Related papers: Probabilistic operator learning: generative modeli…
We present an approach to quantifying both aleatoric and epistemic uncertainty for deep neural networks in image classification, based on generative adversarial networks (GANs). While most works in the literature that use GANs to generate…
Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal fields for new initial conditions or forcing functions.…
In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in building foundation models, as in this framework the model is trained to learn operators and solve differential equations…
An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…
We develop a novel framework for uncertainty quantification in operator learning, the Stochastic Operator Network (SON). SON combines the stochastic optimal control concepts of the Stochastic Neural Network (SNN) with the DeepONet. By…
A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…
In this paper, we investigate the applications of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural…
Bayesian networks provide a modeling language and associated inference algorithm for stochastic domains. They have been successfully applied in a variety of medium-scale applications. However, when faced with a large complex domain, the…
We extend Probability Bracket Notation (PBN), inspired by the Dirac notation in quantum mechanics, to multivariable probability systems and static Bayesian networks (BNs). By defining probability distributions and conditional expectations…
Predictive coding (PC) is an influential theory in computational neuroscience, which argues that the cortex forms unsupervised world models by implementing a hierarchical process of prediction error minimization. PC networks (PCNs) are…
Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…
Predicting simple function classes has been widely used as a testbed for developing theory and understanding of the trained Transformer's in-context learning (ICL) ability. In this paper, we revisit the training of Transformers on linear…
Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…
Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by…
The study of neural operators has paved the way for the development of efficient approaches for solving partial differential equations (PDEs) compared with traditional methods. However, most of the existing neural operators lack the…
Anomaly detection is critical in domains such as cybersecurity and finance, especially when working with large-scale tabular data. Yet, unsupervised anomaly detection-where no labeled anomalies are available-remains challenging because…
Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
In this work we consider the task of relaxing the i.i.d assumption in pattern recognition (or classification), aiming to make existing learning algorithms applicable to a wider range of tasks. Pattern recognition is guessing a discrete…
Object recognition has become a crucial part of machine learning and computer vision recently. The current approach to object recognition involves Deep Learning and uses Convolutional Neural Networks to learn the pixel patterns of the…