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07/13/2023
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions
This paper explores the expressive power of deep neural networks for a d...
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06/29/2023
Why Shallow Networks Struggle with Approximating and Learning High Frequency: A Numerical Study
In this work, a comprehensive numerical study involving analysis and exp...
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01/29/2023
On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network
This paper studies the expressive power of deep neural networks from the...
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06/10/2022
How much can one learn from a single solution of a PDE?
Linear evolution PDE ∂_t u(x,t) = -ℒ u, where ℒ is a strongly elliptic o...
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04/10/2022
How much can one learn a partial differential equation from its solution?
In this work we study the problem about learning a partial differential ...
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12/22/2020
Quantitative PAT with simplified P_N approximation
The photoacoustic tomography (PAT) is a hybrid modality that combines th...
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07/26/2020
A Dual Iterative Refinement Method for Non-rigid Shape Matching
In this work, a simple and efficient dual iterative refinement (DIR) met...
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03/19/2020
Efficient and Robust Shape Correspondence via Sparsity-Enforced Quadratic Assignment
In this work, we introduce a novel local pairwise descriptor and then de...
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01/27/2020
A fast algorithm for time-dependent radiative transport equation based on integral formulation
In this work, we introduce a fast numerical algorithm to solve the time-...
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08/27/2019
Separability of the kernel function in an integral formulation for anisotropic radiative transfer equation
We study in this work an integral formulation for the radiative transfer...
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07/01/2019
A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction
We propose a data-driven approach to solve multiscale elliptic PDEs with...
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05/01/2018
Intrinsic Complexity And Scaling Laws: From Random Fields to Random Vectors
Random fields are commonly used for modeling of spatially (or timely) de...
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02/06/2016
Variational Hamiltonian Monte Carlo via Score Matching
Traditionally, the field of computational Bayesian statistics has been d...
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06/18/2015