相关论文: Sequential Physics-Constrained Neural Operator For…

Two-Stage Robust Optimization (2RO) with discrete uncertainty is challenging, often rendering exact solutions prohibitive. Scenario reduction alleviates this issue by selecting a small, representative subset of scenarios to enable tractable…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…

Driven by advances in hardware and software technologies, nonlinear model predictive control (NMPC) has gained increasing adoption in both industry and academia over the past decades. However, its practical deployment is often limited by…

Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling…

Reconstructing high-resolution turbulent flow fields from severely under-resolved observations is a fundamental inverse problem in computational fluid dynamics and scientific machine learning. Classical interpolation methods fail to recover…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…

We develop a new computational framework to solve sequential Bayesian optimal experimental design (SBOED) problems constrained by large-scale partial differential equations with infinite-dimensional random parameters. We propose an adaptive…

Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive…

Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…

A transport PDE with a spatial integral and recirculation with constant delay has been a benchmark for neural operator approximations of PDE backstepping controllers. Introducing a spatially-varying delay into the model gives rise to a gain…

Multi-scale dynamic wake modeling and prediction are essential for the real-time control and optimization of floating offshore wind turbines (FOWTs). In this study, wakes of FOWTs under coupled surge and pitch motions across a range of…

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and…

Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are…

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical…

Data-driven methods have emerged as powerful tools for modeling the responses of complex nonlinear materials directly from experimental measurements. Among these methods, the data-driven constitutive models present advantages in physical…