# Fingerprint Dive into the research topics where Gi-Ren Liu is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

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### Mathematics

Scaling Limit

Random Field

Phase Retrieval

Multiscaling

Fractional

Diffusion equation

Scaling

Homogenization

Alternating Projections

Initial conditions

Null

Fractional Diffusion

Initialization

Linear partial differential equation

Diffraction

Source Terms

Kinetic Equation

Maxwell's equations

Linear algebra

Modality

Wave Propagation

Electromagnetic Fields

Rescaling

System of equations

Data analysis

Scenarios

Hermite Expansion

Matrix Function

Customers

Data-driven

Gaussian Fields

Limiting

Parabolic Partial Differential Equations

Reaction-diffusion

Operator

Random Vector

Decoupling

Modeling

Renormalization

Heat Equation

Bessel Potential

Riesz Potential

Numerical Experiment

Manifold Learning

Spectral Representation

Shape Analysis

Covariance Function

Spectral Function

Sleep

Heart Rate

### Engineering & Materials Science

Routers

Energy conservation

Partial differential equations

Dispensers

Geometry

Post offices

Energy management

Electric fuses

Electroencephalography

Ethernet

Diffraction patterns

Electricity

Domestic appliances

Energy utilization

Analytical models

Costs

Fusion reactions

Mathematical operators

Experiments

Cameras

Derivatives

Recovery

Internet

Composite materials