Search Results - "IMA journal of numerical analysis"

Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs by Mishra, Siddhartha, Molinaro, Roberto

“…Abstract Physics-informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for partial…”
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Global rates of convergence for nonconvex optimization on manifolds by Boumal, Nicolas, Absil, P-A, Cartis, Coralia

“…Abstract We consider the minimization of a cost function f on a manifold $\mathcal{M}$ using Riemannian gradient descent and Riemannian trust regions (RTR). We…”
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Conforming and nonconforming virtual element methods for elliptic problems by Cangiani, Andrea, Manzini, Gianmarco, Sutton, Oliver J.

“…Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three…”
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Exact and inexact subsampled Newton methods for optimization by Bollapragada, Raghu, Byrd, Richard H, Nocedal, Jorge

“…Abstract The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through…”
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An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data by Jin, Bangti, Lazarov, Raytcho, Zhou, Zhi

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Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions by Zheng, Xiangcheng, Wang, Hong

“…Abstract We study a fully discretized finite element approximation to variable-order Caputo and Riemann–Liouville time-fractional diffusion equations (tFDEs)…”
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Estimates on the generalization error of physics-informed neural networks for approximating PDEs by Mishra, Siddhartha, Molinaro, Roberto

“…Abstract Physics-informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of partial differential equations…”
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Accurately computing the log-sum-exp and softmax functions by Blanchard, Pierre, Higham, Desmond J, Higham, Nicholas J

“…Abstract Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and…”
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Blow-up of error estimates in time-fractional initial-boundary value problems by Chen, Hu, Stynes, Martin

“…Abstract Time-fractional initial-boundary value problems of the form $D_t^\alpha u-p \varDelta u +cu=f$ are considered, where $D_t^\alpha u$ is a Caputo…”
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Error estimates for physics-informed neural networks approximating the Navier–Stokes equations by De Ryck, Tim, Jagtap, Ameya D, Mishra, Siddhartha

“…Abstract We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier–Stokes equations with (extended) physics-informed…”
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Simulation of McKean–Vlasov SDEs with super-linear growth by dos Reis, Gonçalo, Engelhardt, Stefan, Smith, Greig

“…Abstract We present two fully probabilistic Euler schemes, one explicit and one implicit, for the simulation of McKean–Vlasov Stochastic Differential Equations…”
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A fast algorithm for matrix balancing by Knight, P. A., Ruiz, D.

“…As long as a square non-negative matrix A has total support then it can be balanced, that is, we can find a diagonal scaling of A that has row and column sums…”
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An adaptive BDF2 implicit time-stepping method for the phase field crystal model by Liao, Hong-lin, Ji, Bingquan, Zhang, Luming

“…Abstract An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified…”
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Numerical solution of fractional elliptic stochastic PDEs with spatial white noise by Bolin, David, Kirchner, Kristin, Kovács, Mihály

“…Abstract The numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in…”
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Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations by He, Y.

“…In this paper, we consider the initial-boundary value problem for the three-dimensional incompressible magnetohydrodynamic equations. We first establish…”
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Stability and convergence of a second-order mixed finite element method for the Cahn–Hilliard equation by Diegel, Amanda E., Wang, Cheng, Wise, Steven M.

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Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation by Bréhier, Charles-Edouard, Cui, Jianbo, Hong, Jialin

“…Abstract This article analyses an explicit temporal splitting numerical scheme for the stochastic Allen–Cahn equation driven by additive noise in a bounded…”
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Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework by Li, Meng, Zhao, Jikun, Huang, Chengming, Chen, Shaochun

“…Abstract We establish a unified framework to study the conforming and nonconforming virtual element methods (VEMs) for a class of time dependent fourth-order…”
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The Riemannian Barzilai–Borwein method with nonmonotone line search and the matrix geometric mean computation by Iannazzo, Bruno, Porcelli, Margherita

“…Abstract The Barzilai–Borwein (BB) method, an effective gradient descent method with clever choice of the step length, is adapted from nonlinear optimization…”
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An analysis of the Crank–Nicolson method for subdiffusion by Jin, Bangti, Li, Buyang, Zhou, Zhi

“…Abstract In this work, we analyse a Crank-Nicolson type time-stepping scheme for the subdiffusion equation, which involves a Caputo fractional derivative of…”
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