Related papers: Structure-preserving learning for multi-symplectic…
In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential…
Accurate and inexpensive Reduced Order Models (ROMs) for forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control in engineering problems. Galerkin projection based Reduced Order…
A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method is a predictor-corrector strategy to define the grid…
Machine learning methods are widely used in the natural sciences to model and predict physical systems from observation data. Yet, they are often used as poorly understood "black boxes," disregarding existing mathematical structure and…
Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
This article discusses a newly developed online manifold learning method, subspace iteration using reduced models (SIRM), for the dimensionality reduction of dynamical systems. This method may be viewed as subspace iteration combined with a…
In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. However, these methods may suffer from limited accuracy, high…
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…
This paper is interested in developing reduced order models (ROMs) for repeated simulation of fractional elliptic partial differential equations (PDEs) for multiple values of the parameters (e.g., diffusion coefficients or fractional…
Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…
This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method…
For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach to construct entropy conservative/ dissipative…
We study geometric properties of Krylov projection methods for large and sparse linear Hamiltonian systems. We consider in particular energy preservation. We discuss the connection to structure preserving model reduction. We illustrate the…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
This paper concerns preservation of velocity and pressure equilibria in smooth, compressible, multicomponent flows in the inviscid limit. First, we derive the velocity-equilibrium and pressure-equilibrium conditions of a standard…
Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…
We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems in pH form permit energy-based modeling and intuitive…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…