The study of Lagrangian equations and gradient estimates occupies a critical niche at the intersection of partial differential equations, differential geometry, and variational calculus. Lagrangian ...

SIAM Journal on Numerical Analysis, Vol. 49, No. 5/6 (2011), pp. 2017-2038 (22 pages) General autonomous stochastic differential equations (SDEs) driven by one-dimensional Brownian motion in the ...

We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three. Gradient estimates are also derived for critical ...

An important class of nonlinear models involves a dynamic description of the response rather than an explicit description. These models arise often in chemical kinetics, pharmacokinetics, and ...

Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve.

Dr. James McCaffrey of Microsoft Research explains stochastic gradient descent (SGD) neural network training, specifically implementing a bio-inspired optimization technique called differential ...

Any straight line graph has a constant gradient, which is calculated by the change in 𝑦 divided by the change in 𝑥, along any section of the graph. The gradient is measuring the steepness of the ...