The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations

We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these...

Fuzzy Adaptive Output-Feedback Constrained Trajectory Tracking Control for HFVs with Fixed-Time Convergence

This article proposes an output-feedback fixed-time trajectory tracking control methodology for hypersonic flight vehicles subject to asymmetric output constraints. In contrast to the state of the art, the most distinguishing feature of our control design lies in avoiding using conventional recursive design methods (e.g., backstepping...

Monte Carlo simulation of SDEs using GANs

Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito ^ stochastic differential equations (SDEs). We propose a scheme that approximates the path-wise conditional...

Earth pressure in narrow cohesive-fictional soils behind retaining walls rotated about the top: An analytical approach

There is currently a lack of an available design approach to estimate the earth pressure in narrow backfills behind retaining walls rotated about the top (RT). The considerations of some significant factors, primarily load transfer mechanisms (soil arching effect and horizontal shear stress in soils), failure mechanisms (shape and number of...

Characterization of epoxy-asphalt binders by differential scanning calorimetry

Asphalt binders incorporating different modifiers is a common practice but empirically driven in most of the cases. Therefore, the fundamental understanding of modification mechanisms in asphalt binders is needed to design polymer modified binders in a controllable manner, especially today in which new modification technologies are proposed....

A Novel Disturbance Observer Design for a Larger Class of Nonlinear Strict-Feedback Systems via Improved DSC Technique

A novel scheme for disturbance observer is designed for an extended class of strict-feedback nonlinear systems with possibly unbounded, non-smooth, and state-independent compounded disturbance. To overcome these problems in disturbance observer design, the typical slide mode differentiators are improved by introducing hyperbolic tangent...

The non-smoothness problem in disturbance observer design: A set-invariance-based adaptive fuzzy control method

This work removes the critical assumptions of continuity, differentiability, and state-independent boundedness, which are typical of compounded disturbances in disturbance observer-based adaptive designs. Crucial in removing such assumptions are a novel observer-based design with state-dependent gain in place of a constant one, and a novel...