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Everything about Gradient
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field whose value at a point gives the direction and the rate of fastest increase. The nabla symbol, pronounced "del", denotes the vector differential operator. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: GradientA 5-minute orientation
- Skim a recent paper: Independent gradient model based on Hirshfeld partition: A new method for visual study of interactions in chemical systemsInfluential work since 2022
- Pick up a classic book: The Lost WorldThe most-reprinted book on the subject
- Read the landmark paper: Generalized Gradient Approximation Made SimpleCited 211,952 times
- Go sideways: Derivative (multivariable calculus)A closely related topic
- Go sideways: DelA closely related topic
📖 Definitions
Noun A slope or incline.
Noun A rate of inclination or declination of a slope.
Noun The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.
Noun The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
🏆 Landmark papers (most cited)
Generalized Gradient Approximation Made Simple
Gradient-based learning applied to document recognition
Greedy function approximation: A gradient boosting machine.
Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
Profiling of complex microbial populations by denaturing gradient gel electrophoresis analysis of polymerase chain reaction-amplified genes coding for 16S rRNA
COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient
🆕 Influential since 2022
Independent gradient model based on Hirshfeld partition: A new method for visual study of interactions in chemical systems
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus
Iontronic pressure sensor with high sensitivity over ultra-broad linear range enabled by laser-induced gradient micro-pyramids
Predictive Performances of Ensemble Machine Learning Algorithms in Landslide Susceptibility Mapping Using Random Forest, Extreme Gradient Boosting (XGBoost) and Natural Gradient Boosting (NGBoost)
📚 Books worth reading
The Lost WorldMichael Crichton · 1995
An introduction to radioimmunoassay and related techniquesT. Chard · 1978
Soft matter gradient surfacesJan Genzer · 2011
Conjugate gradient type methods for ill-posed problemsMartin Hanke · 1995
Functionally graded materialsHui-Shen Shen · 2009
Functionalized Nanomaterials IIVineet Kumar, Praveen Guleria · 2021- 📕Preconditioned conjugate-gradient methods for low-speed flow calculationsKumud Ajmani · 1993
- 📕Swept-wing receptivity studies using distributed roughnessW. S. Saric · 1998
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Derivative (multivariable calculus) In mathematics, the derivative of a function at a point is the linear part of the best affine approximation to the function near the point. In one-variable…
- Del Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by ∇ (the nabla…
- Partial derivative In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held…
- Vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space ℝn. A vector field…
- Function of several real variables In mathematics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being…
- Fréchet derivative In mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative…
- Tangent vector In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential…
- Legendre transformation In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface…