Related papers: Arbitrary high-order, conservative and positive pr…
Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the…
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…
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…
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
This chapter focuses on variable maturation delay or, more precisely, on the mathematical description of a size-structured population consuming an unstructured resource. When the resource concentration is a known function of time, we can…
Revisionist integral deferred correction (RIDC) methods are a family of parallel--in--time methods to solve systems of initial values problems. The approach is able to bootstrap lower order time integrators to provide high order…
Many time-dependent partial differential equations (PDEs) can be transformed into an ordinary differential equations (ODEs) containing moderately stiff and non-stiff terms after spatial semi-discretization. In the present paper, we…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…
This paper considers the optimal boundary control of chemical systems described by advection-diffusion-reaction (ADR) equations. We use a discontinuous Galerkin finite element method (DG-FEM) for the spatial discretization of the governing…
The first-order linear positivity preserving schemes in time are available for the time dependent Poisson-Nernst-Planck (PNP) equations, second-order linear ones are still challenging. In this paper, we propose the first- and second-order…
We propose an algorithm for low Mach number reacting flows subjected to electric field that includes the chemical production and transport of charged species. This work is an extension of a multi-implicit spectral deferred correction…
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for…
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems. For such schemes, a classical stability analysis does not…
Minimization of energy in gradient systems leads to formation of oscillatory and Turing patterns in reaction-diffusion systems. These patterns should be accurately computed using fine space and time meshes over long time horizons to reach…
When a chaotic system is to be stabilized to a unstable orbit, delayed measurement of the system limits the applicability of chaos control techniqes. These limitations are analyzed and control schemes as linear predictive logging control…
A fourth-order exponential time differencing (ETD) Runge-Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction-diffusion equations (RDE). By approximating the matrix exponential in the…
PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel strategy is based on the newly developed exponential scalar…