Related papers: Ordinary differential equations for regularized va…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
We consider state-dependent delay equations (SDDE) obtained by adding delays to a planar ordinary differential equation with a limit cycle. These situations appear in models of several physical processes, where small delay effects are…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…
This work establishes that an optimal transport~(OT) problem regularized by a given $f$-divergence admits the same solution as another OT problem regularized by a different $g$-divergence, under an appropriate transformation of the cost…
In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the universal approximation properties of SA-NODEs for dynamical…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
We investigate an approach for the numerical solution of differential equations which is based on the perfect discretization of actions. Such perfect discretizations show up at the fixed points of renormalization group transformations. This…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…
We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
We develop a general approach to prove global regularity estimates for quadratic optimal transport using the entropic regularisation of the problem and the Prekopa-Leindler inequality.
In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…