1 code implementation • 6 Mar 2024 • Yanlai Chen, Yajie Ji, Akil Narayan, Zhenli Xu
We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs framework.
no code implementations • 26 Jan 2024 • Caleb C. Berggren, David Jiang, Y. F. Jack Wang, Jake A. Bergquist, Lindsay C. Rupp, Zexin Liu, Rob S. MacLeod, Akil Narayan, Lucas H. Timmins
Unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter summarizing contribution of the embedded fibers to the overall artery stiffness.
1 code implementation • 29 Sep 2023 • Shibo Li, Xin Yu, Wei Xing, Mike Kirby, Akil Narayan, Shandian Zhe
To overcome this problem, we propose Multi-Resolution Active learning of FNO (MRA-FNO), which can dynamically select the input functions and resolutions to lower the data cost as much as possible while optimizing the learning efficiency.
no code implementations • 23 Oct 2022 • Shibo Li, Michael Penwarden, Yiming Xu, Conor Tillinghast, Akil Narayan, Robert M. Kirby, Shandian Zhe
However, the performance of multi-domain PINNs is sensitive to the choice of the interface conditions.
no code implementations • 8 Jul 2022 • Zheng Wang, Yiming Xu, Conor Tillinghast, Shibo Li, Akil Narayan, Shandian Zhe
High-order interaction events are common in real-world applications.
no code implementations • 19 Apr 2022 • Justin Baker, Hedi Xia, Yiwei Wang, Elena Cherkaev, Akil Narayan, Long Chen, Jack Xin, Andrea L. Bertozzi, Stanley J. Osher, Bao Wang
Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers.
1 code implementation • 8 Apr 2022 • Jarom D. Hogue, Robert M. Kirby, Akil Narayan
Deep learning using neural networks is an effective technique for generating models of complex data.
1 code implementation • 24 Feb 2022 • Justin Baker, Elena Cherkaev, Akil Narayan, Bao Wang
We compare HBNODE with other popular ROMs on several complex dynamical systems, including the von K\'{a}rm\'{a}n Street flow, the Kurganov-Petrova-Popov equation, and the one-dimensional Euler equations for fluids modeling.
1 code implementation • 25 Nov 2021 • Elizabeth Qian, Jemima M. Tabeart, Christopher Beattie, Serkan Gugercin, Jiahua Jiang, Peter R. Kramer, Akil Narayan
We introduce Gramian definitions relevant to the inference setting and propose a balanced truncation approach based on these inference Gramians that yield a reduced dynamical system that can be used to cheaply approximate the posterior mean and covariance.
no code implementations • 26 Oct 2021 • Michael Penwarden, Shandian Zhe, Akil Narayan, Robert M. Kirby
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world.
BIG-bench Machine Learning Physics-informed machine learning +1
no code implementations • 16 Oct 2021 • Shibo Li, Zheng Wang, Akil Narayan, Robert Kirby, Shandian Zhe
the initialization, we only need to run the standard ODE solver twice -- one is forward in time that evolves a long trajectory of gradient flow for the sampled task; the other is backward and solves the adjoint ODE.
no code implementations • 25 Jun 2021 • Michael Penwarden, Shandian Zhe, Akil Narayan, Robert M. Kirby
Candidates for this approach are simulation methodologies for which there are fidelity differences connected with significant computational cost differences.
no code implementations • 29 Mar 2021 • Yiming Xu, Vahid Keshavarzzadeh, Robert M. Kirby, Akil Narayan
Multifidelity approximation is an important technique in scientific computation and simulation.
no code implementations • 28 Jan 2021 • Zexin Liu, Akil Narayan
Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure.
Numerical Analysis Numerical Analysis 33D45, 42C10, 65D15
no code implementations • 11 Jan 2021 • Yiming Xu, Akil Narayan
A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain.
Numerical Analysis Numerical Analysis Probability Computation
no code implementations • 13 Apr 2020 • Yiming Xu, Akil Narayan, Hoang Tran, Clayton G. Webster
We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice.