Works (22)
Updated: December 3rd, 2024 00:40
2024 journal article
ON THE TRAINING AND GENERALIZATION OF DEEP OPERATOR NETWORKS
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 46(4), C273–C296.
author keywords: deep operator networks; divide-and-conquer; sequential training method; generalization error analysis
open access via arxiv.org (repository)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 8, 2024
2024 journal article
S-OPT: A POINTS SELECTION ALGORITHM FOR HYPER-REDUCTION IN REDUCED ORDER MODELS
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 46(4), B474–B501.
author keywords: reduced order modeling; nonlinear model reduction; Galerkin projection; hyper-reduction; sampling algorithm
Sources: Web Of Science, NC State University Libraries
Added: September 23, 2024
2024 journal article
tLaSDI: Thermodynamics-informed latent space dynamics identification
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 429.
author keywords: Thermodynamics; Reduced order modeling; Autoencoder; Error estimates; Nonlinear-manifold ROM
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 8, 2024
2023 journal article
Accelerating gradient descent and Adam via fractional gradients
Neural Networks, 161, 185–201.
TL;DR:
The superiority of CfGD and CfAdam are demonstrated on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
2023 journal article
ERROR ESTIMATES OF RESIDUAL MINIMIZATION USING NEURAL NETWORKS FOR LINEAR PDES
Journal of Machine Learning for Modeling and Computing, 4(4), 73–101.
Sources: Crossref, NC State University Libraries
Added: January 27, 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.
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
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
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, NC State University Libraries
Added: January 24, 2024
2021 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
2021 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.
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
2021 journal article
Identification of Corrupted Data via $k$-Means Clustering for Function Approximation
CSIAM Transactions on Applied Mathematics, 2(1), 81–107.
Contributors: J. Hou *, * & D. Xiu*
Sources: ORCID, Crossref, NC State University Libraries
Added: January 24, 2024
2021 journal article
Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance
SIAM Journal on Scientific Computing, 43(5), A3438–A3468.
TL;DR:
A new iterative training method is proposed, the Active Neuron Least Squares (ANLS), characterised by the explicit adjustment of the activation pattern at each step, which is designed to enable a quick exit from a plateau.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
2020 journal article
Dying ReLU and Initialization: Theory and Numerical Examples
Communications in Computational Physics, 28(5), 1671–1706.
Contributors: * , Y. Su * & G. Karniadakis
TL;DR:
It is shown that even for rectified linear unit activation, deep and narrow neural networks (NNs) will converge to erroneous mean or median states of the target function depending on the loss with high probability.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: January 24, 2024
2020 journal article
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
Communications in Computational Physics, 28(5), 2042–2074.
Contributors: J. Darbon * & G. Karniadakis
TL;DR:
This is the first theoretical work that shows the consistency of PINNs, and it is shown that the sequence of minimizers strongly converges to the PDE solution in $C^0$.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: January 24, 2024
2020 journal article
TRAINABILITY OF ReLU NETWORKS AND DATA-DEPENDENT INITIALIZATION
Journal of Machine Learning for Modeling and Computing, 1(1), 39–74.
Source: ORCID
Added: January 24, 2024
2018 journal article
Sequential function approximation with noisy data
Journal of Computational Physics, 371, 363–381.
TL;DR:
This work presents a sequential method for approximating an unknown function sequentially using random noisy samples, which results in a simple numerical implementation using only vector operations and avoids the need to store the entire data set.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
2017 journal article
A Randomized Algorithm for Multivariate Function Approximation
SIAM Journal on Scientific Computing, 39(3), A983–A1002.
TL;DR:
This paper demonstrates that by conducting the approximation randomly one sample at a time the RK method converges, and establishes the optimal sampling probability measure to achieve the optimal rate of convergence.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
2017 journal article
A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation
SIAM Journal on Scientific Computing, 39(5), A1811–A1833.
TL;DR:
By using a new randomized algorithm and taking advantage of the tensor structure of the grids, a highly efficient algorithm can be constructed that can be lower than the standard methods, when applicable, such as least squares.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
2017 journal article
Sparse Approximation using $\ell_1-\ell_2$ Minimization and Its Application to Stochastic Collocation
SIAM Journal on Scientific Computing, 39(1), A229–A254.
TL;DR:
Theoretical estimates regarding its recoverability for both sparse and nonsparse signals are presented and the recoverability of both the standard $\ell_1-\ell_2$ minimization and Chebyshev weighted versions are studied.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
2016 journal article
Correcting Data Corruption Errors for Multivariate Function Approximation
SIAM Journal on Scientific Computing, 38(4), A2492–A2511.
TL;DR:
This work proves that the sparse corruption errors can be effectively eliminated by using $\ell_1$-minimization, also known as the least absolute deviations method, and establishes probabilistic error bounds of the $\ell-1- minimization solution with the corrupted data.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Source: ORCID
Added: January 24, 2024
2016 journal article
Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression
SIAM Journal on Scientific Computing, 38(1), A385–A411.
TL;DR:
This paper presents a quasi-optimal sample set for ordinary least squares (OLS) regression, and presents its efficient implementation via a greedy algorithm, along with several numerical examples to demonstrate its efficacy.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
2016 journal article
On a near optimal sampling strategy for least squares polynomial regression
Journal of Computational Physics, 326, 931–946.
TL;DR:
A sampling strategy of least squares polynomial regression that first choose samples from the pluripotential equilibrium measure and then re-order the samples by the quasi-optimal algorithm is presented.
(via Semantic Scholar)
Source: ORCID
Added: January 24, 2024
Employment
Updated: October 5th, 2023 20:43
2023 - present
North Carolina State University Raleigh, US
Assistant Professor
Mathematics
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