Related papers: Descriptor approach for eliminating spurious eigen…
In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection…
Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…
Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing…
Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
In the identification of differential equations from data, significant progresses have been made with the weak/integral formulation. In this paper, we explore the direction of finding more efficient and robust test functions adaptively…
How do the geometric properties of a domain impact the spectrum of an operator defined on it? How do we compute accurate and reliable approximations of these spectra? The former question is studied in spectral geometry, and the latter is a…
In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
This work presents a procedure to solve the Euler equations by explicitly updating, in a conservative manner, a generic thermodynamic variable such as temperature, pressure or entropy instead of the total energy. The presented procedure is…
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…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
This paper presents a secular term removal methodology based on the homotopy perturbation method for analytical solutions of nonlinear problems with periodic boundary condition. The analytical solution for groundwater response to tidal…
Quality-Diversity optimization is a new family of optimization algorithms that, instead of searching for a single optimal solution to solving a task, searches for a large collection of solutions that all solve the task in a different way.…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
Normalizing flow models have risen as a popular solution to the problem of density estimation, enabling high-quality synthetic data generation as well as exact probability density evaluation. However, in contexts where individuals are…
Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…
The characteristic decomposition for GRMHD is not known in a form useful for current numerical simulations. This prevents us from using the most accurate known computational methods, such as full-wave Riemann solvers. In this paper, we…
The adiabatic hydrodynamization framework is a promising framework within which to describe and characterize pre-hydrodynamic attractors in a model-independent fashion. Using this framework, we define a procedure to identify a…