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Multi-scale Physical Representations for Approximating PDE Solutions with Graph Neural Operators [PDF]
TAG-ML, 2022 Representing physical signals at different scales is among the most challenging problems in engineering. Several multi-scale modeling tools have been developed to describe physical systems governed by \emph{Partial Differential Equations} (PDEs).
Léon Migus +3 more
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L2-Gain Analysis of Coupled Linear 2D PDEs using Linear PI Inequalities [PDF]
IEEE Conference on Decision and Control, 2022 In this paper, we present a new method for estimating the L2 -gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using semidefinite programming. It has previously been shown that, for any such PDE,
Declan S. Jagt, M. Peet
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A PIE Representation of Coupled Linear 2D PDEs and Stability Analysis using LPIs [PDF]
American Control Conference, 2021 This paper presents a Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in two spatial variables. PIEs are an algebraic state-space representation of infinite-dimensional systems and have been used to model 1D
Declan S. Jagt, M. Peet
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Functional Law of Large Numbers and PDEs for Epidemic Models with Infection-Age Dependent Infectivity [PDF]
Applied Mathematics and Optimization, 2021 We study epidemic models where the infectivity of each individual is a random function of the infection age (the elapsed time since infection). To describe the epidemic evolution dynamics, we use a stochastic process that tracks the number of individuals
Guo-Dong Pang, É. Pardoux
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Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains [PDF]
SIAM Journal on Scientific Computing, 2019 Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored.
T. Tang +3 more
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Multitime hybrid differential games with multiple integral functional [PDF]
Optimization Letters, 2017 The purpose of this paper to formulate and to prove theorems about multitime differential games based on a multiple integral functional and an m-flow as constraint. The most important idea is to use a generating vector field for value functions.
C. Udrişte +2 more
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Hyperasymptotic Solutions for Certain Partial Differential Equations [PDF]
, 2017 We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalization is based on the method of Borel summability, which
S. Michalik, Maria Suwi'nska
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FUNDAMENTAL SOLUTIONS IN COMPUTATIONAL FLUID DYNAMICS
Advances in Fluid Mechanics XII, 2018 With the boundary element method (BEM), the velocity-vorticity formulation is introduced and the overall Navier–Stokes problem is partitioned into the kinetic and kinematic parts.
L. Skerget, A. Tadeu, J. Ravnik
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Higher-order diffusion and Cahn-Hilliard-type models revisited on the half-line [PDF]
Mathematical Models and Methods in Applied SciencesIn this paper, we solve explicitly and analyze rigorously inhomogeneous initial-boundary-value problems (IBVP) for several fourth-order variations of the traditional diffusion equation and the associated linearized Cahn-Hilliard (C-H) model (also ...
A. Chatziafratis +4 more
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Bulk‐Surface Coupled PDE With an Open Boundary [PDF]
Studies in applied mathematics (Cambridge)We study a bulk‐surface coupled Laplace system involving an embedded open boundary. The problem is reformulated as an integro‐differential equation using boundary integral representations, for which we establish existence and uniqueness of the solution ...
Charles L. Epstein +2 more
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