Related papers: Radial Basis Operator Networks
Financial time series are characterised by their nonstationarity and autocorrelation. Even if these time series are differenced, technically ensuring their stationarity, they experience regular covariate shifts and concept drifts. Against…
The modern digital engineering design often requires costly repeated simulations for different scenarios. The prediction capability of neural networks (NNs) makes them suitable surrogates for providing design insights. However, only a few…
With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…
Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require deep domain expertise. Numerical simulations present an…
Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as…
Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…
In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via…
Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…
Artificial neural networks (ANNs) have now been widely used for industry applications and also played more important roles in fundamental researches. Although most ANN hardware systems are electronically based, optical implementation is…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
Neural networks are widely used to approximate unknown functions in control. A common neural network architecture uses a single hidden layer (i.e. a shallow network), in which the input parameters are fixed in advance and only the output…
Accurate global Subseasonal-to-Seasonal (S2S) climate forecasting is critical for disaster preparedness and resource management, yet it remains challenging due to chaotic atmospheric dynamics. Existing models predominantly treat atmospheric…
Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…
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…
This paper introduces a network architecture, called dynoNet, utilizing linear dynamical operators as elementary building blocks. Owing to the dynamical nature of these blocks, dynoNet networks are tailored for sequence modeling and system…
Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by…
We propose to take a novel approach to robot system design where each building block of a larger system is represented as a differentiable program, i.e. a deep neural network. This representation allows for integrating algorithmic planning…
Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…