Related papers: Conservative parameterization schemes
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…
A characteristic of existing predictive process monitoring techniques is to first construct a predictive model based on past process executions, and then use it to predict the future of new ongoing cases, without the possibility of updating…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…
We are interested in building schemes for the compressible Euler equations that are also locally conserving the angular momentum. We present a general framework, describe a few examples of schemes and show results. These schemes can be of…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out.…
Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
Global Climate Models (GCMs) are the primary tool to simulate climate evolution and assess the impacts of climate change. However, they often operate at a coarse spatial resolution that limits their accuracy in reproducing local-scale…
In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then,…
Stochastic parametrisations are used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared to a deterministic model, a stochastic model represents `model uncertainty', i.e., sources…
Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…