Related papers: Generative Network-Based Reduced-Order Model for P…

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…

Cardio-mechanical models can be used to support clinical decision-making. Unfortunately, the substantial computational effort involved in many cardiac models hinders their application in the clinic, despite the fact that they may provide…

Nonlinear partial differential equations (PDEs) are pivotal in modeling complex physical systems, yet traditional Physics-Informed Neural Networks (PINNs) often struggle with unresolved residuals in critical spatiotemporal regions and…

In many real-world problems, there is a limited set of training data, but an abundance of unlabeled data. We propose a new method, Generative Posterior Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in…

Reduced-order models (ROMs) can efficiently simulate high-dimensional physical systems but lack robust uncertainty quantification methods. Existing approaches are frequently architecture- or training-specific, which limits flexibility and…

This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for…

Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

This work focuses on the space-time reduced-order modeling (ROM) method for solving large-scale uncertainty quantification (UQ) problems with multiple random coefficients. In contrast with the traditional space ROM approach, which performs…

We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated…

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of…

We present a deep learning model for data-driven simulations of random dynamical systems without a distributional assumption. The deep learning model consists of a recurrent neural network, which aims to learn the time marching structure,…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…

Reliable training of generative adversarial networks (GANs) typically require massive datasets in order to model complicated distributions. However, in several applications, training samples obey invariances that are \textit{a priori}…