Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data [PDF]
Journal of Computational Physics, 2023 We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions.
R. Stephany, Christopher Earls
semanticscholar +4 more sources
Existence and uniqueness of weak solutions to quasilinear PDEs with critical data
20 pages. Compared to version 2, the proof of Prop. 3.4(d) is updated and Rem.
Bechtel, Sebastian, Auscher, Pascal
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Quasi-linear PDEs and forward-backward stochastic differential equations: weak solutions [PDF]
, 2017 In this paper, we study the existence, uniqueness and the probabilistic representation of the weak solutions of quasi-linear parabolic and elliptic partial differential equations (PDEs) in the Sobolev space H1ρ(Rd). For this, we study first the solutions
Huaizhong Zhao (1247379) +2 more
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Learning-based solutions to nonlinear hyperbolic PDEs: Empirical insights on generalization errors [PDF]
arXiv.org, 2023 We study learning weak solutions to nonlinear hyperbolic partial differential equations (H-PDE), which have been difficult to learn due to discontinuities in their solutions. We use a physics-informed variant of the Fourier Neural Operator ($\pi$-FNO) to
Bilal Thonnam Thodi +2 more
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Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes [PDF]
The Cryosphere, 2022 The incorporation of vapor transport has become a key demand for snowpack modeling in which accompanied phase changes give rise to a new, nonlinear coupling in the heat and mass equations.
K. Schürholt +3 more
doaj +1 more source
On the regularity of solutions of some linear parabolic path-dependent PDEs [PDF]
Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2023 We study a class of linear parabolic path-dependent PDEs (PPDEs) defined on the space of c\`adl\`ag paths $x \in D([0,T])$, in which the coefficient functions at time $t$ depend on $x(t)$ and $\int_{0}^{t}x(s)dA_{s}$, for some (deterministic) continuous ...
B. Bouchard, Xiaolu Tan
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On compact 4th order finite-difference schemes for the wave equation
Mathematical Modelling and Analysis, 2021 We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the n-dimensional nonhomogeneous wave equation, n≥ 1.
Alexander Zlotnik, Olga Kireeva
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Estimates of Mild Solutions of Navier–Stokes Equations in Weak Herz-Type Besov–Morrey Spaces
Mathematics, 2022 The main goal of this article is to provide estimates of mild solutions of Navier–Stokes equations with arbitrary external forces in Rn for n≥2 on proposed weak Herz-type Besov–Morrey spaces.
Ruslan Abdulkadirov, Pavel Lyakhov
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Bounded weak solutions to elliptic PDE with data in Orlicz spaces [PDF]
Journal of Differential Equations, 2021 A classical regularity result is that non-negative solutions to the Dirichlet problem $Δu =f$ in a bounded domain $Ω$, where $f\in L^q(Ω)$, $q>\frac{n}2$, satisfy $\|u\|_{L^\infty(Ω)} \leq C\|f\|_{L^q(Ω)}$. We extend this result in three ways: we replace the Laplacian with a degenerate elliptic operator; we show that we can take the data $f$ in an ...
Cruz-Uribe, David, Rodney, Scott
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Bayesian neural networks for weak solution of PDEs with uncertainty quantification
CoRR, 2021 37 pages, 25 ...
Xiaoxuan Zhang, Krishna C. Garikipati
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