no code implementations • 8 Apr 2024 • Jiayuan Dong, Christian Jacobsen, Mehdi Khalloufi, Maryam Akram, Wanjiao Liu, Karthik Duraisamy, Xun Huan
Variational OED (vOED), in contrast, estimates a lower bound of the EIG without likelihood evaluations by approximating the posterior distributions with variational forms, and then tightens the bound by optimizing its variational parameters.
no code implementations • 16 Jan 2024 • Christian Jacobsen, Jiayuan Dong, Mehdi Khalloufi, Xun Huan, Karthik Duraisamy, Maryam Akram, Wanjiao Liu
We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements.
no code implementations • 16 Dec 2023 • Christian Jacobsen, Yilin Zhuang, Karthik Duraisamy
Secondly, we showcase the potential and versatility of score-based generative models in various physics tasks, specifically highlighting surrogate modeling as well as probabilistic field reconstruction and inversion from sparse measurements.
no code implementations • 24 Aug 2023 • Marcial Sanchis-Agudo, Yuning Wang, Luca Guastoni, Karthik Duraisamy, Ricardo Vinuesa
To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention which we demonstrate in time-series reconstruction and prediction.
no code implementations • 24 Apr 2023 • Shaowu Pan, Karthik Duraisamy
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace.
1 code implementation • 21 Sep 2021 • Elnaz Rezaian, Cheng Huang, Karthik Duraisamy
Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable.
no code implementations • 15 Sep 2021 • Christian Jacobsen, Karthik Duraisamy
We illustrate comparisons between disentangled and entangled representations by juxtaposing learned latent distributions and the true generative factors in a model porous flow problem.
1 code implementation • NeurIPS 2021 • Jiayang Xu, Aniruddhe Pradhan, Karthik Duraisamy
Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes.
1 code implementation • 14 Sep 2021 • James Duvall, Karthik Duraisamy, Shaowu Pan
Test cases include a vehicle-aerodynamics problem with complex geometry and limited training data, with a design-variable hypernetwork performing best, with a competitive time-to-best-model despite a much greater parameter count.
no code implementations • 27 Jan 2021 • Karthik Duraisamy
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts.
Variational Inference Information Theory Information Theory Probability 62B10 G.3; H.1.1
1 code implementation • 25 Feb 2020 • Shaowu Pan, Nicholas Arnold-Medabalimi, Karthik Duraisamy
Despite being endowed with a richer dictionary of nonlinear observables, nonlinear variants of the DMD, such as extended/kernel dynamic mode decomposition (EDMD/KDMD) are seldom applied to large-scale problems primarily due to the difficulty of discerning the Koopman invariant subspace from thousands of resulting Koopman eigenmodes.
no code implementations • 23 Dec 2019 • Jiayang Xu, Karthik Duraisamy
A fully-connected network is used as the third level to learn the mapping between these latent variables and the global parameters from training data, and predict them for new parameters.
1 code implementation • 9 Jun 2019 • Shaowu Pan, Karthik Duraisamy
In this work, we formalize the problem of learning the continuous-time Koopman operator with deep neural networks in a measure-theoretic framework.
1 code implementation • 4 Feb 2019 • Behdad Davoudi, Ehsan Taheri, Karthik Duraisamy, Balaji Jayaraman, Ilya Kolmanovsky
A reduced-order version of the atmospheric boundary layer data as well as the popular Dryden model are used to assess the impact of accuracy of the wind field model on the predicted vehicle performance and trajectory.
Fluid Dynamics Atmospheric and Oceanic Physics Applied Physics
no code implementations • 31 May 2018 • Shaowu Pan, Karthik Duraisamy
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data.
1 code implementation • 25 Mar 2018 • Shaowu Pan, Karthik Duraisamy
In this work, we present a framework of operator inference to extract the governing dynamics of closure from data in a compact, non-Markovian form.