Works Published in 2022

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Displaying works 1 - 20 of 172 in total

Sorted by most recent date added to the index first, which may not be the same as publication date order.

2022 chapter

Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules

In Association for Women in Mathematics Series.

By: E. Gasparovic*, M. Gommel*, E. Purvine*, R. Sazdanovic n, B. Wang*, Y. Wang*, L. Ziegelmeier*

UN Sustainable Development Goal Categories
13. Climate Action (OpenAlex)
Source: ORCID
Added: January 28, 2024

2022 journal article

GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems

TL;DR: It is proved theoretically that GFINNs are sufficiently expressive to learn the underlying equations, hence establishing the universal approximation theorem. (via Semantic Scholar)
Sources: ORCID, Crossref
Added: January 24, 2024

2022 journal article

Effects of depth, width, and initialization: A convergence analysis of layer-wise training for deep linear neural networks

Analysis and Applications, 20(01), 73–119.

By: Y. Shin*

TL;DR: A general convergence analysis of BCGD is established and the optimal learning rate is found, which results in the fastest decrease in the loss, which is found that the use of deep networks could drastically accelerate convergence when it is compared to those of a depth 1 network, even when the computational cost is considered. (via Semantic Scholar)
Source: ORCID
Added: January 24, 2024

2022 journal article

Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

Neurocomputing, 468, 165–180.

TL;DR: A new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions that are designed to get rid of any saturation region by injecting sinusoidal fluctuations, which include trainable parameters. (via Semantic Scholar)
Source: ORCID
Added: January 24, 2024

2022 journal article

Approximation rates of DeepONets for learning operators arising from advection–diffusion equations

Neural Networks, 153, 411–426.

TL;DR: It is found that the approximation rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators. (via Semantic Scholar)
Source: ORCID
Added: January 24, 2024

2022 journal article

Active Neuron Least Squares: A training method for multivariate rectified neural networks

SIAM Journal on Scientific Computing, 44(4), A2253–A2275.

By: M. Ainsworth & Y. Shin*

UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Source: ORCID
Added: January 24, 2024

2022 article

The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation

By: A. Abhishek, T. Le*, L. Nguyen & T. Khan

Source: ORCID
Added: January 23, 2024

2022 journal article

The Gradient Descent Method for the Convexification to Solve Boundary Value Problems of Quasi-Linear PDEs and a Coefficient Inverse Problem

Journal of Scientific Computing, 91(3).

By: T. Le* & L. Nguyen*

Contributors: T. Le* & L. Nguyen*

TL;DR: The global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a Hilbert space is studied and proved to establish a general framework to numerically solve boundary value problems for quasi-linear partial differential equations (PDEs) with noisy Cauchy data. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2022 article

The Carleman convexification method for Hamilton-Jacobi equations on the whole space

ArXiv.

By: H. Le, T. Le* & L. Nguyen

Contributors: H. Le, T. Le* & L. Nguyen

Source: ORCID
Added: January 23, 2024

2022 article

Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method

ArXiv.

By: T. Le*

Contributors: T. Le*

Source: ORCID
Added: January 23, 2024

2022 journal article

Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data

Inverse Problems, 38(4).

By: T. Le*, M. Klibanov, L. Nguyen, A. Sullivan & L. Nguyen

Contributors: T. Le*, M. Klibanov, L. Nguyen, A. Sullivan & L. Nguyen

TL;DR: It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2022 journal article

A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data

Journal of Inverse and Ill-Posed Problems, 30(2), 265–286.

Contributors: T. Le* & L. Nguyen*

Source: ORCID
Added: January 23, 2024

2022 journal article

A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications

Computers & Mathematics with Applications, 125, 13–24.

TL;DR: A new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE by using the quasi-reversibility method with a suitable Carleman weight function is proposed. (via Semantic Scholar)
Source: ORCID
Added: January 23, 2024

2022 book

Integration in Finite Terms: Fundamental Sources

Michael Singer

Ed(s): C. Raab & M. Singer

Source: Crossref
Added: November 8, 2023

2022 conference paper

Solving Linear Systems on a GPU with Hierarchically Off-Diagonal Low-Rank Approximations

SC22: International Conference for High Performance Computing, Networking, Storage and Analysis, 1–15.

Event: SC22: International Conference for High Performance Computing, Networking, Storage and Analysis

TL;DR: Algorithms for factorizing HODLR matrices and for applying the factorizations on a GPU leverage the efficiency of batched dense linear algebra, and they scale nearly linearly with the matrix size when the numerical ranks are fixed. (via Semantic Scholar)
Sources: ORCID, Crossref
Added: November 1, 2023

2022 journal article

Overlapping Domain Decomposition Preconditioner for Integral Equations

SIAM Journal on Scientific Computing, 44(6), A3617–A3644.

By: C. Chen* & G. Biros

TL;DR: This work introduces a new preconditioner based on a novel overlapping domain decomposition that can be combined efficiently with existing fast direct solvers and applies the recursive skeletonization to subproblems associated with every subdomain. (via Semantic Scholar)
Sources: ORCID, Crossref
Added: November 1, 2023

2022 journal article

Weakly viscoelastic film flowing down a rotating inclined plane

Physics of Fluids, 34(1).

Source: ORCID
Added: October 13, 2023

2022 journal article

Falling liquid films on a slippery substrate with variable fluid properties

International Journal of Non-Linear Mechanics, 147.

Contributors: S. Chattopadhyay*, P. Boragunde*, A. Gaonkar*, A. Barua* & A. Mukhopadhyay*

Source: ORCID
Added: October 13, 2023

2022 chapter

Effects of Strong Viscosity with Variable Fluid Properties on Falling Film Instability

In NODYCON Conference Proceedings Series (pp. 75–85).

Source: ORCID
Added: October 13, 2023

2022 journal article

Effect of odd-viscosity on the dynamics and stability of a thin liquid film flowing down on a vertical moving plate

International Journal of Non-Linear Mechanics, 140.

Source: ORCID
Added: October 13, 2023

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