Jan Sickmann Hesthaven

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Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

A non-intrusive reduced-basis (RB) method is proposed for parametrized unsteady flows. A set of reduced basis functions are extracted from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD), and the coefficients of the redu ...

Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential to provide a gene ...

A new approach is proposed to detect edges based on an artificial neural network (ANN). Some elementary continuous and discontinuous functions interpolated in the polynomial space and their continuity are used as the training sets to train a back propagati ...

This paper proposes an approach for high-order time integration within a multi-domain setting for time- fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to p ...

This paper is devoted to determining a space-dependent source term in an inverse problem of the time-fractional diffusion equation. We use a fully-discrete method based on a finite difference scheme in time and a local discontinuous Galerkin method (LDG) i ...

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouvi ...

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted space. To obtain the schemes this expansion is terminated after terms. We study t ...

A non-intrusive reduced basis (RB) method is proposed for parametrized nonlinear structural analysis undergoing large deformations and with elasto-plastic constitutive relations. In this method, a reduced basis is constructed from a set of full-order snaps ...

We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions ...

A reduced basis method based on a physics-informed machine learning framework is developed for efficient reduced-order modeling of parametrized partial differential equations (PDEs). A feedforward neural network is used to approximate the mapping from the ...

In this paper, a new high-order multiscale finite element method is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the multiscale finite element method developed in [3], but a more explicit multiscale finite ...

Solving hyperbolic conservation laws on general grids can be important to reduce the computational complexity and increase accuracy in many applications. However, the use of non-uniform grids can introduce challenges when using high-order methods. We propo ...

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel reduction method for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our stud ...

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...

We introduce a greedy non-intrusive reduced order method(ROM) for parameterized time-dependent problems with an emphasis on problems in fluid dynamics. The non-intrusive ROM is based on two-level proper orthogonal decomposition(POD) to extract temporal and ...

In the strong scaling limit, the performance of conventional spatial domain decomposition techniques for the parallel solution of PDEs saturates. When sub-domains become small, halo-communication and other overheard come to dominate. A potential path beyon ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

In this paper, we propose a three-level linearized implicit difference scheme for the two-dimensional spatial fractional nonlinear complex Ginzburg-Landau equation. We prove that the difference scheme is stable and convergent under mild conditions. The opt ...

We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and in more traditional scenarios where the generation of waveforms us ...

Jan Sickmann Hesthaven

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Constraint-aware neural networks for Riemann problems

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

Discovery of Slow Variables in a Class Of Multiscale Stochastic Systems Via Neural Networks

An edge detector based on artificial neural network with application to hybrid Compact-WENO finite difference schemes

A Multi-domain Spectral Method for Time-fractional Differential Equations

Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method

Spectral methods for tempered fractional differential equations

High-Order Accurate Local Schemes for Fractional Differential Equations

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics

Physics-informed machine learning for reduced-order modeling of nonlinear problems

High-order multiscale finite element method for elliptic problems

RBF Based CWENO Method

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

A greedy non-intrusive reduced order model for fluid dynamics

Communication-aware adaptive parareal with application to a nonlinear hyperbolic system of partial dierential equations

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation

Fast prediction and evaluation of gravitational waveforms using surrogate models