNet and COCO-Stuff remains challenging in unconditional…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Many machine learning algorithms can be interpreted as procedures for estimating functions defined on the data distribution. In this paper we present a conceptual framework that formulates a wide range of learning problems as variational…

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected…

Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…

Convolutional neural networks (CNNs) are extremely popular and effective for image classification tasks but tend to be overly confident in their predictions. Various works have sought to quantify uncertainty associated with these models,…

Semantic segmentation methods can not directly identify abnormal objects in images. Anomaly Segmentation algorithm from this realistic setting can distinguish between in-distribution objects and Out-Of-Distribution (OOD) objects and output…

We present an interactive approach to train a deep neural network pixel classifier for the segmentation of neuronal structures. An interactive training scheme reduces the extremely tedious manual annotation task that is typically required…

Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their…

Humans demonstrate remarkable abilities to predict physical events in complex scenes. Two classes of models for physical scene understanding have recently been proposed: "Intuitive Physics Engines", or IPEs, which posit that people make…