Results 31 to 40 of about 11,098 (108)
Inverse Design in Nanophotonics via Representation Learning
Advanced Optical Materials, Volume 14, Issue 1, 9 January 2026.This review frames machine learning (ML) in nanophotonics through a classification based on where ML is applied. We categorize methods as either output‐side, which create differentiable surrogates for solving Maxwell's partial differential equations (PDEs), or input‐side, which learn compact representations of device geometry.
Reza Marzban +2 more
wiley +1 more source
, 2015 We describe a topological method to study the dynamics of dissipative PDEs on a torus with rapidly oscillating forcing terms. We show that a dissipative PDE, which is invariant with respect to Galilean transformations, with a large average initial ...
Cyranka, Jacek, Zgliczyński, Piotr
core +1 more source
Communications on Pure and Applied Mathematics, Volume 79, Issue 1, Page 3-88, January 2026.Abstract We address the problem of regularity of solutions ui(t,x1,…,xN)$u^i(t, x^1, \ldots, x^N)$ to a family of semilinear parabolic systems of N$N$ equations, which describe closed‐loop equilibria of some N$N$‐player differential games with Lagrangian having quadratic behaviour in the velocity variable, running costs fi(x)$f^i(x)$ and final costs gi(
Marco Cirant, Davide Francesco Redaelli
wiley +1 more source
, 2019 In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine-Hugoniot condition that the shocks ...
Alonso-Orán, Diego +2 more
core +1 more source
Neural Controlled Differential Equation and Its Application in Pharmacokinetics and Pharmacodynamics
CPT: Pharmacometrics &Systems Pharmacology, Volume 15, Issue 1, January 2026.Neural controlled differential equations (NCDE), driven by control variables, are capable to learn the discontinuous dynamics in the PK and PD datasets. ABSTRACT With the recent advances in machine learning (ML) and artificial intelligence (AI), data‐driven modeling approaches for pharmacokinetics (PK) and pharmacodynamics (PD) have gained popularity ...
Zhisong Wu +5 more
wiley +1 more source
A new time‐stepping strategy and boundary treatment to improve recent 2D traffic model
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 1, January 2026.Abstract We show how a recently published 2D model for traffic flow can be further improved. Besides other improvements and simplifications, we present not only a method to compute the necessary time step restrictions, but also a subcycling for the inflow and outflow.
Friedemann Kemm
wiley +1 more source
Journal of the American Ceramic Society, Volume 109, Issue 1, January 2026.Abstract Silicon carbide (SiC) is a promising material for hypersonic thermal protection systems, but its complex oxidation behavior—marked by transitions between passive, active, and interfacial bubbling regimes—can lead to catastrophic failure. Existing SiC models typically focus exclusively on either passive or active oxidation.
Théo A. Rulko, Raúl A. Radovitzky
wiley +1 more source
A Design of an Axisymmetric Roof With a Horizontal Rotation Axis
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT This research proposes a novel roof design whose shape follows the mathematical model of an ideal hanging surface. The resulting roof is a surface of revolution, but its rotation axis is horizontal, which challenges conventional intuition because the axis is perpendicular to the direction of gravity.
Rafael López
wiley +1 more source
Parametric PDEs: Sparse or Low-Rank Approximations?
, 2016 We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse polynomial ...
Bachmayr, Markus +2 more
core
International Journal for Numerical Methods in Engineering, Volume 126, Issue 23, 15 December 2025.ABSTRACT We develop efficient hyperreduction methods for projection‐based model reduction of nonlinear partial differential equations (PDEs) with a large number of parameters and/or large parametric extents. Our formulation is based on the empirical quadrature procedure (EQP), which solves an optimization problem that involves “residual‐matching ...
Adrian Humphry, Masayuki Yano
wiley +1 more source