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Found 26 papers, 7 papers with code
Approximation of Solution Operators for High-dimensional PDEs
Using the computational technique of neural ordinary differential equation, we learn the control over the parameter space such that from any initial starting point, the controlled trajectories closely approximate the solutions to the PDE.
Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks
In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions.
Learned Alternating Minimization Algorithm for Dual-domain Sparse-View CT Reconstruction
We propose a novel Learned Alternating Minimization Algorithm (LAMA) for dual-domain sparse-view CT image reconstruction.
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs
Numerical experiments on different high-dimensional evolution PDEs with various initial conditions demonstrate the promising results of the proposed method.
A Learnable Variational Model for Joint Multimodal MRI Reconstruction and Synthesis
In this paper, we propose a novel deep-learning model for joint reconstruction and synthesis of multi-modal MRI using incomplete k-space data of several source modalities as inputs.
Low-rank Matrix Recovery With Unknown Correspondence
We study a matrix recovery problem with unknown correspondence: given the observation matrix $M_o=[A,\tilde P B]$, where $\tilde P$ is an unknown permutation matrix, we aim to recover the underlying matrix $M=[A, B]$.
An Optimization-Based Meta-Learning Model for MRI Reconstruction with Diverse Dataset
In this model, the learnable regularization function contains a task-invariant common feature encoder and task-specific learner represented by a shallow network.
Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions.
An Optimal Control Framework for Joint-channel Parallel MRI Reconstruction without Coil Sensitivities
We cast the reconstruction network as a structured discrete-time optimal control system, resulting in an optimal control formulation of parameter training where the parameters of the objective function play the role of control variables.
Influence Estimation and Maximization via Neural Mean-Field Dynamics
Directly using information diffusion cascade data, our framework can simultaneously learn the structure of the diffusion network and the evolution of node infection probabilities.
Provably Convergent Learned Inexact Descent Algorithm for Low-Dose CT Reconstruction
We propose a provably convergent method, called Efficient Learned Descent Algorithm (ELDA), for low-dose CT (LDCT) reconstruction.
A Hypergradient Approach to Robust Regression without Correspondence
Due to the combinatorial nature of the problem, most existing methods are only applicable when the sample size is small, and limited to linear regression models.
Deep Parallel MRI Reconstruction Network Without Coil Sensitivities
We propose a novel deep neural network architecture by mapping the robust proximal gradient scheme for fast image reconstruction in parallel MRI (pMRI) with regularization function trained from data.
Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems.
Network Diffusions via Neural Mean-Field Dynamics
We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks.
A Novel Learnable Gradient Descent Type Algorithm for Non-convex Non-smooth Inverse Problems
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently.
Numerical Solution of Inverse Problems by Weak Adversarial Networks
We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems.
Learning Cost Functions for Optimal Transport
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples.
Weak Adversarial Networks for High-dimensional Partial Differential Equations
The weak solution and the test function in the weak formulation are then parameterized as the primal and adversarial networks respectively, which are alternately updated to approximate the optimal network parameter setting.
Numerical Analysis Numerical Analysis
Learning to Match via Inverse Optimal Transport
We emphasize that the discrete optimal transport plays the role of a variational principle which gives rise to an optimization-based framework for modeling the observed empirical matching data.
Predicting User Activity Level In Point Processes With Mass Transport Equation
Point processes are powerful tools to model user activities and have a plethora of applications in social sciences.
Learning Deep Mean Field Games for Modeling Large Population Behavior
We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space.
Wasserstein Learning of Deep Generative Point Process Models
Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena.
Fake News Mitigation via Point Process Based Intervention
We propose the first multistage intervention framework that tackles fake news in social networks by combining reinforcement learning with a point process network activity model.
Coarse-to-Fine Classification via Parametric and Nonparametric Models for Computer-Aided Diagnosis
Classification is one of the core problems in Computer-Aided Diagnosis (CAD), targeting for early cancer detection using 3D medical imaging interpretation.
Projection Onto A Simplex
This mini-paper presents a fast and simple algorithm to compute the projection onto the canonical simplex $\triangle^n$.
Optimization and Control 49M37 G.1.6
