Related papers: Probabilistic operator learning: generative modeli…

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems.…

Deploying deep learning models on Internet of Things (IoT) devices often faces challenges due to limited memory resources and computing capabilities. Cooperative inference is an important method for addressing this issue, requiring the…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Accurately quantifying long-term risk probabilities in diverse stochastic systems is essential for safety-critical control. However, existing sampling-based and partial differential equation (PDE)-based methods often struggle to handle…

We propose a new physics-informed neural network framework, IDPINN, based on the enhancement of initialization and domain decomposition to improve prediction accuracy. We train a PINN using a small dataset to obtain an initial network…

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…

Although current salient object detection (SOD) works have achieved significant progress, they are limited when it comes to the integrity of the predicted salient regions. We define the concept of integrity at both a micro and macro level.…

We present a method for learning the parameters of a Bayesian network with prior knowledge about the signs of influences between variables. Our method accommodates not just the standard signs, but provides for context-specific signs as…

Neural processes (NPs) are a powerful family of meta-learning models that seek to approximate the posterior predictive map of the ground-truth stochastic process from which each dataset in a meta-dataset is sampled. There are many cases in…

Causal discovery from observational data is challenging, especially with large datasets and complex relationships. Traditional methods often struggle with scalability and capturing global structural information. To overcome these…

PAGODA (Probabilistic Autonomous Goal-Directed Agent) is a model for autonomous learning in probabilistic domains [desJardins, 1992] that incorporates innovative techniques for using the agent's existing knowledge to guide and constrain the…

We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear…

A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…

Operator learning has emerged as a promising paradigm for approximating solution operators of partial differential equations (PDEs). However, conventional approaches typically rely on pointwise function discretizations, which often suffer…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator…

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Modern implicit generative models such as generative adversarial networks (GANs) are generally known to suffer from issues such as instability, uninterpretability, and difficulty in assessing their performance. If we see these implicit…